multiplying and dividing integers problem solving

Integers Worksheets

Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.

If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.

We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.

Most Popular Integers Worksheets this Week

Integer Resources

Coordinate graph paper can be very useful when studying integers. Coordinate geometry is a practical application of integers and can give students practice with using integers while learning another related skill. Coordinate graph paper can be found on the Graph Paper page:

Coordinate Graph Paper

Integer number lines can be used for various math activities including operations with integers, counting, comparing, ordering, etc.

• Integer Number Lines Integers Number Lines from -10 to 10 Integers Number Lines from -15 to 15 Integers Number Lines from -20 to 20 Integers Number Lines from -25 to 25 OLD Integer Number Lines

Comparing and Ordering Integers

For students who are just starting with integers, it is very helpful if they can use an integer number line to compare integers and to see how the placement of integers works. They should quickly realize that negative numbers are counter-intuitive because they are probably quite used to larger absolute values meaning larger numbers. The reverse is the case, of course, with negative numbers. Students should be able to recognize easily that a positive number is always greater than a negative number and that between two negative integers, the one with the lesser absolute value is actually the greater number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.

• Comparing Integers Worksheets Comparing Positive and Negative Integers (-9 to +9) Comparing Positive and Negative Integers (-15 to +15) Comparing Positive and Negative Integers (-25 to +25) Comparing Positive and Negative Integers (-50 to +50) Comparing Positive and Negative Integers (-99 to +99) Comparing Negative Integers (-15 to -1)

By close proximity, we mean that the integers being compared differ very little in value. Depending on the range, we have allowed various differences between the two integers being compared. In the first set where the range is -9 to 9, the difference between the two numbers is always 1. With the largest range, a difference of up to 5 is allowed. These worksheets will help students further hone their ability to visualize and conceptualize the idea of negative numbers and will serve as a foundation for all the other worksheets on this page.

• Comparing Integers in Close Proximity Comparing Positive and Negative Integers (-9 to +9) in Close Proximity Comparing Positive and Negative Integers (-15 to +15) in Close Proximity Comparing Positive and Negative Integers (-25 to +25) in Close Proximity Comparing Positive and Negative Integers (-50 to +50) in Close Proximity Comparing Positive and Negative Integers (-99 to +99) in Close Proximity
• Ordering Integers Worksheets Ordering Integers on a Number Line Ordering Integers (range -9 to 9) Ordering Integers (range -20 to 20) Ordering Integers (range -50 to 50) Ordering Integers (range -99 to 99) Ordering Integers (range -999 to 999) Ordering Negative Integers (range -9 to -1) Ordering Negative Integers (range -99 to -10) Ordering Negative Integers (range -999 to -100)

Adding and Subtracting Integers

Two-color counters are fantastic manipulatives for teaching and learning about integer addition. Two-color counters are usually plastic chips that come with yellow on one side and red on the other side. They might be available in other colors, so you'll have to substitute your own colors in the following description.

Adding with two-color counters is actually quite easy. You model the first number with a pile of chips flipped to the correct side and you also model the second number with a pile of chips flipped to the correct side; then you mash them all together, take out the zeros (if any) and behold, you have your answer! Need further elaboration? Read on!

The correct side means using red to model negative numbers and yellow to model positive numbers. You would model —5 with five red chips and 7 with seven yellow chips. Mashing them together should be straight forward although, you'll want to caution your students to be less exuberant than usual, so none of the chips get flipped. Taking out the zeros means removing as many pairs of yellow and red chips as you can. You can do this because —1 and 1 when added together equals zero (this is called the zero principle). If you remove the zeros, you don't affect the answer. The benefit of removing the zeros, however, is that you always end up with only one color and as a consequence, the answer to the integer question. If you have no chips left at the end, the answer is zero!

• Adding Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (75 Questions) ✎ Adding Integers from -12 to 12 (75 Questions) ✎ Adding Integers from -15 to 15 (75 Questions) ✎ Adding Integers from -20 to 20 (75 Questions) ✎ Adding Integers from -25 to 25 (75 Questions) ✎ Adding Integers from -50 to 50 (75 Questions) ✎ Adding Integers from -99 to 99 (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (50 Questions) ✎ Adding Integers from -12 to 12 (50 Questions) ✎ Adding Integers from -15 to 15 (50 Questions) ✎ Adding Integers from -20 to 20 (50 Questions) ✎ Adding Integers from -25 to 25 (50 Questions) ✎ Adding Integers from -50 to 50 (50 Questions) ✎ Adding Integers from -99 to 99 (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding Integers from -9 to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -12 to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -15 to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -20 to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -25 to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -50 to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding Integers from -99 to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Addition Worksheets 3-Digit Integer Addition (Vertically Arranged) 3-Digit Positive Plus a Negative Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Positive Integer Addition (Vertically Arranged) 3-Digit Negative Plus a Negative Integer Addition (Vertically Arranged)

Subtracting with integer chips is a little different. Integer subtraction can be thought of as removing. To subtract with integer chips, begin by modeling the first number (the minuend) with integer chips. Next, remove the chips that would represent the second number from your pile and you will have your answer. Unfortunately, that isn't all there is to it. This works beautifully if you have enough of the right color chip to remove, but often times you don't. For example, 5 - (-5), would require five yellow chips to start and would also require the removal of five red chips, but there aren't any red chips! Thank goodness, we have the zero principle. Adding or subtracting zero (a red chip and a yellow chip) has no effect on the original number, so we could add as many zeros as we wanted to the pile, and the number would still be the same. All that is needed then is to add as many zeros (pairs of red and yellow chips) as needed until there are enough of the correct color chip to remove. In our example 5 - (-5), you would add 5 zeros, so that you could remove five red chips. You would then be left with 10 yellow chips (or +10) which is the answer to the question.

• Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (75 Questions) ✎ Subtracting Integers from -12 to 12 (75 Questions) ✎ Subtracting Integers from -15 to 15 (75 Questions) ✎ Subtracting Integers from -20 to 20 (75 Questions) ✎ Subtracting Integers from -25 to 25 (75 Questions) ✎ Subtracting Integers from -50 to 50 (75 Questions) ✎ Subtracting Integers from -99 to 99 (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (50 Questions) ✎ Subtracting Integers from -12 to 12 (50 Questions) ✎ Subtracting Integers from -15 to 15 (50 Questions) ✎ Subtracting Integers from -20 to 20 (50 Questions) ✎ Subtracting Integers from -25 to 25 (50 Questions) ✎ Subtracting Integers from -50 to 50 (50 Questions) ✎ Subtracting Integers from -99 to 99 (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎
• Vertically Arranged Integer Subtraction Worksheets 3-Digit Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Positive Minus a Negative Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Positive Integer Subtraction (Vertically Arranged) 3-Digit Negative Minus a Negative Integer Subtraction (Vertically Arranged)

The worksheets in this section include addition and subtraction on the same page. Students will have to pay close attention to the signs and apply their knowledge of integer addition and subtraction to each question. The use of counters or number lines could be helpful to some students.

• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (75 Questions) ✎ Adding & Subtracting Integers from -10 to 10 (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-5) to (+5) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-9) to (+9) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (75 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 75 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (75 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (75 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (50 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 50 Questions Per Page (No Parentheses) Adding & Subtracting Integers from -9 to 9 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -12 to 12 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -15 to 15 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -20 to 20 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -25 to 25 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -50 to 50 No Parentheses (50 Questions) ✎ Adding & Subtracting Integers from -99 to 99 No Parentheses (50 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (Some Parentheses) Adding & Subtracting Integers from -9 to 9 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -12 to 12 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -15 to 15 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -20 to 20 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -25 to 25 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -50 to 50 (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from -99 to 99 (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (All Parentheses) Adding & Subtracting Integers from (-9) to (+9) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to (+12) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to (+15) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to (+20) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to (+25) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to (+50) All Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to (+99) All Parentheses (Large Print; 25 Questions) ✎
• Adding and Subtracting Integers Worksheets with 25 Large Print Questions Per Page (No Parentheses) Adding & Subtracting Integers from (-9) to 9 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-12) to 12 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-15) to 15 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-20) to 20 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-25) to 25 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-50) to 50 No Parentheses (Large Print; 25 Questions) ✎ Adding & Subtracting Integers from (-99) to 99 No Parentheses (Large Print; 25 Questions) ✎

These worksheets include groups of questions that all result in positive or negative sums or differences. They can be used to help students see more clearly how certain integer questions end up with positive and negative results. In the case of addition of negative and positive integers, some people suggest looking for the "heavier" value to determine whether the sum will be positive of negative. More technically, it would be the integer with the greater absolute value. For example, in the question (−2) + 5, the absolute value of the positive integer is greater, so the sum will be positive.

In subtraction questions, the focus is on the subtrahend (the value being subtracted). In positive minus positive questions, if the subtrahend is greater than the minuend, the answer will be negative. In negative minus negative questions, if the subtrahend has a greater absolute value, the answer will be positive. Vice-versa for both situations. Alternatively, students can always convert subtraction questions to addition questions by changing the signs (e.g. (−5) − (−7) is the same as (−5) + 7; 3 − 5 is the same as 3 + (−5)).

• Scaffolded Integer Addition and Subtraction Positive Plus Negative Integer Addition (Scaffolded) ✎ Negative Plus Positive Integer Addition (Scaffolded) ✎ Mixed Integer Addition (Scaffolded) ✎ Positive Minus Positive Integer Subtraction (Scaffolded) ✎ Negative Minus Negative Integer Subtraction (Scaffolded) ✎

Multiplying and Dividing Integers

Multiplying integers is very similar to multiplication facts except students need to learn the rules for the negative and positive signs. In short, they are:

In words, multiplying two positives or two negatives together results in a positive product, and multiplying a negative and a positive in either order results in a negative product. So, -8 × 8, 8 × (-8), -8 × (-8) and 8 × 8 all result in an absolute value of 64, but in two cases, the answer is positive (64) and in two cases the answer is negative (-64).

Should you wish to develop some "real-world" examples of integer multiplication, it might be a stretch due to the abstract nature of negative numbers. Sure, you could come up with some scenario about owing a debt and removing the debt in previous months, but this may only result in confusion. For now students can learn the rules of multiplying integers and worry about the analogies later!

• Multiplying Integers with 100 Questions Per Page Multiplying Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying Mixed Integers from -20 to 20 (100 Questions) ✎ Multiplying Mixed Integers from -50 to 50 (100 Questions) ✎
• Multiplying Integers with 50 Questions Per Page Multiplying Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying Integers with 25 Large Print Questions Per Page Multiplying Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

Luckily (for your students), the rules of dividing integers are the same as the rules for multiplying:

Dividing a positive by a positive integer or a negative by a negative integer will result in a positive integer. Dividing a negative by a positive integer or a positive by a negative integer will result in a negative integer. A good grasp of division facts and a knowledge of the rules for multiplying and dividing integers will go a long way in helping your students master integer division. Use the worksheets in this section to guide students along.

• Dividing Integers with 100 Questions Per Page Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (100 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (100 Questions) ✎ Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (100 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (100 Questions) ✎
• Dividing Integers with 50 Questions Per Page Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Dividing Positive by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Positive Integers from -9 to 9 (50 Questions) ✎ Dividing Negative by Negative Integers from -9 to 9 (50 Questions) ✎ Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Dividing Positive by Negative Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Positive Integers from -12 to 12 (50 Questions) ✎ Dividing Negative by Negative Integers from -12 to 12 (50 Questions) ✎
• Dividing Integers with 25 Large Print Questions Per Page Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Positive by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Dividing Negative by Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

This section includes worksheets with both multiplying and dividing integers on the same page. As long as students know their facts and the integer rules for multiplying and dividing, their sole worry will be to pay attention to the operation signs.

• Multiplying and Dividing Integers with 100 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (100 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (100 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (100 Questions) ✎
• Multiplying and Dividing Integers with 75 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (75 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (75 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (75 Questions) ✎
• Multiplying and Dividing Integers with 50 Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (50 Questions) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (50 Questions) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (50 Questions) ✎
• Multiplying and Dividing Integers with 25 Large Print Questions Per Page Multiplying and Dividing Mixed Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -9 to 9 (25 Questions; Large Print) ✎ Multiplying and Dividing Mixed Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Positive and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Positive Integers from -12 to 12 (25 Questions; Large Print) ✎ Multiplying and Dividing Negative and Negative Integers from -12 to 12 (25 Questions; Large Print) ✎

All Operations with Integers

In this section, the integers math worksheets include all of the operations. Students will need to pay attention to the operations and the signs and use mental math or another strategy to arrive at the correct answers. It should go without saying that students need to know their basic addition, subtraction, multiplication and division facts and rules regarding operations with integers before they should complete any of these worksheets independently. Of course, the worksheets can be used as a source of questions for lessons, tests or other learning activities.

• All Operations with Integers with 50 Questions Per Page (Some Parentheses) All operations with integers from -9 to 9 (50 Questions) ✎ All operations with integers from -12 to 12 (50 Questions) ✎ All operations with integers from -15 to 15 (50 Questions) ✎ All operations with integers from -20 to 20 (50 Questions) ✎ All operations with integers from -25 to 25 (50 Questions) ✎ All operations with integers from -50 to 50 (50 Questions) ✎ All operations with integers from -99 to 99 (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (All Parentheses) All operations with integers from (-9) to (+9) All Parentheses (50 Questions) ✎ All operations with integers from (-12) to (+12) All Parentheses (50 Questions) ✎ All operations with integers from (-15) to (+15) All Parentheses (50 Questions) ✎ All operations with integers from (-20) to (+20) All Parentheses (50 Questions) ✎ All operations with integers from (-25) to (+25) All Parentheses (50 Questions) ✎ All operations with integers from (-50) to (+50) All Parentheses (50 Questions) ✎ All operations with integers from (-99) to (+99) All Parentheses (50 Questions) ✎
• All Operations with Integers with 50 Questions Per Page (No Parentheses) All operations with integers from -9 to 9 No Parentheses (50 Questions) ✎ All operations with integers from -12 to 12 No Parentheses (50 Questions) ✎ All operations with integers from -15 to 15 No Parentheses (50 Questions) ✎ All operations with integers from -20 to 20 No Parentheses (50 Questions) ✎ All operations with integers from -25 to 25 No Parentheses (50 Questions) ✎ All operations with integers from -50 to 50 No Parentheses (50 Questions) ✎ All operations with integers from -99 to 99 No Parentheses (50 Questions) ✎

Order of operations with integers can be found on the Order of Operations page:

Order of Operations with Integers

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M and D Integers

Multiplying and dividing integers

Here you will learn strategies on how to multiply and divide integers, including using visual models as well as using the number line.

