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• Math Article

Arithmetic Questions

Arithmetic Questions and solutions are given here contain various problems on numbers and simplification of numerical expressions. Practising these solved questions of arithmetic will help you boost problem-solving skills and enhance your speed of working with numerical simplification problems. As we know, basic arithmetic questions involve simple addition/subtraction/multiplication/division problems. Let’s solve problems in arithmetic here in this article.

What is arithmetic?

In mathematics, arithmetic is the act of working with numbers, which means performing various operations such as addition, subtraction, multiplication, and division. And these operations are referred to as arithmetic operations. Also, we use the BODMAS rule to solve arithmetic questions accurately.

Click here to learn in detail about arithmetic .

Arithmetic Questions and Answers

1. The total age of three kids in a family is 27 years. What will be the total of their ages after three years?

Total age of three kids = 27 years

After three years, the age of each kid will increase by 3.

So, the total age after three years = 27 + 3 × 3

Therefore, the total age of three kids after three years will be 36 years.

2. Find the product of all the numbers present on the calculator pad.

Numbers on the calculator pad = 0,1, 2, 3, 4, 5, 6, 7, 8, 9

Product of all these numbers = 0 × 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 = 0 {since the product of any number with 0 is also 0)

3. Jessi ran 12 laps every day for two weeks. How many laps did she run in all?

Number of laps ran by Jessi in a day = 12

Number of day = 2 weeks = 2 × 7 days = 14 days

Total laps run by Jessi in 2 weeks = 12 × 14 = 168

4. Simplify: 133 – 19 × 2 + 15

133 – 19 × 2 + 15

= 133 – 38 + 15

= 148 – 38

Therefore, 133 – 19 × 2 + 15 = 110.

5. Find the next term of the arithmetic sequence 177, 173, 169, 165,…

Given arithmetic sequence is:

177, 173, 169, 165,…

Here, 173 – 177 = -4

169 – 173 = -4

165 – 169 = -4

So, the next term = 165 – 4 = 161

6. Kamal’s annual income is Rs. 288000. His annual savings amount to Rs. 36000. What is his total yearly expenditure?

The annual income of Kamal = Rs. 288000

Annual savings = Rs. 36000

Total yearly expenditure of Kamal = Rs. 288000 – Rs. 36000 = Rs. 252000

7. Find the value of 45 ÷ 9 × 3 + 15 – 6

45 ÷ 9 × 3 + 15 – 6

= 5 × 3 + 15 – 6

= 15 + 15 – 6

= 30 – 6

Hence, the value of 45 ÷ 9 × 3 + 15 – 6 is 24.

8. Simplify the numerical expression: [36 ÷ (-9)] ÷ [(-24) ÷ 6]

[36 ÷ (-9)] ÷ [(-24) ÷ 6]

This can be written as:

= (36/-9) ÷ (-24/6)

= (-4) ÷ (-4)

Thus, [36 ÷ (-9)] ÷ [(-24) ÷ 6] = 1.

9. Find the missing number in the following: 7 – 24 ÷ 8 × m + 6 = 1

7 – 24 ÷ 8 × m + 6 = 1

7 – (24/8) × m + 6 = 1

7 – 3 × m + 6 = 1

13 – 3 × m = 1

⇒ 3 × m = 13 – 1

⇒ 3 × m = 12

Therefore, the missing number is 4.

10. Mehak bought 96 toys priced equally for Rs. 12960. The amount of Rs. 1015 is still left with him. Find the cost of each toy and the amount he had.

Number of toys Mehak bought = 96 toys

Cost of 96 toys = 12960

Cost of one toy = 12960/96 = 135

Amount left with him = 1015

Amount he gave = 12960

Amount he had initially = 12960 + 1015 = 13975

Thus, the cost of each toy was Rs. 135, and he had the amount of Rs. 13975.

Practice Questions on Arithmetic

• Simplify: 19 × 8 + 25 − 2 ÷ (44 − 2)
• Find the value of 4 + 64 × (30 ÷ 5).
• The cost of one apple is Rs. 24. Find the cost of 15 such apples.
• A shoe factory manufactured 70,000 shoes in 60 days. How many shoes did it manufacture per day?
• A chicken pen held 7 chickens. Each chicken lays 5 eggs a day. How many eggs would they get altogether after 32 days?

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Basic Arithmetic

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In order to access this I need to be confident with:

Here you will learn about arithmetic, including key terminology and mathematical symbols, using the four operations with positive and negative integers, and inverse operations.

Students will first learn about arithmetic as part of number and operations in 4th and 5th grade and continue to build on this knowledge in the number system in 6th and 7th grade.

What is arithmetic?

Arithmetic is the study of numbers and the operations between them. It is an elementary branch of mathematics.

The definition of arithmetic comes from the Greek word “arithmos”, meaning number, or the art of counting.

To solve problems using basic arithmetic, you need to understand and use the four operations.

The four operations you will be using are: addition , subtraction , multiplication, and division .

Arithmetic with four operations

Below is a table showing the four operations of arithmetic with their associated symbols.

Each operation has a different function that you should be confident with using.

Addition is the operation of combining two or more numbers together.

The two numbers can be represented by a and b, and c will represent the sum of a and b.

This would be written as a+b=c and pronounced a plus b is equal to c.

Addition is commutative, which means that the order in which addition is carried out does not matter.

For example,

Addition can be done with positive and negative integers, fractions, and decimals.

Addition represents a movement up the number line. Here are some examples:

In order to solve addition problems with larger numbers, you can use the standard algorithm.

For example, 347+21 :

It is important to consider the place value of each digit and line up the corresponding digits in each number.

[FREE] Arithmetic Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of arithmetic. 10+ questions with answers to identify areas of strength and support!

Subtraction

Subtraction is the operation of finding the difference between two numbers.

The number remaining when the number b is subtracted from the number c would equal a, or the answer to a subtraction problem.

This would be written as c-b=a and pronounced c take away b is equal to a.

Subtraction is not commutative. If the order of the numbers within the calculation changes, the result will change.

Subtraction can also be done with positive and negative integers, fractions, and decimals. Subtraction represents a movement down the number line. Here are some examples:

In order to solve subtraction problems with larger numbers, you can use the standard algorithm.

It is important to consider the place value of each digit and line up the corresponding digits and decimal place in each number.

Multiplication

Multiplication is essentially repeated addition.

If you have n copies of a, you multiply a by n to find how many are in the new set, m.

This is the same as calculating a+a+a+… \, n times.

This would be written as n\times{a}=m and pronounced n times a is equal to m.

The product is the answer you get when multiplying one number by another. The multiplicand is the quantity to be multiplied by the multiplier, which will give you a product.

multiplicand \times multiplier = product

In this calculation,

6 is the multiplicand , 3 is the multiplier and the answer, 18 is the product .

The product will be 0 if either the multiplicand or multiplier is 0.

