Multiplication and Division Equations with Exercise

Key Concepts

• Write and solve a multiplication equation.

• Write and solve for the dividend in a division equation.

• Write and solve for the divisor in a division equation.

Introduction

Solving multiplication or division equation: 

Inverse operations “undo” each other. Properties of equality say that you can multiply or divide both sides of an equation by the same number and the two sides of the equation remains equal. 

4.4.1 Write and solve a multiplication equation 

Example 1: 

Natalie picked the same number of tomatoes each day. In 4 days, she picked 52 tomatoes. How many tomatoes did Natalie pick each day? Let n represent the number of tomatoes Natalie picked on each day. 

Solution: 

One Way: 

You can use a balance to represent the equation. 

Another way: 

Draw a bar diagram to represent the situation. 

4.4.2 Write and solve for the dividend in a division equation 

Example 2: 

Michelle and her 4 sisters spent an equal amount of time cleaning their home. Their parents added their times. They found that each of the 5 girls spent 2 hours cleaning. Let c be the total number of hours the girls spent cleaning. Write and solve a division equation to find the total number of hours the girls spent cleaning. 

Solution: 

4.3.3 Write and solve for the divisor in a division equation 

Example 3: 

Alice is reading a 648-page book. She reads 18 pages each day. Write and solve a division equation to find the number of days, d, it will take Alice to finish her book. 

Solution: 

Draw a bar diagram to represent the situation. 

One way: 

Solve the division equation

6481864818

= d. 

Divide to solve for d. 

Another way: 

Solve the multiplication equation 18d = 648. 

18d1818d18

=

6481864818

d = 36 

Check: 

Exercise:

1. Name the inverse operation you will use to get the variable alone on one side of the equation. 5p = 50 5p ÷ 5 = 50 ÷ 5

2. Name the inverse operation you will use to get the variable alone on one side of the equation. n + 9 = 3 n+ 9 x9=3 x9

3. Fill in the blanks. n ÷ 16 = 4 n 4. 16 x 16 = 4 x

4. Fill in the blanks. 15 = r x3 15+ = r x 3 ÷

5. Explain how to get the variable alone in the following equation. 44 = 2k

6. Explain how to get the variable alone in the following equation. m ÷ 6 = 12

7. Six friends shared the cost of a boat rental equally. Each friend paid $14. How much did the boat rental cost?

8. A school group is planning a trip to Miami, Florida. There are 29 people going on the trip. They agreed to share the total cost of the trip equally. lets equal each person’s share of the cost. What is each person’s share of the cost?

9. Matthew typed 1,125 words in 15 minutes. Let w represent the number of words typed each minute. If Lob typed the same numberof words each minute, how many words did she type in 1 minute?

10. Gary has 3,330 toothpicks. He wants to use them all to make a floor mat with 18 equal rows. Use the bar diagram to write a division equation. Then solve the equation to find how many toothpicks Gary should use in each row.

What have we learned:

• Write and solve a multiplication equation by usinga bar diagram, a balance, or an equation.

• Write and solve a division equation by usinga bar diagram, a balance, or an equation and find the dividend or divisor.

Concept Map