Students will first learn about integers in 6th grade math as part of their work with the number system and expand that knowledge to operations with integers in the 7th grade.

What are multiplying and dividing integers?

Multiplying and dividing integers is when you multiply or divide two or more integers together to give a product or quotient that can be either positive or negative.

You can multiply and divide integers using visual models or a rule.

Do you notice a pattern or rule?

Rule for multiplying integers:

• If the integers have the same sign , the product will be positive .
• If the integers have different signs , the product will be negative .

Rule for dividing integers:

• If the integers have the same sign , the quotient will be positive .
• If the integers have different signs , the quotient will be negative .

Common Core State Standards

How does this apply to 6th grade math and 7th grade math?

• Grade 6: Number System (6.NS.C.6) Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
• Grade 7: Number System (7.NS.A.2) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

[FREE] Multiplication and Division Check for Understanding (Grade 4, 5 and 7)

Use this quiz to check your grade 4, 5 and 7 students’ understanding of multiplication and division. 10+ questions with answers covering a range of 4, 5 and 7 grade multiplication and division topics to identify areas of strength and support!

How to multiply and divide integers?

In order to add and subtract integers using counters:

• If the integers have the same sign, the product or quotient is positive.  If not, go to step 2.

If the integers have different signs, the product or quotient is negative.

Find the product or quotient.

Multiplying and dividing integers examples

Example 1: multiplying integers with the same sign.

Multiply: (-4) \times(-12)= \, ?

• If the integers have the same sign, the product or quotient is positive. If they don’t go to step 2. 

-4 and -12 have the same sign so the product is positive.

2 If the integers have different signs, the product or quotient is negative.

Integers have the same sign.

3 Find the product or quotient.

(-4) \times(-12)=48

Example 2: multiplying integers with different signs

Multiply: (-13) \times 8= \, ?

If the integers have the same sign, the product or quotient is positive.  If not, go to step 2.

-13 and 8 do not have the same sign.

The integers have different signs so the product is negative.

Find the product or the quotient.

(-13) \times 8=-104

Example 3: dividing integers with the same sign

Divide: \cfrac{(-18)}{(-3)}= \, ?

-18 and -3 have the same sign so the quotient will be positive.

\cfrac{(-18)}{(-3)}=6

Example 4: dividing integers with different signs

Divide: -120 \div 3= \, ?

-120 and 3 do not have the same sign.

-120 and 3 have different signs so the quotient will be negative.

-120 \div 3=-40

Example 5: multiplying integers word problem

From sea level, a submarine descends 25 \, ft. per minute (-25 \, ft.).

After 6 minutes, the submarine’s distance can be modeled by (-25) \times 6 = \, d , where d is the submarine in relation to sea level.

How far below sea level is the submarine?

-25 and 6 do not have the same sign.

-25 and 6 have different signs so the product will be negative.

-25 \times 6=-150

Because the submarine is descending, after 6 minutes it will be 150 feet below sea level.

Example 6: dividing integer word problems

On a certain winter day, the temperature changed at a rate of -4 degrees Fahrenheit per hour.

After a specific amount of time, the change in temperature was -36 degrees Fahrenheit, which is modeled by (-36) \div (-4) = \, h, where h represents the amount of hours.

How long did it take for the change in temperature to be -36 degrees Fahrenheit?

-36 and -4 have the same sign so the quotient is positive.

The integers have the same sign.

(-36) \div(-4)=9

Teaching tips for multiplying and dividing integers

• Multiplying and dividing integers are foundational skills for Algebra 1. Using manipulatives helps students formulate conceptual understanding.
• Have students identify the patterns with multiplying and dividing integers so that they can figure out the rules on their own.
• Although practice integer worksheets have their place, have students practice problems through digital games or scavenger hunts around the room to make it engaging.
• Reinforce essential vocabulary such as dividend, divisor, quotient, factors,  and product.

Easy mistakes to make

• Mixing up the rules for multiplication and division For example, when multiplying integers with the same sign, you get a negative product, and when dividing integers with the same sign, you get a negative quotient.
• Mixing up the rules of multiplication and division with addition and subtraction For example, applying the rule of addition of integers to (15) \div(-3)=5 where the absolute value of 15 is greater than the absolute value of 3 so the answer must be positive.

Related multiplication and division lessons

This multiplying and dividing integers topic guide is part of our series on multiplication and division. You may find it helpful to start with the main multiplication and division topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

• Multiplication and division
• Multiplying multi-digit numbers
• Understanding multiplication
• Multiplication and division within 100
• Long division
• Multiplying and dividing rational numbers
• Understanding division
• Dividing multi-digit numbers
• Multiplicative comparison

Practice multiplying and dividing integers

1. Multiply: (6) \times(-2)=\text { ? }

Using the rule for multiplying integers, 6 and -2 have different signs, so the product is negative.

(6) \times(-2)=-12

You can check your answer with counters.

6 groups of -2 counters is -12 counters

2. Multiply: (-15) \times(-3)= \text { ? }

Using the rule for multiplying integers, -15 and -3 have the same sign, so the product is positive.

(-15) \times(-3)=45

3. Divide: (-52) \div(4)= \text { ? }

Using the rule for dividing integers, -52 and 4 have different signs, so the quotient is negative.

(-52) \div(4)=-13

4. Divide: \cfrac{(-72)}{(-9)}= \text { ? }

Using the rule for dividing integers, -72 and -9 have the same sign, so the quotient is positive.

\cfrac{(-72)}{(-9)}=8

5. Multiply: (-190) \times(-10)= \text { ? }

Using the rule for multiplying integers, -190 and -10 have the same sign, so the product is positive.

(-190) \times(-10)=1900

6. A deep sea diver descends at a rate of 10 feet per minute below sea level. The diver descends at this rate for 8 minutes, which can be modeled by 8 \times (-10) = d, where d is how far the diver is below sea level. After 8 minutes, how far did the diver descend?

Using the rule, the signs of the numbers are different, so the product is negative.

8 \times(-10)=-80

The diver descended to -80 feet.

Multiplying and dividing integers FAQs

When it comes to sets of numbers, whole numbers are 0 and positive whole numbers. The set of integers includes all negative whole numbers, 0, and all positive whole numbers.

Multiplication and division of integers help when simplifying algebraic expressions and solving equations.

Yes, positive numbers are to the right of 0 and negative numbers are to the left of 0.

The positive sign does not necessarily need to be written in front of a number. For example, +5 is the same as 5. The positive sign is understood.

The next lessons are

• Types of numbers
• Rounding numbers
• Factors and multiples

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Find out how we can help your students achieve success with our math tutoring programs .

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Integers: Multiplication and Division Worksheets

This page contains printable worksheets which emphasize integer multiplication and division to 6th grade, 7th grade, and 8th grade students. Practice pages here contain exercises on multiplication squares, in-out boxes, evaluating expressions, filling in missing integers, and more. Procure some of these worksheets for free!

