This document provides examples for solving equations by getting the variable alone using multiplication or division. It explains that to get the variable alone, you can multiply or divide both sides of the equation by the same number. Several examples are worked through step-by-step showing multiplying or dividing both sides to isolate the variable, then solving for its value. The goal is to demonstrate how to use properties of equality to solve equations algebraically.

1. 5-12 Solving
Multiplication & Dividing
Equations
Math Notes
Algebra and Functions 1.1

2. Skills Needed...

3. Skills Needed...
Tell what you would do to get
the variable alone.

4. Skills Needed...
Tell what you would do to get
the variable alone.
x ÷ 20

5. Skills Needed...
Tell what you would do to get
the variable alone.
x ÷ 20
Multiply by 20

6. Properties of Equality

7. Properties of Equality
You can multiply the same number to
both sides of an equation.

8. Properties of Equality
You can multiply the same number to
both sides of an equation.
You can divide the same number from
both sides of an equation.

9. Example 1
2 x 4= 8

10. Example 1
2x4 =8

11. Example 1
2 x 4 ÷ 4 = 8÷ 4

12. Example 1
2 x 4 ÷ 4 = 8÷ 4
2 = 2

13. Example 2
30 ÷ 6 = 5

14. Example 2
30 ÷ 6 =5

15. Example 2
30 ÷ 6 x 6= 5 x 6

16. Example 2
30 ÷ 6 x 6= 5 x 6
30 = 30

17. Example 3
Solve p x 5 = 25

18. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
to get the variable alone?

19. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
Divide by 5
to get the variable alone?

20. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
Divide by 5
to get the variable alone?
STEP TWO: Use the Property
of Equality and divide by 5
on both sides.

21. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
Divide by 5
to get the variable alone?
STEP TWO: Use the Property
of Equality and divide by 5 p x 5 ÷ 5 = 25 ÷ 5
on both sides.

22. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
Divide by 5
to get the variable alone?
STEP TWO: Use the Property
of Equality and divide by 5 p x 5 ÷ 5 = 25 ÷ 5
on both sides.
STEP THREE: x 5 ÷ 5 cancel out.
What is 25 ÷ 5?

23. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
Divide by 5
to get the variable alone?
STEP TWO: Use the Property
of Equality and divide by 5 p x 5 ÷ 5 = 25 ÷ 5
on both sides.
STEP THREE: x 5 ÷ 5 cancel out.
What is 25 ÷ 5?

24. Example 3
Solve p x 5 = 25
STEP ONE: What can you do
Divide by 5
to get the variable alone?
STEP TWO: Use the Property
of Equality and divide by 5 p x 5 ÷ 5 = 25 ÷ 5
on both sides.
STEP THREE: x 5 ÷ 5 cancel out. p = 5
What is 25 ÷ 5?

25. Example 4
Solve n ÷ 4 = 7

26. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
to get the variable alone?

27. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
Multiply by 4
to get the variable alone?

28. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
Multiply by 4
to get the variable alone?
STEP TWO: Use the Property
of Equality and multiply by 4
on both sides.

29. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
Multiply by 4
to get the variable alone?
STEP TWO: Use the Property
of Equality and multiply by 4
on both sides.
n÷4x4=7x4

30. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
Multiply by 4
to get the variable alone?
STEP TWO: Use the Property
of Equality and multiply by 4
on both sides.
n÷4x4=7x4
STEP THREE: ÷ 4 x 4 cancel out.
What is 7 x 4?

31. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
Multiply by 4
to get the variable alone?
STEP TWO: Use the Property
of Equality and multiply by 4
on both sides.
n÷4x4=7x4
STEP THREE: ÷ 4 x 4 cancel out.
What is 7 x 4?

32. Example 4
Solve n ÷ 4 = 7
STEP ONE: What can you do
Multiply by 4
to get the variable alone?
STEP TWO: Use the Property
of Equality and multiply by 4
on both sides.
n÷4x4=7x4
STEP THREE: ÷ 4 x 4 cancel out. n = 28
What is 7 x 4?