﻿ Solving Multiplication and Division Equations | Problems & Solutions

# Solving Multiplication and Division Equations

Solving Multiplication and Division Equations
• Page 1
1.
Which inequality is represented by the graph?

 a. 9 > 3$y$ b. 4$x$ < - 2 c. 5$x$ < 10 d. 2$x$ > 4

2.
Which of the following is a solution of the equation $x$ - 7 = - 12?
 a. - 5 b. 5 c. - 19 d. 19

3.
Which operation would you use to solve 3$x$ = $\frac{1}{2}$?
 a. divide by $\frac{1}{2}$ b. multiply by 2 c. divide by 3 d. multiply by 3

4.
One out of every five gallons of milk produced worldwide is consumed everyday in the United States. If about 7000000 gallons of milk is consumed a day at this rate, then how much milk is produced per day?
 a. 9000000 gallons b. 35000000 gallons c. 36000000 gallons d. 34000000 gallons

#### Solution:

Let y be the number of gallons of milk produced each day.

15 y = 7000000
[Original equation.]

5 x 15 y = 7000000 x 5
[Multiply by 5 on both sides.]

y = 35000000
[Simplify.]

About 35000000 gallons of milk is produced each day.

5.
Solve:
- 4$y$ = - 124
 a. 31 b. - 31 c. - 93 d. 62

#### Solution:

- 4y = - 124
[Original equation.]

- 4y- 4 = - 124- 4
[Divide each side by - 4.]

y = 31
[Simplify.]

6.
Solve for the variable in the equation.
2$a$ = - 6
 a. - 8 b. - 4 c. - 3 d. 3

#### Solution:

2a = - 6
[Original equation.]

(2a)2 = - 62
[Divide each side by 2.]

a = - 3
[Simplify.]

7.
Jim rented a beach cabin at $8 for each day of stay. He paid$64 towards rent. Solve the equation 8$D$ = 64 to find the number of days he stayed in the cabin.
 a. 7 b. 9 c. 8 d. 10

#### Solution:

8 x D = 64
[Original equation.]

8 x D8 = 648
[Divide by 8 on each side.]

D = 8
[Simplify.]

Jim stayed in the cabin for 8 days.

8.
About $\frac{2}{3}$ of the population of a country owns a car. What is the total population of the country, if there are about 200,000,000 people with cars?
 a. 400,000,000 b. 300,000,000 c. 600, 000,000 d. 200,000,000

#### Solution:

Let N be the total population of the country.

2 / 3 N = 200,000,000
[Write the data as an equation.]

(3) x 2 / 3 N = (3) x 200,000,000
[Multiply each side by 3.]

2N = 600,000,000
[Simplify.]

2N / 2 = 600,000,000 / 2
[Divide each side by 2.]

N = 300,000,000
[Simplify.]

The total population of the country is 300,000,000.

9.
Solve the equation = 6 to find the value of the variable $m$.
 a. - 24 b. - 29 c. - 27 d. - 25

#### Solution:

m- 4 = 6
[Original equation.]

(- 4) × m- 4 = (- 4) × 6
[Multiply each side by - 4.]

m = - 24
[Simplify.]

The value of the variable m in the equation is - 24.

10.
Danielle shopped for 4 hours and purchased 20 dresses. Find the average number of dresses she purchased per hour.
 a. 7 b. 6 c. 5 d. 4

#### Solution:

Let d be the average number of dresses Danielle purchased in one hour.

4d = 20
[Write the data as an equation.]

(4d)4 = 204
[Divide each side by 4.]

d = 5
[Simplify.]

The average number of dresses that Danielle purchased in one hour is 5.