Multiplication is commutative. The order in which the calculation is performed does not matter.

Multiplication can be done with positive and negative integers, fractions, and decimals. When multiplying positive and negative numbers, the following rules apply:

To solve multiplication problems with larger numbers, you can use an area model.

Division shares or breaks a number into equal sized numbers of groups.

If the number m can be shared equally between n groups, with no remainder, then this is written as m\div{n}=a and pronounced m divided by n is equal to a.

The quotient is the answer you get when dividing one number by another.

The word quotient comes from Latin and means ‘how many times’. When dividing, you are finding out ‘how many times’ a number goes into another number.

dividend \div divisor = quotient

8 is the dividend , 4 is the divisor and the answer, 2 is the quotient.

The quotient will only be 0 if the dividend is 0 but the divisor is not.

Unlike multiplication, division is not commutative. If the order of the numbers within the calculation changes, the result will change.

12\div{4} ≠ {4}\div{12}

Division can also be done with positive and negative integers, fractions, and decimals. When dividing positive and negative numbers, the following rules apply:

To perform division problems with larger numbers, you can use long division.

Inverse operations

Inverse operations reverse an operation that has been carried out. Below is a table outlining some operations along with their inverse operations.

Note that you can switch the columns so the inverse operation of subtraction is addition and the inverse operation of division is multiplication, etc.

Using the inverse operations helps us see relationships between numbers and are often referred to as fact families. Fact families show the relationship between the same set of numbers, just as inverse operations do.

Step-by-step guide : Inverse operations (coming soon)

When solving problems involving basic arithmetic operations, it is important to apply the order of operations, or PEMDAS. PEMDAS tells us what order to perform the operations in.

P arentheses

M ultiplication

S ubtraction

In the calculation

multiplication should be done before the addition.

Common Core State Standards

How does this relate to 4th, 5th, and 6th grade math?

• Grade 4: Number and Operations in Base 10 (4.NBT.4) Fluently add and subtract multi-digit whole numbers using the standard algorithm.
• Grade 5: Number and Operations in Base Ten (5.NBT.5) Fluently multiply multi-digit whole numbers using the standard algorithm.
• Grade 5: Number and Operations – Fractions (5.NF.1) Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
• Grade 5: Number and Operations – Fractions (5.NF.4) Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
• Grade 6: The Number System (6.NS.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, example, by using visual fraction models and equations to represent the problem.
• Grade 6: The Number System (6.NS.2) Fluently divide multi-digit numbers using the standard algorithm.
• Grade 6: The Number System (6.NS.3) Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• Grade 6: The Number System (6.NS.5) Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (example, temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
• Grade 7: The Number System (7.NS.A.1) Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
• Grade 7: The Number System (7.NS.A.2) Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

How to use arithmetic with positive and negative numbers

In order to use arithmetic with positive and negative numbers:

Determine which operation you will use.

• Perform the chosen operation .

Arithmetic examples

Example 1: addition with decimals.

Calculate the value of 10.9+34.3.

Here you will use addition.

2 Perform the chosen operation.

Using the standard algorithm, you have:

Starting on the right, the tenths place, you add 9+3=12. The tenths column value of 2 is placed below the answer line, and the 1 is carried above the addition problem, so that you can add it to the next column total (the units column).

Adding 0, 4, and the 1 that was carried from the tenths column, you have 0+4+1=5 and so 5 goes into the answer bar for the units column.

The final column requires us to add 1 and 3, \, 1+3=4 and so you put a 4 in the tens column.

So 10.9+34.3=45.2.

Example 2: subtraction (word problem)

96 mathematicians attended a celebration party at a hotel. 38 mathematicians stayed overnight. How many mathematicians did not stay overnight?

Here you will use subtraction. You need to solve 96-38.

Perform the chosen operation.

Writing subtraction using the standard algorithm, you have:

Starting from the units column, 6-8 is a negative number, so you have to borrow from the tens column.

16-8=8 and so the value for the units column is 8.

Continuing with the tens column, you have 8-3=5.

58 guests did not stay overnight.

Example 3: multiplication (word problem)

A sack can hold 36 potatoes. A farmer packs 24 sacks of potatoes with no leftover potatoes. How many potatoes does the farmer pack?

As there are 36 potatoes per sack and 24 sacks, you will multiply these values.

Using the area model, you have:

By multiplying each row value by each column value, you get:

Adding the new values in the area model, you have:

The farmer packs 864 potatoes.

Example 4: division (word problem)

A bar of chocolate is made up of 84 individual cubes. The bar is 6 cubes wide. How many rows does the chocolate bar have?

Each column contains 6 cubes and there are 84 cubes in total. You will need to divide 84 by 6 to determine the number of rows in the chocolate bar.

Using partial quotients, you have:

You will think of a multiple of 6 that will get you as close to 84, without going over.

6 \times 10=60

You will think of another multiple of 6 that will get you as close to 24 as possible, without going over.

\begin{aligned} & 6 \times 4=24 \\\\ & 24-24=0 \end{aligned}

You will add your two partial quotients together 10 + 4 = 14.

The chocolate bar has 14 rows.

Example 5: addition, with negative numbers

Calculate (-3)+(-2).

Here, you are solving an addition problem with the two negative numbers.

+ and - together make a - therefore

-3+-2=-3-2=-5

Example 6: subtraction, with negative numbers

Calculate 5-(-3).

Here you will subtract -3 from 5.

Two - signs together make a + therefore

Example 7: multiplication, with negative numbers

Calculate 8\times(-2).

Here you will use multiplication.

8\times(-2)=-16.

Example 8: division, with negative numbers

Calculate \cfrac{-120}{-3}.

A fraction is the division of two quantities and so here you would use division. The numerator is known as the dividend and the denominator is known as the divisor. The result of division is called a quotient.

Teaching tips for arithmetic

• If a student is struggling with using algorithms with the given operation, they need more experience with concrete models.
• When teaching students to use the algorithm for division, or long division, provide graph paper for students to use to keep their work neat and legible.
• Be sure to practice a problem solving method when working with word problems. Students may be able to solve a given equation, but struggle when having to pull information out of and comprehend a word problem.
• The use of a number line can be very impactful when working with positive and negative numbers.

Easy mistakes to make

• Parentheses are not an arithmetic operation Operations allow us to perform calculations between two or more numbers. In the associative property, parentheses dictate the order in which this should be completed and so they are technically not an operation. However, parentheses are sometimes used in place of multiplication symbols, for example, 6(7-3).
• Multiplying by \bf{0} by any number equals \bf{0} It is important to remember that multiplying anything by 0 gives the answer 0.
• Multiplying, instead of dividing, when working with fractions Mistakes can easily be made when dividing fractions. When dividing a number by a fraction, a commonly seen error is that the value is multiplied by the fraction instead. For example, 12\div\frac{1}{2}=6 is incorrect. Instead, the correct answer is 12\div\frac{1}{2}=12\times{2}=24.
• Knowing the value of decimal places are important It’s important that students remember the concept of place value when solving with decimals. Knowing the value of the numbers you are performing an operation with is crucial.

