*This Math quiz is called 'Equations with Variables (Multiply and Divide)' and it has been written by teachers to help you if you are studying the subject at middle school. Playing educational quizzes is a fabulous way to learn if you are in the 6th, 7th or 8th grade - aged 11 to 14.*

* It costs only $12.50 per month to play this quiz and over 3,500 others that help you with your school work. You can subscribe on the page at Join Us*

Let’s look at the following equations.

X - 5 = 10

In order to solve an equation with a variable, we need to make the expressions have the same value. Here, clearly X cannot equal 10 because 10 - 5 would be “5”. So how do we make the “X” equal “10”?

In a variable equation we must either add or subtract the known number in the unknown expression. In the above equation the unknown expression is “X - 5”. As this shows the number “5” is being subtracted from “X” we must add 5 to 5 as follows:

X - 5 + 5

(NOTE: If 5 was being added in the first expression, then we would have to subtract 5 as follows: X + 5 – 5)

We must then do the equal math to the known express of “10” as follows:

10 + 5

The new equation will now look as follows:

X - 5 + 5 = 10 + 5

We now add 10 + 5 = 15 and that makes the value of “X” equal 15.

15 - 5 = 10 so X = 15

However, sometimes we are faced with a different variable such as 7X = 21. When we see this type of equation, we will need to divide the number in the unknown express with the number in the known expression and then multiply the number found in the unknown expression with the answer. For example:

7X = 21 becomes X = 21 ÷ 7

21 ÷ 7 = 3

7 x 3 = 21

X = 3

1.

18X = 504

18

28

38

48

2.

36X = 432

24

396

112

12

36X = 432 ÷ 36

432 ÷ 36 = 12

12 x 36 = 432

X = 12

432 ÷ 36 = 12

12 x 36 = 432

X = 12

3.

14X = 98

42

84

7

1372

14X = 98 ÷ 14

98 ÷ 14 = 7

7 x 14 = 98

X = 7

98 ÷ 14 = 7

7 x 14 = 98

X = 7

4.

10X = 100

100

10

1000

1

10X = 100 ÷ 10

100 ÷ 10 = 10

10 x 10 = 100

X = 10

100 ÷ 10 = 10

10 x 10 = 100

X = 10

5.

9X = 117

13

1053

23

43

9X = 117 ÷ 9

117 ÷ 9 = 13

13 x 9 = 117

X = 13

117 ÷ 9 = 13

13 x 9 = 117

X = 13

6.

25X = 400

16

26

6

36

25X = 400 ÷ 25

400 ÷ 25 = 16

16 x 25 = 400

X = 16

400 ÷ 25 = 16

16 x 25 = 400

X = 16

7.

8X = 40

6

320

32

5

8X = 40 ÷ 8

40 ÷ 8 = 5

5 x 8 = 40

X = 5

40 ÷ 8 = 5

5 x 8 = 40

X = 5

8.

2X = 366

83

93

133

183

2X = 366 ÷ 2

366 ÷ 2 = 183

183 x 2 = 366

X = 183

366 ÷ 2 = 183

183 x 2 = 366

X = 183

9.

123X = 1107

19

21

9

27

123X = 1107 ÷ 123

1107 ÷ 123 = 9

9 x 123 = 1107

X = 9

1107 ÷ 123 = 9

9 x 123 = 1107

X = 9

10.

22X = 594

572

27

52

157

22X = 594 ÷ 22

594 ÷ 22 = 27

27 x 22 = 594

X = 27

594 ÷ 22 = 27

27 x 22 = 594

X = 27

504 ÷ 18 = 28

28 x 18 = 504

X = 28