Multiplying Integers

Multiplication of Integers

Multiply the integers to find the product. A total of 48 problems are given in these integer worksheets for practice.

• Download the set

Multiplication Squares | 2x2

Conceptualize the fundamentals of multiplying integers with this bath of interesting 2x2 squares. Multiply the integers in the rows and columns and write the products in the squares.

Multiplication Squares | 3x3

Get students to multiply the positive and negative numbers in each row and column and fill in the empty boxes in each 3x3 square.

Multiplying 3 or 4 Integers

Find the product of the integers. Apply the multiplication sign rule. Each worksheet consists of ten problems.

Integer Multiplication Table

Practice multiplying integers from -10 to +10 with this super simple table. Apply the rules where products turn positive when integers with similar signs are multiplied and negative with differing signs. Get ready to master integer multiplication effortlessly!

Dividing Integers

Integer Division

Perform the division operation on the integers to find the quotient in these three pdf worksheets.

Multiplying and Dividing Integers - Mixed

Multiplying and Dividing Integers

Simplify the integer equations by performing multiplication and division operations.

Missing Integers: Multiplication and Division

Find the missing integer in each equation. There are 16 problems in each worksheet.

In-and-Out boxes: Multiply and Divide

Fill in the in-and-out boxes according to the rule mentioned in each problem. There are six rules given in each worksheet.

Evaluate: Multiply and Divide

Evaluate the expressions by substituting the values in the variables. Each printable worksheet for grade 7 and grade 8 contains four problems with three expressions each.

Multiplication Chart

Integer Multiplication Charts | Display Charts

Designed to assist 6th grade students with multiplication of integers, this array of charts focuses on multiplication of integers from -5 to +5 and -10 to +10. Explore these visual aids and comprehend the two rules of multiplication of integers.

Related Worksheets

» Adding and Subtracting Integers

» Comparing and Ordering Integers

» Integers on a Number Line

» Multiplication and Division Fact Family

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How to Multiply and Divide Integers? (+FREE Worksheet!)

Do you know integers? Join us in this post to learn more about integers and learn how to multiply and divide them in simple ways.

Any number that can be displayed without a fraction is called an integer. For example, the numbers \(-1, -4, 0, 5, 10\) are integers because we can specify them without having to display a regular fraction.

It can be said that integers consist of three categories:

• Positive integers
• Negative integers

Multiplying and dividing integers is just like simple multiplying and dividing, the only difference being that you have to specify the answer sign before you do the multiplying or dividing operation.

Here you learn how to multiply and divide integers using integers multiplication and division rules.

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Related topics.

• How to Add and Subtract Integers
• How to Order Integers and Numbers
• How to Use Order of Operations
• How to Solve Integers and Absolute Value Problems

Step-by-step guide to multiplying and dividing integers

To multiply and divide integers, we must do the following 2 steps:

Step 1: Determine the answer sign: When we want to multiply or divide two integers, we first multiply the symbols of the two numbers to determine the answer sign.

• The product of multiplying or dividing two positive numbers is a positive number.
• The product of multiplying or dividing two negative numbers is a positive number.
• The product of multiplying or dividing a positive number and a negative number is a negative number

Use these rules for multiplying and dividing integers:

• \(\color{black}{(negative)} \ × \ \color{ black }{(negative)} = \color{blue}{positive}\)
• \( \color{ black }{(negative)} \ ÷ \ \color{ black }{(negative)} = \color{blue}{positive}\)
• \(\color{ black }{(negative)} \ × \ \color{blue}{(positive)}= \color{ black }{negative}\)
• \( \color{ black }{(negative)} \ ÷ \ \color{blue}{(positive)} = \color{ black }{negative}\)
• \(\color{blue}{(positive)} \ × \ \color{blue}{(positive)}= \color{blue}{positive}\)

Step 2: Once we have found the answer sign, the rest of the work is like a simple multiplication or division: If we have multiplication, we multiply two numbers together. If we have a division, we divide the two numbers.

Multiply and Divide Integers – Example 1:

Solve. \(3 \ \times \ (12 \ – \ 14)=\)

First subtract the numbers in brackets, \(12 \ – \ 14= \ – \ 2 → (3) \ \times \ (- \ 2)=\) Now use this formula: \(\color{ black }{(negative)} \ × \ \color{blue}{(positive)}= \color{ black }{negative}\) \( (3) \ \times \ (- \ 2)= \ – \ 6\)

Multiply and Divide Integers – Example 2:

Solve. \((- \ 8) \ + \ (12 \ \div \ 4)=\)

First divided \( 12\) by \(4\), the numbers in brackets, \(12 \ \div \ 4=3\) \((-8) \ + \ (3)= -8 \ + \ 3= \ – 5\)

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Multiply and divide integers – example 3:.

Solve. \((2-5)×(3)=\)

First subtract the numbers in brackets, \(2-5=-3 → (-3)×(3)=\) Now use this rule: \( \color{ black }{(negative)} \ × \ \color{blue}{(positive)} = \color{ black }{negative}\) \((-3)×(3)= \ -9\)

Multiply and Divide Integers – Example 4:

Solve. \((-12)+(48÷6)=\)

First divided \(48\) by \(6\), the numbers in brackets, \(48÷6=8\) \((-12)+(8)=-12+8= -4\)

Exercises for Multiplying and Dividing Integers

Find each product and quotient..

• \(\color{blue}{(– 8) × (– 2)}\)
• \(\color{blue}{ – 3 × 6 }\)
• \(\color{blue}{(– 4) × 5 × (– 6) }\)
• \(\color{blue}{ – 18 ÷ 3 }\)
• \(\color{blue}{(– 24) ÷ 4}\)
• \(\color{blue}{(– 63) ÷ (– 9)}\)

Download Multiplying and Dividing Integers Worksheet

• \(\color{blue}{16}\)
• \(\color{blue}{ – 18}\)
• \(\color{blue}{120}\)
• \(\color{blue}{ – 6}\)
• \(\color{blue}{ –6}\)
• \(\color{blue}{7}\)

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by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

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Multiplying Integers and Dividing Integers

Dividing Integers

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Multiplying and Dividing Integers Worksheets

Multiplying and dividing integers worksheets promotes an understanding of multiplication and division. These are the basic arithmetic operations that are necessary to know if a student wants to be good at mathematics. The worksheets consist of a variety of questions including multiplication of numbers, division and a combination of both.

Benefits of Multiplying and Dividing Integers Worksheets

If a student does not understand how to multiply and divide numbers, he will never be able to be successful in understanding Mathematics as a subject. The only way to understand such a topic is by solving numerous problems. Multiplying and dividing integers worksheets can aid students in strengthening their concepts and combating confusion.

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1.5: Multiply and Divide Integers

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Learning Objectives

By the end of this section, you will be able to:

• Multiply integers
• Divide integers
• Simplify expressions with integers
• Evaluate variable expressions with integers
• Translate English phrases to algebraic expressions
• Use integers in applications

A more thorough introduction to the topics covered in this section can be found in the Prealgebra chapter, Integers .

Multiply Integers

Since multiplication is mathematical shorthand for repeated addition, our model can easily be applied to show multiplication of integers . Let’s look at this concrete model to see what patterns we notice. We will use the same examples that we used for addition and subtraction. Here, we will use the model just to help us discover the pattern.