Practice arithmetic questions

1. Calculate 8.4+10.7.

Stack the numbers, lining up the decimal points and place values.

Add from right to left, regrouping when necessary.

The answer is 19.1.

2. I bought an item for \$25.13. How much change did I get from \$30?

Stack the numbers, the larger number on top, lining up the decimal points and place values.

Subtract from right to left, regrouping when necessary.

The answer is 4.87.

3. Calculate the 7 th multiple of 9.

List the first multiple of 9 which is 1 \times 9=9.

List the second multiple of 9 which is 2 \times 9=18.

Continue this pattern until you have 7 multiples.

The answer is 63.

4. 120 high school students are divided into small research groups. If there are 20 groups, how many students are in each group?

You need to divide 120 by 20.

You can use mental math to find the solution to this division problem.

You can split the dividend, 120, into two parts that can be easily divided by 20.

Then using math facts, divide both parts by 20.

5. A New York hotel comprises 67 floors above ground and 4 floors below ground. A guest parks on floor -3, in the basement, and is staying on the 43 rd floor of the hotel. How many floors must he go up to get from his car to his hotel room?

You will subtract 43 and -3.

Two – signs together make a + therefore,

so 43- \, -3=43+3

The answer is 46 floors.

6. Anna buys a car for \$9,000. She pays a deposit of \$2,400 and pays the rest off in monthly installments of \$110 per month. How many months will Anna be paying for her car?

This is a two-step problem.

The first step requires subtraction to calculate the remaining amount to pay for the car.

The car was \$9,000 and Anna paid a deposit of \$2,400.

The second step will require division of the remaining amount, \$6,600 by 110, the payment Anna will make each month.

The answer is 60 months.

7. Calculate \cfrac{5}{6}+\cfrac{4}{7}.

First, you will need to find a common denominator between the two fractions. To do this, list the multiples of each number until you find one that both have in common.

You will also need to fix the numerators by multiplying them by the same factor you multiplied the denominator by.

Now that the denominators are the same, you can add the numerators together.

Arithmetic FAQs

Yes, arithmetic is a branch of math that refers to the basic counting of numbers and using operations, such as addition, subtraction, multiplication, and division. Algebra is a branch of math that deals with variables and numbers for solving problems.

A negative number is a number that is less than zero.

The next lessons are

• Properties of equality
• Addition and subtraction
• Multiplication and division
• Calculator skills
• Money word problems
• Skip counting
• Number sense
• Two step word problems

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8.2: Problem Solving with Arithmetic Sequences

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• Page ID 83159

• Jennifer Freidenreich
• Diablo Valley College

Arithmetic sequences, introduced in Section 8.1, have many applications in mathematics and everyday life. This section explores those applications.

Example 8.2.1

A water tank develops a leak. Each week, the tank loses \(5\) gallons of water due to the leak. Initially, the tank is full and contains \(1500\) gallons.

• How many gallons are in the tank \(20\) weeks later?
• How many weeks until the tank is half-full?
• How many weeks until the tank is empty?

This problem can be viewed as either a linear function or as an arithmetic sequence. The table of values give us a few clues towards a formula.

The problem allows us to begin the sequence at whatever \(n\)−value we wish. It’s most convenient to begin at \(n = 0\) and set \(a_0 = 1500\).

Therefore, \(a_n = −5n + 1500\)

Since the leak is first noticed in week one, \(20\) weeks after the initial week corresponds with \(n = 20\). Use the formula where \(\textcolor{red}{n = 20}\):

\(a_{20} = −5(\textcolor{red}{20}) + 1500 = −100 + 1500 = 1400\)

Therefore, \(20\) weeks later, the tank contains \(1400\) gallons of water.

• How many weeks until the tank is half-full? A half-full tank would be \(750\) gallons. We need to find \(n\) when \(\textcolor{red}{a_n = 750}\).

\(\begin{array} &750 &= −5n + 1500 &\text{Substitute \(a_n = 750\) into the general term.} \\ 750 − 1500 &= −5n + 1505 − 1500 &\text{Subtract \(1500\) from each side of the equation.} \\ −750 &= −5n &\text{Simplify each side of the equation.} \\ \dfrac{−750}{−5} &= \dfrac{−5n}{−5} &\text{Divide both sides by \(−5\).} \\ 150 &= n & \end{array}\)

Since \(n\) is the week-number, this answer tells us that on week \(150\), the tank is half full. However, most people would better understand the answer if stated in the following way, “The tank is half full after 150 weeks.” This answer sounds more natural and is preferred.

• How many weeks until the tank is empty? The tank is empty when \(a_n = 0\) gallons. Find \(n\) such that \(\textcolor{red}{a_n = 0}\).

\(\begin{array}& 0 &= −5n + 1500 &\text{Substitute \(a_n=0\) into the general term.} \\ 0 − 1500 &= −5n + 1500 − 1500 &\text{Subtract \(1500\) from each side of the equation.} \\ −1500 &= −5n &\text{Simplify.} \\ \dfrac{−1500}{−5} &= \dfrac{−5n}{−5} &\text{Divide both sides by \(−5\).} \\ 300 &= n & \end{array}\)

Since \(n\) is the week-number, this answer tells us that on week \(300\), the tank is empty. However, most people would better understand the answer if stated in the following way, “ The tank is empty after 300 weeks. ” This answer sounds more natural and is preferred.

Example 8.2.2

Three stages of a pattern are shown below, using matchsticks. Each stage requires a certain number of matchsticks. If we keep up the pattern…

• How many matchsticks are required to make the figure in stage \(34\)?
• What stage would require \(220\) matchsticks?

Let’s create a table of values. Let \(n =\) stage number, and let \(a_n =\) the number of matchsticks used in that stage. Then note the common difference.

Find the value \(a_0\):

\(\begin{array} &a_0 + 3 &= 4 \\ a_0 + 3 − 3 &= 4 − 3 \\ a_0 &= 1 \end{array}\)

The general term of the sequence is:

\(a_n = 3n + 1\)

• Compute \(a_{34}\) to find the number of matchsticks in stage \(34\):

\(a_{34} = 3(\textcolor{red}{34}) + 1 = 103\).

There are \(103\) matchsticks in stage \(34\).

• What stage would require \(220\) matchsticks? We are looking for the stage-number, given the number of matchsticks. Find \(n\) if \(a_n = 220\).

\(\begin{array} &220 &= 3n + 1 \\ 219 &= 3n \\ 73 &= n \end{array}\)

Answer Stage \(73\) would require \(220\) matchsticks.

Example 8.2.3

Cory buys \(5\) items at the grocery store with prices \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) which is an arithmetic sequence. The least expensive item is \($1.89\), while the total cost of the \(5\) items is \($12.95\). What is the cost of each item?

