lesson 2 homework practice add integers

Grade 6 Mathematics Module: Adding Integers

This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.

Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.

Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.

Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.

If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.

This module was designed and written with you in mind. It is here to help you master the skills in adding integers. The scope of this module permits it to be used in many different learning situations. The language used recognizes your diverse vocabulary level. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using.

The module is divided into three lessons, namely:

• Lesson 1 – Adding Integers with Like Signs
• Lesson 2 – Adding Integers with Unlike Signs
• Lesson 3 – Solving Routine and Non-Routine Problems Involving Addition of Integers Using Appropriate Strategies and Tools

After going through this module, you are expected to:

1. describe and interpret addition of integers using materials such as algebra tiles, counters, chips, and cards (M6NS-IIh-155);

2. perform addition of integers (M6NS-IIi-156); and

3. solve routine and non-routine problems involving addition of integers using appropriate strategies and tools.

Grade 6 Mathematics Quarter 2 Self-Learning Module: Adding Integers

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Adding Integers Practice 2

Adding Integers Practice 2: Find the sum of each expression. Click the button below to try all our FREE PDF printable pre-algebra worksheets.

How to Add and Subtract Integers! Try all Pre-Algebra Worksheets! Read more

Practice to add positive and negative integers with all our adding integers worksheets. Hit the button ‘Check Answers’ at the end of the practice sheet to correct your answers. Click ‘Download/Print Worksheet’ button to download or print this worksheet.

Integers are always whole numbers. They can be either positive or negative. There are some rules that you have to follow in order to add and subtract expressions with positive and negative integers.

Adding integers with the same sign

If the signs of the integers match, we will add the given integers together and keep the sum with the same sign.

Example: 5 + 6 = 11

Example: (-5) + (-6) = -11

Adding integers with different signs

If you have to add one positive and one negative number, or two integers with different signs that don’t match, you have to subtract the integers as if they were all positive and keep the answer with the larger integer’s sign.

Example: 5 + (-6) = -1

Example: (-5) + 6 = 1

Although, this worksheet is to add integers, let’s also learn how to subtract integers with the same and different signs.

Subtracting integers with the same sign

This is similar to adding integers with different signs. If the signs of the integers match, we will have to subtract the smaller integer from the larger integer and keep the difference with the larger integer’s sign.

Example: 5 – 6 = -1

Example: (-5) – (-6) = 1

Subtracting integers with different signs

This is similar to adding integers with the same sign.

Example: 5 – (-6) = 11

Example: (-5) – 6 = -11

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2.3: Add Integers (Part 1)

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Learning Objectives

• Model addition of integers
• Simplify expressions with integers
• Evaluate variable expressions with integers
• Translate word phrases to algebraic expressions
• Add integers in applications

be prepared!

Before you get started, take this readiness quiz.

• Evaluate \(x + 8\) when \(x = 6\). If you missed this problem, review Example 2.2.1 .
• Simplify: \(8 + 2(5 + 1)\). If you missed this problem, review Example 2.1.8 .
• Translate the sum of \(3\) and negative \(7\) into an algebraic expression. If you missed this problem, review Table 2.2.3 .

Model Addition of Integers

Now that we have located positive and negative numbers on the number line, it is time to discuss arithmetic operations with integers.

Most students are comfortable with the addition and subtraction facts for positive numbers. But doing addition or subtraction with both positive and negative numbers may be more difficult. This difficulty relates to the way the brain learns.

The brain learns best by working with objects in the real world and then generalizing to abstract concepts. Toddlers learn quickly that if they have two cookies and their older brother steals one, they have only one left. This is a concrete example of \(2 − 1\). Children learn their basic addition and subtraction facts from experiences in their everyday lives. Eventually, they know the number facts without relying on cookies.

Addition and subtraction of negative numbers have fewer real world examples that are meaningful to us. Math teachers have several different approaches, such as number lines, banking, temperatures, and so on, to make these concepts real.

We will model addition and subtraction of negatives with two color counters. We let a blue counter represent a positive and a red counter will represent a negative.

If we have one positive and one negative counter, the value of the pair is zero. They form a neutral pair. The value of this neutral pair is zero as summarized in Figure \(\PageIndex{1}\).

Figure \(\PageIndex{1}\): A blue counter represents +1. A red counter represents −1. Together they add to zero.

We will model four addition facts using the numbers \(5\), \(−5\) and \(3\), \(−3\).

\[5 + 3 \qquad −5 + (−3) \qquad −5 + 3 \qquad 5 + (−3) \nonumber \]

Example \(\PageIndex{1}\): model the expression

Model: \(5 + 3\).