We remember that \(a\cdot b\) means add \(a,\, b\) times. Here, we are using the model just to help us discover the pattern.

The next two examples are more interesting.

What does it mean to multiply \(5\) by \(−3\)? It means subtract \(5, 3\) times. Looking at subtraction as “taking away,” it means to take away \(5, 3\) times. But there is nothing to take away, so we start by adding neutral pairs on the workspace. Then we take away \(5\) three times.

In summary:

\[\begin{array} {ll} {5 \cdot 3 = 15} &{-5(3) = -15} \\ {5(-3) = -15} &{(-5)(-3) = 15} \end{array}\]

Notice that for multiplication of two signed numbers, when the:

• signs are the same , the product is positive .
• signs are different , the product is negative .

We’ll put this all together in the chart below.

MULTIPLICATION OF SIGNED NUMBERS

For multiplication of two signed numbers:

Example \(\PageIndex{1}\)

• \(-9\cdot 3\)
• \(7\cdot 6\)
• \[\begin{array} {ll} {} &{-9\cdot 3} \\ {\text{Multiply, noting that the signs are different, so the product is negative.}} &{-27} \end{array}\]
• \[\begin{array} {ll} {} &{-2(-5)} \\ {\text{Multiply, noting that the signs are same, so the product is positive.}} &{10} \end{array}\]
• \[\begin{array} {ll} {} &{4(-8)} \\ {\text{Multiply, with different signs.}} &{-32} \end{array}\]
• \[\begin{array} {ll} {} &{7\cdot 6} \\ {\text{Multiply, with different signs.}} &{42} \end{array}\]

Try It \(\PageIndex{2}\)

• \(-6\cdot 8\)
• \(5\cdot 12\)

Try It \(\PageIndex{3}\)

• \(-8\cdot 7\)
• \(3\cdot 13\)

When we multiply a number by \(1\), the result is the same number. What happens when we multiply a number by \(−1\)? Let’s multiply a positive number and then a negative number by \(−1\) to see what we get.

\[\begin{array} {lll} {} &{-1\cdot 4} &{-1(-3)}\\ {\text{Multiply.}} &{-4} &{3} \\ {} &{-4\text{ is the opposite of 4.}} &{3\text{ is the opposite of } -3} \end{array}\] Each time we multiply a number by \(−1\), we get its opposite!

MULTIPLICATION BY −1

\[−1a=−a\]

Multiplying a number by \(−1\) gives its opposite.

Example \(\PageIndex{4}\)

• \(-1 \cdot 7\)
• \(-1(-11)\)
• \[\begin{array} {ll} {} &{-1\cdot 7} \\ {\text{Multiply, noting that the signs are different}} &{-7} \\ {\text{so the product is negative.}} &{-7\text{ is the opposite of 7.}} \end{array}\]
• \[\begin{array} {ll} {} &{-1(-11)} \\ {\text{Multiply, noting that the signs are different}} &{11} \\ {\text{so the product is positive.}} &{11\text{ is the opposite of -11.}} \end{array}\]

Try It \(\PageIndex{5}\)

• \(-1\cdot 9\)
• \(-1\cdot(-17)\)

Try It \(\PageIndex{6}\)

• \(-1\cdot 8\)
• \(-1\cdot(-16)\)

Divide Integers

What about division ? Division is the inverse operation of multiplication. So, \(15\div 3=5\) because \(5 \cdot 3 = 15\). In words, this expression says that \(15\) can be divided into three groups of five each because adding five three times gives \(15\). Look at some examples of multiplying integers, to figure out the rules for dividing integers.

\[\begin{array} {ll} {5\cdot 3 = 15\text{ so }15\div 3 = 5} &{-5(3) = -15\text{ so }-15\div 3 = -5} \\ {(-5)(-3) = 15\text{ so }15\div (-3) = -5} &{5(-3) = -15\text{ so }-15\div (-3) = 5} \end{array}\]

Division follows the same rules as multiplication!

For division of two signed numbers, when the:

• signs are the same , the quotient is positive .
• signs are different , the quotient is negative .

And remember that we can always check the answer of a division problem by multiplying.

MULTIPLICATION AND DIVISION OF SIGNED NUMBERS

For multiplication and division of two signed numbers:

• If the signs are the same, the result is positive.
• If the signs are different, the result is negative.

Example \(\PageIndex{7}\)

• \(-27\div 3\)
• \(-100\div (-4)\)
• \[\begin{array} {ll} {} &{-27 \div 3} \\ {\text{Divide, with different signs, the quotient is}} &{-9} \\ {\text{negative.}} &{} \end{array}\]
• \[\begin{array} {ll} {} &{-100 \div (-4)} \\ {\text{Divide, with signs that are the same the}} &{25} \\ {\text{ quotient is negative.}} &{} \end{array}\]

Try It \(\PageIndex{8}\)

• \(-42\div 6\)
• \(-117\div (-3)\)

Try It \(\PageIndex{9}\)

• \(-63\div 7\)
• \(-115\div (-5)\)

Simplify Expressions with Integers

What happens when there are more than two numbers in an expression? The order of operations still applies when negatives are included. Remember My Dear Aunt Sally?

Let’s try some examples. We’ll simplify expressions that use all four operations with integers—addition, subtraction, multiplication, and division. Remember to follow the order of operations.

Example \(\PageIndex{10}\)

\(7(-2)+4(-7)-6\)

\[\begin{array} {ll} {} &{7(-2)+4(-7)-6} \\ {\text{Multiply first.}} &{-14+(-28)-6} \\ {\text{Add.}} &{-42-6} \\{\text{Subtract}} &{-48} \end{array}\]

Try It \(\PageIndex{11}\)

\(8(-3)+5(-7)-4\)

Try It \(\PageIndex{12}\)

\(9(-3)+7(-8)-1\)

Example \(\PageIndex{13}\)

• \((-2)^{4}\)
• \[\begin{array} {ll} {} &{(-2)^{4}} \\ {\text{Write in expanded form.}} &{(-2)(-2)(-2)(-2)} \\ {\text{Multiply}} &{4(-2)(-2)} \\{\text{Multiply}} &{-8(-2)} \\{\text{Multiply}} &{16} \end{array}\]
• \[\begin{array} {ll} {} &{-2^{4}} \\ {\text{Write in expanded form. We are asked to find the opposite of }2^{4}.} &{-(2\cdot 2\cdot 2 \cdot 2)} \\ {\text{Multiply}} &{-(4\cdot 2\cdot 2)} \\{\text{Multiply}} &{-(8\cdot 2)} \\{\text{Multiply}} &{-16} \end{array}\]

Notice the difference in parts (1) and (2). In part (1), the exponent means to raise what is in the parentheses, the \((−2)\) to the \(4^{th}\) power. In part (2), the exponent means to raise just the \(2\) to the \(4^{th}\) power and then take the opposite.

Try It \(\PageIndex{14}\)

• \((-3)^{4}\)

Try It \(\PageIndex{15}\)

• \((-7)^{2}\)

The next example reminds us to simplify inside parentheses first.