Put the \(5\) items in order of expense: least to most and left to right. Because it is an arithmetic sequence, each item is \(d\) more dollars than the previous item. Each item’s price can be written in terms of the price of the least expensive item, \(a_1\), and \(a_1 = $1.89\).

The diagram above gives \(5\) expressions for the costs of the \(5\) items in terms of \(a_1\) and the common difference is \(d\).

\(\begin{array} &a_1 + a_2 + a_3 + a_4 + a_5 &= 12.95 &\text{Total cost of \(5\) items is \($12.95\).} \\ a_1 + (a_1 + d) + (a_1 + 2d) + (a_1 + 3d) + (a_1 + 4d) &= 12.95 &\text{See diagram for substitutions.} \\ 5s_1 + 10d &= 12.95 &\text{Gather like terms.} \\ 5(1.89) + 10d &= 12.95 &a_1 = 1.89. \\ 9.45 + 10d &= 12.95 &\text{Simplify.} \\ 9.45 + 10d − 9.45 &= 12.95 − 9.45 &\text{Subtract \(9.45\) from each side of equation.} \\ 10d &= 3.50 &\text{Simplify. Then divide both sides by \(10\).} \\ d &= 0.35 &\text{The common difference is \($0.35\).} \end{array}\)

Now that we know the common difference, \(d = $0.35\), we can answer the question.

The price of each item is as follows: \($1.89, $2.24, $2.59, $2.94, $3.29\).

Try It! (Exercises)

1. ZKonnect cable company requires customers sign a \(2\)-year contract to use their services. The following describes the penalty for breaking contract: Your services are subject to a minimum term agreement of \(24\) months. If the contract is terminated before the end of the \(24\)-month contract, an early termination fee is assessed in the following manner: \($230\) termination fee is assessed if contract is terminated in the first \(30\) days of service. Thereafter, the termination fee decreases by \($10\) per month of contract.

• If Jack enters contract with ZKonnect on April 1 st of \(2021\), but terminates the service on January 10 th of \(2022\), what are Jack’s early termination fees?
• The general term \(a_n\) describes the termination fees for the stated contract. Describe the meaning of the variable \(n\) in the context of this problem. Find the general term \(a_n\).
• Is the early termination fee a finite sequence or an infinite sequence? Explain.
• Find the value of \(a_{13}\) and interpret its meaning in words.

2. A drug company has manufactured \(4\) million doses of a vaccine to date. They promise additional production at a rate of \(1.2\) million doses/month over the next year.

• How many doses of the vaccine, in total, will have been produced after a year?
• The general term \(a_n\) describes the total number of doses of the vaccine produced. Describe the meaning of the variable \(n\) in the context of this problem. Find the general term\(a_n\).
• Find the value of \(a_8\) and interpret its meaning in words.

3. The theater shown at right has \(22\) seats in the first row of the “A Center” section. Each row behind the first row gains two additional seats.

• Let \(a_n = 22 + 2n\), starting with \(n = 0\). Give the first \(10\) values of this sequence.
• Using \(a_n = 22 + 2n\), Find the value of \(a_{10}\) and interpret its meaning in words in the context of this problem. Careful! Does \(n=\) row number?
• How many seats, in total, are in “A Center” section if there are \(12\) rows in the section?

4) Logs are stacked in a pile with \(48\) logs on the bottom row and \(24\) on the top row. Each row decreases by three logs.

• The stack, as described, has how many rows of logs?
• Write the general term \(a_n\) to describe the number of logs in a row in two different ways. Each general term should produce the same sequence, regardless of its starting \(n\)-value.

i. Start with \(n = 0\).

ii. Start with \(n = 1\).

5) The radii of the target circle are an arithmetic sequence. If the area of the innermost circle is \(\pi \text{un}^2\) and the area of the entire target is \(49 \pi \text{un}^2\), what is the area of the blue ring? [The formula for area of a circle is \(A = \pi r^2\)].

6) Three stages of a pattern are shown below, using matchsticks. Each stage adds another triangle and requires a certain number of matchsticks. If we keep up the pattern…

• What stage would require \(325\) matchsticks?

7) Three stages of a pattern are shown below, using matchsticks. Each stage requires a certain number of matchsticks. If we keep up the pattern…

• How many matchsticks are required to make the figure in stage \(22\)?
• What stage would require \(424\) matchsticks?

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Arithmetic - Sample Questions

Accuplacer placement testing arithmetic - sample questions.

The Arithmetic test (22 questions) measures your skills in three primary categories:

• Operations with whole numbers and fractions. This includes addition, subtraction, multiplication, division and recognizing equivalent fractions and mixed numbers.
• Operations with decimals and percents. This category includes addition, subtraction, multiplication, and division as well as percent problems, decimal recognition, fraction and percent equivalences, and estimation problems.
• Applications and problem-solving. Questions include rate, percent, and measurement problems, geometry problems, and distribution of a quantity into its fractional parts.

Solve each problem and choose your answer from the alternatives given. You may use scratch paper to work problems, but no calculators are allowed on the Arithmetic test.

Sample Question 1

All of the following are ways to write 20 percent of N EXCEPT

Sample Question 2

Which of the following is closest to the square root of 10.5 ?

Sample Question 3

Three people who work full-time are to work together on a project, but their total time on the project is to be equivalent to that of only one person working full-time. If one of the people is budgeted for 1/2 of his time to the project and a second person for 1/3 of her time, what part of the third worker's time should be budgeted to this project?

Arithmetic - Sample Questions Answers

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120 Math Word Problems To Challenge Students Grades 1 to 8

Written by Marcus Guido

Hey teachers! 👋

Use Prodigy to spark a love for math in your students – including when solving word problems!

• Teaching Tools
• Subtraction
• Multiplication
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You sit at your desk, ready to put a math quiz, test or activity together. The questions flow onto the document until you hit a section for word problems.

A jolt of creativity would help. But it doesn’t come.

Whether you’re a 3rd grade teacher or an 8th grade teacher preparing students for high school, translating math concepts into real world examples can certainly be a challenge.

This resource is your jolt of creativity. It provides examples and templates of math word problems for 1st to 8th grade classes.

There are 120 examples in total.

The list of examples is supplemented by tips to create engaging and challenging math word problems.

120 Math word problems, categorized by skill

Addition word problems.

Best for: 1st grade, 2nd grade

1. Adding to 10: Ariel was playing basketball. 1 of her shots went in the hoop. 2 of her shots did not go in the hoop. How many shots were there in total?

2. Adding to 20: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store to get 3 more pieces of gum. How many pieces of gum does Adrianna have now?

3. Adding to 100: Adrianna has 10 pieces of gum to share with her friends. There wasn’t enough gum for all her friends, so she went to the store and got 70 pieces of strawberry gum and 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

4. Adding Slightly over 100: The restaurant has 175 normal chairs and 20 chairs for babies. How many chairs does the restaurant have in total?