Exercise \(\PageIndex{1}\)

Model the expression. \(2 + 4\)

Exercise \(\PageIndex{2}\)

Model the expression. \(2 + 5\)

Example \(\PageIndex{2}\): model the expression

Model: \(−5 + (−3)\).

Exercise \(\PageIndex{3}\)

Model the expression. \(−2 + (−4)\)

Exercise \(\PageIndex{4}\)

Model the expression. \(−2 + (−5)\)

Example \(\PageIndex{1}\) and Example \(\PageIndex{2}\) are very similar. The first example adds \(5\) positives and \(3\) positives—both positives. The second example adds \(5\) negatives and \(3\) negatives—both negatives. In each case, we got a result of \(8\) -- either \(8\) positives or \(8\) negatives. When the signs are the same, the counters are all the same color. Now let’s see what happens when the signs are different.

Example \(\PageIndex{3}\): model the expression

Model: \(−5 + 3\).

Notice that there were more negatives than positives, so the result is negative.

Exercise \(\PageIndex{5}\)

Model the expression, and then simplify: \(2 + (-4)\)

Exercise \(\PageIndex{6}\)

Model the expression, and then simplify: \(2 + (−5)\)

Example \(\PageIndex{4}\): model the expression

Model: \(5 + (−3)\).

Exercise \(\PageIndex{7}\)

Model the expression, and then simplify: \((−2) + 4\)

Exercise \(\PageIndex{8}\)

Model the expression: \((−2) + 5\)

Example \(\PageIndex{5}\): model the addition

Model each addition.

• \(−3 + 6\)
• \(4 + (−5)\)
• \(-2 + (−3)\)
• \(−2 + (−3)\)

Exercise \(\PageIndex{9}\)

• \(−1 + 4\)
• \(4 + (−6)\)
• \(−2 + (−2)\)

Exercise\(\PageIndex{10}\)

• \(−3 + 7\)
• \(2 + (−8)\)
• \(−3 + (−4)\)

Simplify Expressions with Integers

Now that you have modeled adding small positive and negative integers, you can visualize the model in your mind to simplify expressions with any integers.

For example, if you want to add \(37 + (−53)\), you don’t have to count out \(37\) blue counters and \(53\) red counters.

Picture \(37\) blue counters with \(53\) red counters lined up underneath. Since there would be more negative counters than positive counters, the sum would be negative. Because \(53−37 = 16\), there are \(16\) more negative counters.

\[37 + (−53) = −16 \nonumber \]

Let’s try another one. We’ll add \(−74 + (−27)\). Imagine \(74\) red counters and \(27\) more red counters, so we have \(101\) red counters all together. This means the sum is \(−101\).

\[−74 + (−27) = −101 \nonumber \]

Look again at the results of Example \(\PageIndex{1}\) - Example \(\PageIndex{2}\).

Example \(\PageIndex{6}\): simplify

• \(19 + (−47)\)
• \(−32 + 40\)
• Since the signs are different, we subtract \(19\) from \(47\). The answer will be negative because there are more negatives than positives. \(19 + (−47)=−28\)
• The signs are different so we subtract \(32\) from \(40\). The answer will be positive because there are more positives than negatives \(−32 + 40=8\)

Exercise \(\PageIndex{11}\)

Simplify each expression:

• \(15 + (−32)\)
• \(−19 + 76\)

Exercise \(\PageIndex{12}\)

• \(−55 + 9\)
• \(43 + (−17)\)

Example \(\PageIndex{7}\): simplify

Simplify: \(−14 + (−36)\).

Since the signs are the same, we add. The answer will be negative because there are only negatives.

\[−14 + (−36)=−50 \nonumber \]

Exercise \(\PageIndex{13}\)

Simplify the expression: \(−31 + (−19)\)

Exercise \(\PageIndex{14}\)

Simplify the expression: \(−42 + (−28)\)

The techniques we have used up to now extend to more complicated expressions. Remember to follow the order of operations.

Example \(\PageIndex{8}\): simplify

Simplify: \(−5 + 3(−2 + 7)\).

Exercise \(\PageIndex{15}\)

Simplify the expression: \(−2 + 5(−4 + 7)\)

Exercise \(\PageIndex{16}\)

Simplify the expression: \(−4 + 2(−3 + 5)\)

Contributors and Attributions

• Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a  Creative Commons Attribution License 4.0  license.

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Explanation:

Justify Conclusions Write an addition expression to describe each situation. Then find each sum and explain its meaning.

Ronnie receives $40 for his birthday. Then he spends $15 at the movies.

A quarterback is sacked for a loss of 5 yards. On the next play, his team loses 15 yards. Then the team gains 12 yards on the third play.

A pelican starts at 60 feet above sea level. It descends 60 feet to catch a fish.

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