Example \(\PageIndex{16}\)

\(12-3(9 - 12)\)

\[\begin{array} {llll} {} &{12-3(9 - 12)} \\ {\text{Subtract parentheses first}} &{12-3(-3)} \\ {\text{Multiply.}} &{12-(-9)} \\{\text{Multiply}} &{-(8\cdot 2)} \\{\text{Subtract}} &{21} \end{array}\]

Try It \(\PageIndex{17}\)

\(17 - 4(8 - 11)\)

Try It \(\PageIndex{18}\)

\(16 - 6(7 - 13)\)

Example \(\PageIndex{19}\)

\(8(-9)\div (-2)^{3}\)

\[\begin{array} {ll} {} &{8(-9)\div(-2)^{3}} \\ {\text{Exponents first}} &{8(-9)\div(-8)} \\ {\text{Multiply.}} &{-72\div (-8)} \\{\text{Divide}} &{9} \end{array}\]

Try It \(\PageIndex{20}\)

\(12(-9)\div (-3)^{3}\)

Try It \(\PageIndex{21}\)

\(18(-4)\div (-2)^{3}\)

Example \(\PageIndex{22}\)

\(-30\div 2 + (-3)(-7)\)

\[\begin{array} {ll} {} &{-30\div 2 + (-3)(-7)} \\ {\text{Multiply and divide left to right, so divide first.}} &{-15+(-3)(-7)} \\ {\text{Multiply.}} &{-15+ 21} \\{\text{Add}} &{6} \end{array}\]

Try It \(\PageIndex{23}\)

\(-27\div 3 + (-5)(-6)\)

Try It \(\PageIndex{24}\)

\(-32\div 4 + (-2)(-7)\)

Evaluate Variable Expressions with Integers

Remember that to evaluate an expression means to substitute a number for the variable in the expression. Now we can use negative numbers as well as positive numbers.

Example \(\PageIndex{25}\)

When \(n=−5\), evaluate:

• \(−n+1\).
• \[\begin{array} {ll} {} &{n+ 1} \\ {\text{Substitute }{ \color{red}{-5}}\text{ for } n} &{\color{red}{-5}}+1 \\ {\text{Simplify.}} &{-4} \end{array}\]
• \[\begin{array} {ll} {} &{n+ 1} \\ {\text{Substitute }{ \color{red}{-5}}\text{ for } n} &{- {\color{red}{(-5)}} +1} \\ {\text{Simplify.}} &{5+1} \\{\text{Add.}} &{6} \end{array}\]

Try It \(\PageIndex{26}\)

When \(n=−8\), evaluate:

• \(−n+2\).

Try It \(\PageIndex{27}\)

When \(y=−9\), evaluate:

• \(−y+8\).

Example \(\PageIndex{28}\)

Evaluate \((x+y)^{2}\) when \(x = -18\) and \(y = 24\).

\[\begin{array} {ll} {} &{(x+y)^{2}} \\ {\text{Substitute }-18\text{ for }x \text{ and } 24 \text{ for } y} &{(-18 + 24)^{2}} \\ {\text{Add inside parentheses}} &{(6)^{2}} \\{\text{Simplify.}} &{36} \end{array}\]

Try It \(\PageIndex{29}\)

Evaluate \((x+y)^{2}\) when \(x = -15\) and \(y = 29\).

Try It \(\PageIndex{30}\)

Evaluate \((x+y)^{3}\) when \(x = -8\) and \(y = 10\).

Example \(\PageIndex{31}\)

Evaluate \(20 -z \) when

• \(z = -12\)
• \[\begin{array} {ll} {} &{20 - z} \\ {\text{Substitute }12\text{ for }z.} &{20 - 12} \\ {\text{Subtract}} &{8} \end{array}\]
• \[\begin{array} {ll} {} &{20 - z} \\ {\text{Substitute }-12\text{ for }z.} &{20 - (-12)} \\ {\text{Subtract}} &{32} \end{array}\]

Try It \(\PageIndex{32}\)

Evaluate \(17 - k\) when

• \(k = -19\)

Try It \(\PageIndex{33}\)

Evaluate \(-5 - b\) when

• \(b = -14\)

Example \(\PageIndex{34}\)

\(2x^{2} + 3x + 8\) when \(x = 4\).

Substitute \(4\) for \(x\). Use parentheses to show multiplication.

\[\begin{array} {ll} {} &{2x^{2} + 3x + 8} \\ {\text{Substitute }} &{2(4)^{2} + 3(4) + 8} \\ {\text{Evaluate exponents.}} &{2(16) + 3(4) + 8} \\ {\text{Multiply.}} &{32 + 12 + 8} \\{\text{Add.}} &{52} \end{array}\]

Try It \(\PageIndex{35}\)

\(3x^{2} - 2x + 6\) when \(x =-3\).

Try It \(\PageIndex{36}\)

\(4x^{2} - x - 5\) when \(x = -2\).

Translate Phrases to Expressions with Integers

Our earlier work translating English to algebra also applies to phrases that include both positive and negative numbers.

Example \(\PageIndex{37}\)

Translate and simplify: the sum of \(8\) and \(−12\), increased by \(3\).

\[\begin{array} {ll} {} &{\text{the } \textbf{sum} \text{of 8 and -12, increased by 3}} \\ {\text{Translate.}} &{[8 + (-12)] + 3} \\ {\text{Simplify. Be careful not to confuse the}} &{(-4) + 3} \\{\text{brackets with an absolute value sign.}} \\{\text{Add.}} &{-1} \end{array}\]

Try It \(\PageIndex{38}\)

Translate and simplify: the sum of \(9\) and \(−16\), increased by \(4\).

\((9 + (-16)) + 4 - 3\)

Try It \(\PageIndex{39}\)

Translate and simplify: the sum of \(-8\) and \(−12\), increased by \(7\).

\((-8 + (-12)) + 7 - 13\)

When we first introduced the operation symbols, we saw that the expression may be read in several ways. They are listed in the chart below.

Be careful to get a and b in the right order!

Example \(\PageIndex{40}\)

Translate and then simplify

• the difference of \(13\) and \(−21\)
• subtract \(24\) from \(−19\).
• \[\begin{array} {ll} {} &{\text{the } \textbf{difference } \text{of 13 and -21}} \\ {\text{Translate.}} &{13 - (-21)} \\ {\text{Simplify.}} &{34} \end{array}\]
• \[\begin{array} {ll} {} &\textbf{subtract }24 \textbf{ from }-19 \\ {\text{Translate.}} &{-19 - 24} \\ {\text{Remember, subtract b from a means }a - b} &{} \\{\text{Simplify.}} &{-43} \end{array}\]

Try It \(\PageIndex{41}\)

Translate and simplify

• the difference of \(14\) and \(−23\)
• subtract \(21\) from \(−17\).
• \(14 - (-23); 37\)
• \(-17 - 21; -38\)

Try It \(\PageIndex{42}\)

• the difference of \(11\) and \(−19\)
• subtract \(18\) from \(−11\).
• \(11 - (-19); 30\)
• \(-11 - 18; -29\)

Once again, our prior work translating English to algebra transfers to phrases that include both multiplying and dividing integers. Remember that the key word for multiplication is “ product ” and for division is “ quotient .”