5. Adding to 1,000: How many cookies did you sell if you sold 320 chocolate cookies and 270 vanilla cookies?

6. Adding to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In June, the hobby store sold 15,498 more trading cards than normal. In total, how many trading cards did the hobby store sell in June?

7. Adding 3 Numbers: Billy had 2 books at home. He went to the library to take out 2 more books. He then bought 1 book. How many books does Billy have now?

8. Adding 3 Numbers to and over 100: Ashley bought a big bag of candy. The bag had 102 blue candies, 100 red candies and 94 green candies. How many candies were there in total?

Subtraction word problems

Best for: 1st grade, second grade

9. Subtracting to 10: There were 3 pizzas in total at the pizza shop. A customer bought 1 pizza. How many pizzas are left?

10. Subtracting to 20: Your friend said she had 11 stickers. When you helped her clean her desk, she only had a total of 10 stickers. How many stickers are missing?

11. Subtracting to 100: Adrianna has 100 pieces of gum to share with her friends. When she went to the park, she shared 10 pieces of strawberry gum. When she left the park, Adrianna shared another 10 pieces of bubble gum. How many pieces of gum does Adrianna have now?

Practice math word problems with Prodigy Math

Join millions of teachers using Prodigy to make learning fun and differentiate instruction as they answer in-game questions, including math word problems from 1st to 8th grade!

12. Subtracting Slightly over 100: Your team scored a total of 123 points. 67 points were scored in the first half. How many were scored in the second half?

13. Subtracting to 1,000: Nathan has a big ant farm. He decided to sell some of his ants. He started with 965 ants. He sold 213. How many ants does he have now?

14. Subtracting to and over 10,000: The hobby store normally sells 10,576 trading cards per month. In July, the hobby store sold a total of 20,777 trading cards. How many more trading cards did the hobby store sell in July compared with a normal month?

15. Subtracting 3 Numbers: Charlene had a pack of 35 pencil crayons. She gave 6 to her friend Theresa. She gave 3 to her friend Mandy. How many pencil crayons does Charlene have left?

16. Subtracting 3 Numbers to and over 100: Ashley bought a big bag of candy to share with her friends. In total, there were 296 candies. She gave 105 candies to Marissa. She also gave 86 candies to Kayla. How many candies were left?

Multiplication word problems

Best for: 2nd grade, 3rd grade

17. Multiplying 1-Digit Integers: Adrianna needs to cut a pan of brownies into pieces. She cuts 6 even columns and 3 even rows into the pan. How many brownies does she have?

18. Multiplying 2-Digit Integers: A movie theatre has 25 rows of seats with 20 seats in each row. How many seats are there in total?

19. Multiplying Integers Ending with 0: A clothing company has 4 different kinds of sweatshirts. Each year, the company makes 60,000 of each kind of sweatshirt. How many sweatshirts does the company make each year?

20. Multiplying 3 Integers: A bricklayer stacks bricks in 2 rows, with 10 bricks in each row. On top of each row, there is a stack of 6 bricks. How many bricks are there in total?

21. Multiplying 4 Integers: Cayley earns $5 an hour by delivering newspapers. She delivers newspapers 3 days each week, for 4 hours at a time. After delivering newspapers for 8 weeks, how much money will Cayley earn?

Division word problems

Best for: 3rd grade, 4th grade, 5th grade

22. Dividing 1-Digit Integers: If you have 4 pieces of candy split evenly into 2 bags, how many pieces of candy are in each bag?

23. Dividing 2-Digit Integers: If you have 80 tickets for the fair and each ride costs 5 tickets, how many rides can you go on?

24. Dividing Numbers Ending with 0: The school has $20,000 to buy new computer equipment. If each piece of equipment costs $50, how many pieces can the school buy in total?

25. Dividing 3 Integers: Melissa buys 2 packs of tennis balls for $12 in total. All together, there are 6 tennis balls. How much does 1 pack of tennis balls cost? How much does 1 tennis ball cost?

26. Interpreting Remainders: An Italian restaurant receives a shipment of 86 veal cutlets. If it takes 3 cutlets to make a dish, how many cutlets will the restaurant have left over after making as many dishes as possible?

Mixed operations word problems

27. Mixing Addition and Subtraction: There are 235 books in a library. On Monday, 123 books are taken out. On Tuesday, 56 books are brought back. How many books are there now?

28. Mixing Multiplication and Division: There is a group of 10 people who are ordering pizza. If each person gets 2 slices and each pizza has 4 slices, how many pizzas should they order?

29. Mixing Multiplication, Addition and Subtraction: Lana has 2 bags with 2 marbles in each bag. Markus has 2 bags with 3 marbles in each bag. How many more marbles does Markus have?

30. Mixing Division, Addition and Subtraction: Lana has 3 bags with the same amount of marbles in them, totaling 12 marbles. Markus has 3 bags with the same amount of marbles in them, totaling 18 marbles. How many more marbles does Markus have in each bag?

Ordering and number sense word problems

31. Counting to Preview Multiplication: There are 2 chalkboards in your classroom. If each chalkboard needs 2 pieces of chalk, how many pieces do you need in total?

32. Counting to Preview Division: There are 3 chalkboards in your classroom. Each chalkboard has 2 pieces of chalk. This means there are 6 pieces of chalk in total. If you take 1 piece of chalk away from each chalkboard, how many will there be in total?

33. Composing Numbers: What number is 6 tens and 10 ones?

34. Guessing Numbers: I have a 7 in the tens place. I have an even number in the ones place. I am lower than 74. What number am I?

35. Finding the Order: In the hockey game, Mitchell scored more points than William but fewer points than Auston. Who scored the most points? Who scored the fewest points?

Fractions word problems

Best for: 3rd grade, 4th grade, 5th grade, 6th grade

36. Finding Fractions of a Group: Julia went to 10 houses on her street for Halloween. 5 of the houses gave her a chocolate bar. What fraction of houses on Julia’s street gave her a chocolate bar?

37. Finding Unit Fractions: Heather is painting a portrait of her best friend, Lisa. To make it easier, she divides the portrait into 6 equal parts. What fraction represents each part of the portrait?

38. Adding Fractions with Like Denominators: Noah walks ⅓ of a kilometre to school each day. He also walks ⅓ of a kilometre to get home after school. How many kilometres does he walk in total?

39. Subtracting Fractions with Like Denominators: Last week, Whitney counted the number of juice boxes she had for school lunches. She had ⅗ of a case. This week, it’s down to ⅕ of a case. How much of the case did Whitney drink?

40. Adding Whole Numbers and Fractions with Like Denominators: At lunchtime, an ice cream parlor served 6 ¼ scoops of chocolate ice cream, 5 ¾ scoops of vanilla and 2 ¾ scoops of strawberry. How many scoops of ice cream did the parlor serve in total?

41. Subtracting Whole Numbers and Fractions with Like Denominators: For a party, Jaime had 5 ⅓ bottles of cola for her friends to drink. She drank ⅓ of a bottle herself. Her friends drank 3 ⅓. How many bottles of cola does Jaime have left?

42. Adding Fractions with Unlike Denominators: Kevin completed ½ of an assignment at school. When he was home that evening, he completed ⅚ of another assignment. How many assignments did Kevin complete?

43. Subtracting Fractions with Unlike Denominators: Packing school lunches for her kids, Patty used ⅞ of a package of ham. She also used ½ of a package of turkey. How much more ham than turkey did Patty use?

44. Multiplying Fractions: During gym class on Wednesday, the students ran for ¼ of a kilometre. On Thursday, they ran ½ as many kilometres as on Wednesday. How many kilometres did the students run on Thursday? Write your answer as a fraction.

45. Dividing Fractions: A clothing manufacturer uses ⅕ of a bottle of colour dye to make one pair of pants. The manufacturer used ⅘ of a bottle yesterday. How many pairs of pants did the manufacturer make?

46. Multiplying Fractions with Whole Numbers: Mark drank ⅚ of a carton of milk this week. Frank drank 7 times more milk than Mark. How many cartons of milk did Frank drink? Write your answer as a fraction, or as a whole or mixed number.

Decimals word problems

Best for: 4th grade, 5th grade

47. Adding Decimals: You have 2.6 grams of yogurt in your bowl and you add another spoonful of 1.3 grams. How much yogurt do you have in total?

48. Subtracting Decimals: Gemma had 25.75 grams of frosting to make a cake. She decided to use only 15.5 grams of the frosting. How much frosting does Gemma have left?

49. Multiplying Decimals with Whole Numbers: Marshall walks a total of 0.9 kilometres to and from school each day. After 4 days, how many kilometres will he have walked?

50. Dividing Decimals by Whole Numbers: To make the Leaning Tower of Pisa from spaghetti, Mrs. Robinson bought 2.5 kilograms of spaghetti. Her students were able to make 10 leaning towers in total. How many kilograms of spaghetti does it take to make 1 leaning tower?

51. Mixing Addition and Subtraction of Decimals: Rocco has 1.5 litres of orange soda and 2.25 litres of grape soda in his fridge. Antonio has 1.15 litres of orange soda and 0.62 litres of grape soda. How much more soda does Rocco have than Angelo?

52. Mixing Multiplication and Division of Decimals: 4 days a week, Laura practices martial arts for 1.5 hours. Considering a week is 7 days, what is her average practice time per day each week?

Comparing and sequencing word problems

Best for: Kindergarten, 1st grade, 2nd grade

53. Comparing 1-Digit Integers: You have 3 apples and your friend has 5 apples. Who has more?

54. Comparing 2-Digit Integers: You have 50 candies and your friend has 75 candies. Who has more?

55. Comparing Different Variables: There are 5 basketballs on the playground. There are 7 footballs on the playground. Are there more basketballs or footballs?

56. Sequencing 1-Digit Integers: Erik has 0 stickers. Every day he gets 1 more sticker. How many days until he gets 3 stickers?

57. Skip-Counting by Odd Numbers: Natalie began at 5. She skip-counted by fives. Could she have said the number 20?

58. Skip-Counting by Even Numbers: Natasha began at 0. She skip-counted by eights. Could she have said the number 36?

59. Sequencing 2-Digit Numbers: Each month, Jeremy adds the same number of cards to his baseball card collection. In January, he had 36. 48 in February. 60 in March. How many baseball cards will Jeremy have in April?

Time word problems

66. Converting Hours into Minutes: Jeremy helped his mom for 1 hour. For how many minutes was he helping her?

69. Adding Time: If you wake up at 7:00 a.m. and it takes you 1 hour and 30 minutes to get ready and walk to school, at what time will you get to school?

70. Subtracting Time: If a train departs at 2:00 p.m. and arrives at 4:00 p.m., how long were passengers on the train for?

71. Finding Start and End Times: Rebecca left her dad’s store to go home at twenty to seven in the evening. Forty minutes later, she was home. What time was it when she arrived home?

Money word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade, 5th grade

60. Adding Money: Thomas and Matthew are saving up money to buy a video game together. Thomas has saved $30. Matthew has saved $35. How much money have they saved up together in total?

61. Subtracting Money: Thomas has $80 saved up. He uses his money to buy a video game. The video game costs $67. How much money does he have left?

62. Multiplying Money: Tim gets $5 for delivering the paper. How much money will he have after delivering the paper 3 times?

63. Dividing Money: Robert spent $184.59 to buy 3 hockey sticks. If each hockey stick was the same price, how much did 1 cost?

64. Adding Money with Decimals: You went to the store and bought gum for $1.25 and a sucker for $0.50. How much was your total?

65. Subtracting Money with Decimals: You went to the store with $5.50. You bought gum for $1.25, a chocolate bar for $1.15 and a sucker for $0.50. How much money do you have left?

67. Applying Proportional Relationships to Money: Jakob wants to invite 20 friends to his birthday, which will cost his parents $250. If he decides to invite 15 friends instead, how much money will it cost his parents? Assume the relationship is directly proportional.

68. Applying Percentages to Money: Retta put $100.00 in a bank account that gains 20% interest annually. How much interest will be accumulated in 1 year? And if she makes no withdrawals, how much money will be in the account after 1 year?

Physical measurement word problems

Best for: 1st grade, 2nd grade, 3rd grade, 4th grade

72. Comparing Measurements: Cassandra’s ruler is 22 centimetres long. April’s ruler is 30 centimetres long. How many centimetres longer is April’s ruler?

73. Contextualizing Measurements: Picture a school bus. Which unit of measurement would best describe the length of the bus? Centimetres, metres or kilometres?

74. Adding Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Last year, Micha’s dad used 100 litres of gas. This year, her dad used 90 litres of gas. How much gas did he use in total for the two years?

75. Subtracting Measurements: Micha’s dad wants to try to save money on gas, so he has been tracking how much he uses. Over the past two years, Micha’s dad used 200 litres of gas. This year, he used 100 litres of gas. How much gas did he use last year?

76. Multiplying Volume and Mass: Kiera wants to make sure she has strong bones, so she drinks 2 litres of milk every week. After 3 weeks, how many litres of milk will Kiera drink?

77. Dividing Volume and Mass: Lillian is doing some gardening, so she bought 1 kilogram of soil. She wants to spread the soil evenly between her 2 plants. How much will each plant get?

78. Converting Mass: Inger goes to the grocery store and buys 3 squashes that each weigh 500 grams. How many kilograms of squash did Inger buy?

79. Converting Volume: Shad has a lemonade stand and sold 20 cups of lemonade. Each cup was 500 millilitres. How many litres did Shad sell in total?