Example \(\PageIndex{43}\)

Translate to an algebraic expression and simplify if possible: the product of \(−2\) and \(14\).

\[\begin{array} {ll} {} &{\text{the product of }-2 \text{ and } 14} \\ {\text{Translate.}} &{(-2)(14)} \\{\text{Simplify.}} &{-28} \end{array}\]

Try It \(\PageIndex{44}\)

Translate to an algebraic expression and simplify if possible: the product of \(−5\) and \(12\).

\(-5(12); -60\)

Try It \(\PageIndex{45}\)

Translate to an algebraic expression and simplify if possible: the product of \(8\) and \(-13\).

\(-8(13); -104\)

Example \(\PageIndex{46}\)

Translate to an algebraic expression and simplify if possible: the quotient of \(−56\) and \(−7\).

\[\begin{array} {ll} {} &{\text{the quotient of }-56 \text{ and } -7} \\ {\text{Translate.}} &{-56\div(-7)} \\{\text{Simplify.}} &{8} \end{array}\]

Try It \(\PageIndex{47}\)

Translate to an algebraic expression and simplify if possible: the quotient of \(−63\) and \(−9\).

\(-63\div (-9); 7\)

Try It \(\PageIndex{48}\)

Translate to an algebraic expression and simplify if possible: the quotient of \(−72\) and \(−9\).

\(-72\div (-9); 8\)

Use Integers in Applications

We’ll outline a plan to solve applications. It’s hard to find something if we don’t know what we’re looking for or what to call it! So when we solve an application, we first need to determine what the problem is asking us to find. Then we’ll write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.

How to Apply a Strategy to Solve Applications with Integers

Example \(\PageIndex{49}\)

The temperature in Urbana, Illinois one morning was \(11\) degrees. By mid-afternoon, the temperature had dropped to \(−9\) degrees. What was the difference of the morning and afternoon temperatures?

Try It \(\PageIndex{50}\)

The temperature in Anchorage, Alaska one morning was \(15\) degrees. By mid-afternoon the temperature had dropped to \(30\) degrees below zero. What was the difference in the morning and afternoon temperatures?

The difference in temperatures was \(45\) degrees.

Try It \(\PageIndex{51}\)

The temperature in Denver was \(−6\) degrees at lunchtime. By sunset the temperature had dropped to \(−15\) degrees. What was the difference in the lunchtime and sunset temperatures?

The difference in temperatures was \(9\) degrees.

APPLY A STRATEGY TO SOLVE APPLICATIONS WITH INTEGERS.

• Read the problem. Make sure all the words and ideas are understood
• Identify what we are asked to find.
• Write a phrase that gives the information to find it.
• Translate the phrase to an expression.
• Simplify the expression.
• Answer the question with a complete sentence.

Example \(\PageIndex{52}\)

The Mustangs football team received three penalties in the third quarter. Each penalty gave them a loss of fifteen yards. What is the number of yards lost?

Try It \(\PageIndex{53}\)

The Bears played poorly and had seven penalties in the game. Each penalty resulted in a loss of \(15\) yards. What is the number of yards lost due to penalties?

The Bears lost \(105\) yards.

Try It \(\PageIndex{54}\)

Bill uses the ATM on campus because it is convenient. However, each time he uses it he is charged a $2 fee. Last month he used the ATM eight times. How much was his total fee for using the ATM?

A $16 fee was deducted from his checking account.

Key Concepts

• Same signs—Product is positive
• Different signs—Product is negative
• Identify what you are asked to find.

Multiplying and Dividing Integers: Advanced Lesson

With this lesson, students will learn about positive and negative numbers and learn the rules for multiplying and dividing by them.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to add another activity. For this activity, students will flip over two playing cards and multiply (red for negative, black for positive). Students collect the cards if they get the right answer, and the student with the most cards at the end wins.

Description

Additional information, what our multiplying and dividing integers lesson plan includes.

Lesson Objectives and Overview: Multiplying and Dividing Integers introduces students to working with positive and negative integers. The included manipulative is a great way for students to visualize the concept and practice solving problems. This lesson is for students in 6th grade.

Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the orange box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. There are no supplies needed for this lesson. To prepare for this lesson ahead of time, you can copy the handouts.

Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. An optional addition to this lesson is to add another activity. For this activity, students will flip over two playing cards and multiply (red for negative, black for positive). Students collect the cards if they get the right answer, and the student with the most cards at the end wins. If some of your students have trouble multiplying or dividing, they can use a calculator.

Teacher Notes

The teacher notes page includes a paragraph with additional guidelines and things to think about as you begin to plan your lesson. This page also includes lines that you can use to add your own notes as you’re preparing for this lesson.

MULTIPLYING AND DIVIDING INTEGERS LESSON PLAN CONTENT PAGES

Integers (multiplying and dividing).

The Multiplying and Dividing Integers lesson plan includes one page of content. The lesson begins by explaining how to multiply or divide integers with the same sign. To do this, you multiply or divide the number regularly. The answer will always be positive. Next, the lesson explains how to multiply or divide integers with different signs. You also multiply the integers regularly, but in this case, the answer will always be negative. The lesson includes an example for each scenario.

MULTIPLYING AND DIVIDING INTEGERS LESSON PLAN WORKSHEETS

The Multiplying and Dividing Integers lesson plan includes three worksheets: an activity worksheet, a practice worksheet, and a homework assignment. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

TIC-TAC-TOE ACTIVITY WORKSHEET

The activity worksheet asks students to use a tic-tac-toe table to reinforce the rules for multiplying or dividing integers. They will use the table included on the worksheet and will place positive signs on one diagonal and fill in the rest of the places with negative signs. They will then use the table to fill in various statements related to the lesson material.

SOLVING PROBLEMS PRACTICE WORKSHEET

For the practice worksheet, students will solve multiplication and division problems using what they learned during the lesson.

MULTIPLYING AND DIVIDING INTEGERS HOMEWORK ASSIGNMENT

The homework assignment asks students to fill in the tic tac toe board and answer question about it. They will also solve 12 multiplication and division problems.

Worksheet Answer Keys

This lesson plan includes answer keys for the activity worksheet, the practice worksheet, and the homework assignment.  If you choose to administer the lesson pages to your students via PDF, you will need to save a new file that omits these pages. Otherwise, you can simply print out the applicable pages and keep these as reference for yourself when grading assignments.

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Multiplying And Dividing Integers Worksheets

Created: October 28, 2022

Last updated: June 6, 2023

A multiply and dividing integers worksheets for graders help them to grasp the rationale behind these operations. Integer multiplication and division are foundational mathematical concepts that will stay with the learner as they progress through school.

Free multiplying and dividing integers worksheets

Multiply And Divide Integers Worksheet

Multiplying And Dividing Integers Word Problems Worksheets

Multiplication And Division Of Integers Worksheet

Integer Multiplication And Division Worksheet

Multiplication And Division Integers Worksheet

Multiplying And Dividing Integers Worksheet 6Th Grade

Using free multiplying and dividing integers worksheets can boost kids’ problem-solving abilities and self-confidence.

If used by 7th graders, multiplying and dividing integers word problems worksheets cover vital topics such as finding the products of two integers, principles of multiplying or dividing integers, applying integers, and finding the quotient after dividing two integers.

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Math for Kids

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Printable multiplying and dividing integers worksheet PDF

Multiplying and dividing integers worksheets pdf.