80. Converting Length: Stacy and Milda are comparing their heights. Stacy is 1.5 meters tall. Milda is 10 centimetres taller than Stacy. What is Milda’s height in centimetres?

81. Understanding Distance and Direction: A bus leaves the school to take students on a field trip. The bus travels 10 kilometres south, 10 kilometres west, another 5 kilometres south and 15 kilometres north. To return to the school, in which direction does the bus have to travel? How many kilometres must it travel in that direction?

Ratios and percentages word problems

Best for: 4th grade, 5th grade, 6th grade

82. Finding a Missing Number: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. Jenny has 28 trophies. How many does Meredith have?

83. Finding Missing Numbers: The ratio of Jenny’s trophies to Meredith’s trophies is 7:4. The difference between the numbers is 12. What are the numbers?

84. Comparing Ratios: The school’s junior band has 10 saxophone players and 20 trumpet players. The school’s senior band has 18 saxophone players and 29 trumpet players. Which band has the higher ratio of trumpet to saxophone players?

85. Determining Percentages: Mary surveyed students in her school to find out what their favourite sports were. Out of 1,200 students, 455 said hockey was their favourite sport. What percentage of students said hockey was their favourite sport?

86. Determining Percent of Change: A decade ago, Oakville’s population was 67,624 people. Now, it is 190% larger. What is Oakville’s current population?

87. Determining Percents of Numbers: At the ice skate rental stand, 60% of 120 skates are for boys. If the rest of the skates are for girls, how many are there?

88. Calculating Averages: For 4 weeks, William volunteered as a helper for swimming classes. The first week, he volunteered for 8 hours. He volunteered for 12 hours in the second week, and another 12 hours in the third week. The fourth week, he volunteered for 9 hours. For how many hours did he volunteer per week, on average?

Probability and data relationships word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade

89. Understanding the Premise of Probability: John wants to know his class’s favourite TV show, so he surveys all of the boys. Will the sample be representative or biased?

90. Understanding Tangible Probability: The faces on a fair number die are labelled 1, 2, 3, 4, 5 and 6. You roll the die 12 times. How many times should you expect to roll a 1?

91. Exploring Complementary Events: The numbers 1 to 50 are in a hat. If the probability of drawing an even number is 25/50, what is the probability of NOT drawing an even number? Express this probability as a fraction.

92. Exploring Experimental Probability: A pizza shop has recently sold 15 pizzas. 5 of those pizzas were pepperoni. Answering with a fraction, what is the experimental probability that he next pizza will be pepperoni?

93. Introducing Data Relationships: Maurita and Felice each take 4 tests. Here are the results of Maurita’s 4 tests: 4, 4, 4, 4. Here are the results for 3 of Felice’s 4 tests: 3, 3, 3. If Maurita’s mean for the 4 tests is 1 point higher than Felice’s, what’s the score of Felice’s 4th test?

94. Introducing Proportional Relationships: Store A is selling 7 pounds of bananas for $7.00. Store B is selling 3 pounds of bananas for $6.00. Which store has the better deal?

95. Writing Equations for Proportional Relationships: Lionel loves soccer, but has trouble motivating himself to practice. So, he incentivizes himself through video games. There is a proportional relationship between the amount of drills Lionel completes, in x , and for how many hours he plays video games, in y . When Lionel completes 10 drills, he plays video games for 30 minutes. Write the equation for the relationship between x and y .

Geometry word problems

Best for: 4th grade, 5th grade, 6th grade, 7th grade, 8th grade

96. Introducing Perimeter:  The theatre has 4 chairs in a row. There are 5 rows. Using rows as your unit of measurement, what is the perimeter?

97. Introducing Area: The theatre has 4 chairs in a row. There are 5 rows. How many chairs are there in total?

98. Introducing Volume: Aaron wants to know how much candy his container can hold. The container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. What is the container’s volume?

99. Understanding 2D Shapes: Kevin draws a shape with 4 equal sides. What shape did he draw?

100. Finding the Perimeter of 2D Shapes: Mitchell wrote his homework questions on a piece of square paper. Each side of the paper is 8 centimetres. What is the perimeter?

101. Determining the Area of 2D Shapes: A single trading card is 9 centimetres long by 6 centimetres wide. What is its area?

102. Understanding 3D Shapes: Martha draws a shape that has 6 square faces. What shape did she draw?

103. Determining the Surface Area of 3D Shapes: What is the surface area of a cube that has a width of 2cm, height of 2 cm and length of 2 cm?

104. Determining the Volume of 3D Shapes: Aaron’s candy container is 20 centimetres tall, 10 centimetres long and 10 centimetres wide. Bruce’s container is 25 centimetres tall, 9 centimetres long and 9 centimetres wide. Find the volume of each container. Based on volume, whose container can hold more candy?

105. Identifying Right-Angled Triangles: A triangle has the following side lengths: 3 cm, 4 cm and 5 cm. Is this triangle a right-angled triangle?

106. Identifying Equilateral Triangles: A triangle has the following side lengths: 4 cm, 4 cm and 4 cm. What kind of triangle is it?

107. Identifying Isosceles Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 5 cm. What kind of triangle is it?

108. Identifying Scalene Triangles: A triangle has the following side lengths: 4 cm, 5 cm and 6 cm. What kind of triangle is it?

109. Finding the Perimeter of Triangles: Luigi built a tent in the shape of an equilateral triangle. The perimeter is 21 metres. What is the length of each of the tent’s sides?

110. Determining the Area of Triangles: What is the area of a triangle with a base of 2 units and a height of 3 units?

111. Applying Pythagorean Theorem: A right triangle has one non-hypotenuse side length of 3 inches and the hypotenuse measures 5 inches. What is the length of the other non-hypotenuse side?

112. Finding a Circle’s Diameter: Jasmin bought a new round backpack. Its area is 370 square centimetres. What is the round backpack’s diameter?

113. Finding a Circle's Area: Captain America’s circular shield has a diameter of 76.2 centimetres. What is the area of his shield?

114. Finding a Circle’s Radius: Skylar lives on a farm, where his dad keeps a circular corn maze. The corn maze has a diameter of 2 kilometres. What is the maze’s radius?

Variables word problems

Best for: 6th grade, 7th grade, 8th grade

115. Identifying Independent and Dependent Variables: Victoria is baking muffins for her class. The number of muffins she makes is based on how many classmates she has. For this equation, m is the number of muffins and c is the number of classmates. Which variable is independent and which variable is dependent?

116. Writing Variable Expressions for Addition: Last soccer season, Trish scored g goals. Alexa scored 4 more goals than Trish. Write an expression that shows how many goals Alexa scored.

117. Writing Variable Expressions for Subtraction: Elizabeth eats a healthy, balanced breakfast b times a week. Madison sometimes skips breakfast. In total, Madison eats 3 fewer breakfasts a week than Elizabeth. Write an expression that shows how many times a week Madison eats breakfast.

118. Writing Variable Expressions for Multiplication: Last hockey season, Jack scored g goals. Patrik scored twice as many goals than Jack. Write an expression that shows how many goals Patrik scored.

119. Writing Variable Expressions for Division: Amanda has c chocolate bars. She wants to distribute the chocolate bars evenly among 3 friends. Write an expression that shows how many chocolate bars 1 of her friends will receive.

120. Solving Two-Variable Equations: This equation shows how the amount Lucas earns from his after-school job depends on how many hours he works: e = 12h . The variable h represents how many hours he works. The variable e represents how much money he earns. How much money will Lucas earn after working for 6 hours?

How to easily make your own math word problems & word problems worksheets

Armed with 120 examples to spark ideas, making your own math word problems can engage your students and ensure alignment with lessons. Do:

• Link to Student Interests:  By framing your word problems with student interests, you’ll likely grab attention. For example, if most of your class loves American football, a measurement problem could involve the throwing distance of a famous quarterback.
• Make Questions Topical:  Writing a word problem that reflects current events or issues can engage students by giving them a clear, tangible way to apply their knowledge.
• Include Student Names:  Naming a question’s characters after your students is an easy way make subject matter relatable, helping them work through the problem.
• Be Explicit:  Repeating keywords distills the question, helping students focus on the core problem.
• Test Reading Comprehension:  Flowery word choice and long sentences can hide a question’s key elements. Instead, use concise phrasing and grade-level vocabulary.
• Focus on Similar Interests:  Framing too many questions with related interests -- such as football and basketball -- can alienate or disengage some students.
• Feature Red Herrings:  Including unnecessary information introduces another problem-solving element, overwhelming many elementary students.

A key to differentiated instruction , word problems that students can relate to and contextualize will capture interest more than generic and abstract ones.

Final thoughts about math word problems

You’ll likely get the most out of this resource by using the problems as templates, slightly modifying them by applying the above tips. In doing so, they’ll be more relevant to -- and engaging for -- your students.

Regardless, having 120 curriculum-aligned math word problems at your fingertips should help you deliver skill-building challenges and thought-provoking assessments.

The result?

A greater understanding of how your students process content and demonstrate understanding, informing your ongoing teaching approach.

ASVAB Arithmetic Reasoning Practice Test

ASVAB Math Test Prep

Congratulations - you have completed .

You scored %%SCORE%% out of %%TOTAL%%.

Your performance has been rated as %%RATING%%

There are 5 blue marbles, 4 red marbles, and 3 yellow marbles in a box. If Jim randomly selects a marble from the box, what is the probability of selecting a red or yellow marble?

If kayla left a \$10.47 tip on a breakfast that cost \$87.25, what percentage was the tip, a phone company charges \$2 for the first five minutes of a phone call and 30 cents per minute thereafter. if malik makes a phone call that lasts 25 minutes, what will be the total cost of the phone call, if 10 inches on a map represents an actual distance of 100 feet, then what actual distance does 25 inches on the map represent, five years ago, amy was three times as old as mike. if mike is 10 years old now, how old is amy.

At a used book store, Valentina purchased three books for \$2.65 each. If she paid with a \$20 bill, how much change did she receive?

Mia earns \$8.10 per hour and worked 40 hours. charlotte earns \$10.80 per hour. how many hours would charlotte need to work to equal mia’s earnings over 40 hours, aisha wants to paint the walls of a room. she knows that each can of paint contains one gallon. a half gallon will completely cover a 55 square feet of wall. each of the four walls of the room is 10 feet high. two of the walls are 10 feet wide and two of the walls are 15 feet wide. how many 1-gallon buckets of paint does aisha need to buy in order to fully paint the room, there are 4 red marbles and 8 green marbles in a box. if emma randomly selects a marble from the box, what is the probability of her selecting a red marble.

Oscar purchased a new hat that was on sale for \$5.06. The original price was \$9.20. What percentage discount was the sale price?

There are two pizza ovens in a restaurant. oven #1 burns three times as many pizzas as oven #2. if the restaurant had a total of 12 burnt pizzas on saturday, how many pizzas did oven #2 burn, sofía is driving to texas. she travels at 70 kilometers per hour for 2 hours, and 63 kilometers per hour for 5 hours. over the 7 hour time period what was sofía’s average speed, stephen signed up to bring 5 gallons of lemonade to the company picnic. he has a 5-gallon bucket which contains 3.5 gallons of lemonade. how many pints of lemonade will he need to add in order to fill the bucket, if a car travels 360 kilometers in 5 hours, how many kilometers will it travel in 9 hours when driving at the same speed, maya purchased a boat for \$18,340. its value depreciated by 15% in the first year she owned it. what was her boat worth at the end of this first year, the radar system beeps once every second. how many times will it beep in 3 days.

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The resources on this page will hopefully help you teach AO2 and AO3 of the new GCSE specification - problem solving and reasoning.

This brief lesson is designed to lead students into thinking about how to solve mathematical problems. It features ideas of strategies to use, clear steps to follow and plenty of opportunities for discussion.

The PixiMaths problem solving booklets are aimed at "crossover" marks (questions that will be on both higher and foundation) so will be accessed by most students. The booklets are collated Edexcel exam questions; you may well recognise them from elsewhere. Each booklet has 70 marks worth of questions and will probably last two lessons, including time to go through answers with your students. There is one for each area of the new GCSE specification and they are designed to complement the PixiMaths year 11 SOL.

These problem solving starter packs are great to support students with problem solving skills. I've used them this year for two out of four lessons each week, then used Numeracy Ninjas as starters for the other two lessons.  When I first introduced the booklets, I encouraged my students to use scaffolds like those mentioned here , then gradually weaned them off the scaffolds. I give students some time to work independently, then time to discuss with their peers, then we go through it as a class. The levels correspond very roughly to the new GCSE grades.

Some of my favourite websites have plenty of other excellent resources to support you and your students in these assessment objectives.

@TessMaths has written some great stuff for BBC Bitesize.

There are some intersting though-provoking problems at Open Middle.

I'm sure you've seen it before, but if not, check it out now! Nrich is where it's at if your want to provide enrichment and problem solving in your lessons.

MathsBot  by @StudyMaths has everything, and if you scroll to the bottom of the homepage you'll find puzzles and problem solving too.

I may be a little biased because I love Edexcel, but these question packs are really useful.

The UKMT has a mentoring scheme that provides fantastic problem solving resources , all complete with answers.

I have only recently been shown Maths Problem Solving and it is awesome - there are links to problem solving resources for all areas of maths, as well as plenty of general problem solving too. Definitely worth exploring!

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How One Family Lost $900,000 in a Timeshare Scam

A mexican drug cartel is targeting seniors and their timeshares..

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A massive scam targeting older Americans who own timeshare properties has resulted in hundreds of millions of dollars sent to Mexico.

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