Multiplying And Dividing Integers Worksheet

Multiply And Dividing Integers Worksheets

Multiplying And Dividing Integers Worksheet PDF

You don’t need to use your computer whenever you want your kids to practice with the integer worksheet. Having the printable version available on Brighterly will help you keep your kids busy and teach them to learn independently.

With a paper worksheet, your kid can repeatedly practice without supervision. This continued practice leads to mastery of the concept.

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As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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7th Grade Multiplying and Dividing Integers Worksheets

Integers are a set of whole numbers and their opposites. These seventh grade multiplying and dividing integers worksheet s are really helpful to enhance a student’s knowledge about operations on integers by modeling and solving problems based on real life scenarios. ...Read More Read Less

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Choose math worksheets by topic, 7th grade multiplying and dividing integers worksheets explained:.

The multiplying and dividing integers worksheets for grade 7 helps students to understand the procedure that supports the multiplication and division of integers. The concept of multiplying and dividing integers will follow the student through each grade in their journey through math across higher grades. In these worksheets a student will go through the concepts such as the rules of multiplication, multiplication of integers with same or a different sign, rules of division, finding quotients of integers with the same or different sign and use of integers to model real life questions. These seventh grade multiplying and dividing integers worksheets contain questions related to the following topics:

• Multiplying integers with same or different signs: The product of two integers with the same sign is positive but the product of two integers with different signs is negative.
• Dividing integers with same or different signs: The quotient of two integers with the same sign is positive and the quotient of two integers with different signs is negative.  
• Applying multiplication and division on integers to model real life problems: The online free multiplying and dividing integers worksheets for grade 7 contain context based questions where integers are used to represent quantities and operations(multiplication and division) are applied to find the solution of problems.  

If you feel the need to refresh your understanding about multiplying and dividing integers as a concept, click on the following links:

• Integers on number line and their comparison
• Adding multiplying and dividing integers
• Operations on multiplying and dividing integers using signs and inductive reasoning
• Dividing operations on multiplying and dividing integers
• Properties of multiplying and dividing integers

Benefits of 7th Grade multiplying and dividing integers worksheets:

• Integers worksheets (Easy): The worksheets for multiplying and dividing integers in the seventh grade aid the learner in recalling multiple terms and operations associated with integers. The learner is attracted to learn concepts and use them in the classroom by solving the problems in the free printable or online worksheets.  
• Integers worksheets (medium): The learner can use various integer operations to answer various problems by using the multiplying and dividing integers worksheets for grade 7. These worksheets are both printable and online. Additionally, it enhances the student's ability to quickly solve addition and subtraction problems involving integers. These worksheets also help students improve their aptitude.
• Integers worksheets (Hard): These free worksheets for seventh grade that are available online and in print format explain specific types of problems whose solutions require two or more steps to complete, suggesting that more than two operations (addition and subtraction) on integers may be necessary to answer the problem. This equips students to develop solutions to such complex challenges. These worksheets also assist students in developing their problem solving abilities for upcoming grades.    

Printable PDFs & Online 7th Grade Worksheets:

Free printable worksheets for multiplying and dividing integers in the seventh grade are a great way to improve a student’s problem solving abilities and get them ready for assessments like standardized examinations and aptitude tests. Grade 7 multiplying and dividing integers worksheets help the student to gain a thorough understanding of how to apply concepts they employ while solving the worksheets. Attempting difficult questions that are found in higher grades is a bonus. The grade 7 multiplying and dividing integers worksheets include fundamental concepts like rules of multiplying or dividing integers, finding the product of two integers, finding the quotient after dividing two integers and using integers through simulating real world situations. Timed online worksheets also help the student to enhance time management skills, especially while solving particular types of questions. With these timed worksheets the student can also compare scores and time spent on the worksheets with classmates and challenge them as well.

Write down the general rules of multiplication.

Four rules of multiplying integers are: 

• Positive × Positive = Positive
• Positive × Negative = Negative
• Negative × Positive = Negative
• Negative × Negative = Positive

What will be the sign of product if two integers have different signs?

The product of two integers with different signs is always a negative number, so the sign of the product is ‘minus’.

How can hard level problems help a student in the journey through mathematics?

Hard level problems are context based and may have solutions with multiple steps. Students will have to apply the basic concepts as well as two or more operations to solve some problems. These hard level problems prepare a student to enhance aptitude skills and gear up for future grades.

What if the divisor is zero?

The quotient obtained by dividing an integer by zero is undefined.

How are 7th grade multiplying and dividing integers worksheets advantageous to students?

When students solve worksheets on their own, it promotes active learning as they feel a sense of accomplishment. It raises the curiosity level about multiplying and dividing integers in relation to specific topics, and in turn, enables them to take up more challenging questions. In the multiplying and dividing integers worksheets for grade 7 from BYJU’S math, students also learn the method of applying step-wise solutions that further strengthens their understanding about multiplying and dividing integers.

Why are these interactive worksheets necessary for students?

Free online grade 7 multiplying and dividing integers worksheets link learning multiple concepts with a fun element as they are interactive. These worksheets follow the common core math structure and assist students to be completely familiar with the methods and terms used in 7th grade.

Study the examples below and see if you spot any patterns. Can you figure out the rules for multiplying and dividing integers? Try it first before clicking "Show Me" to see the rules.

• The product of two positive integers or two negative integers is positive.
• The product of a positive integer and a negative integer is negative.
• The quotient of two positive integers or two negative integers is positive.
• The quotient of a positive integer and a negative integer is negative.

Multiplying and Dividing Integers: Problem Solving

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DIVIDING INTEGERS WORD PROBLEMS

We can use integer division to solve real-world problems. For some problems, we may need to perform more than one step.

And also, we have to be sure to check that the sign of the quotient makes sense for the situation.

Problem 1 :

Jake answers questions in two different online Olympic trivia quizzes. In each quiz, he loses points when he gives an incorrect answer. The table shows the points lost for each wrong answer in each quiz and Jake’s total  points lost in each quiz. In which quiz did he have more wrong answers ?

Step 1 : 

To find the number of incorrect answers in the winter quiz, divide the total points lost by the number of points lost per wrong answer.

-33 ÷ (-3)  =  11

Find the number of incorrect answers Jake gave in the summer quiz. Divide the total points lost by the number of points lost per wrong answer.

-56 ÷ (-7)  =  8

Compare the numbers of wrong answers.

So, Jake had more wrong answers in the winter quiz.

Problem 2 :

A penalty in Meteor-Mania is -5 seconds. A penalty in Cosmic Calamity is -7 seconds. Yolanda had penalties totaling -25 seconds in a game of Meteor-Mania and -35 seconds in a game of Cosmic Calamity. In which game did Yolanda receive more penalties ? Justify your answer.

To find the number of times Yolanda received penalties in Meteor-Mania, divide the total penalties by penalties per time.

-25 ÷ (-5)  =  5

In the game of  Meteor-Mania, s he received penalties 5 times  

Step 2 : 

To find the number of times Yolanda received penalties in  Cosmic Calamity , divide the total penalties by penalties per time.

-35 ÷ (-7)  =  5

In the game of  Cosmic Calamity, s he received penalties 5 times.

Compare the number of times she received penalties in both the games. 

5  =  5

Yolanda received the same number of penalties in each game

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