1. Solving Equations by Multiplying or Dividing
Objective: Solve equations using the multiplication and division properties of equality.

2. Minute Check
Solve each equation.
x – 3 = 5

3. Minute Check
Solve each equation.
x – 3 = 5 8

4. Minute Check
Solve each equation.
x – 3 = 5
y + 9 = 7

5. Minute Check
Solve each equation.
x – 3 = 5
y + 9 = 7 -2

6. Minute Check
Solve each equation.
x – 3 = 5
y + 9 = 7
13 = m – 6

7. Minute Check
Solve each equation.
x – 3 = 5
y + 9 = 7
13 = m – 6 19

8. Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6

9. Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6

10. Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6
f + 4 = -5

11. Minute Check Solve each equation. x – 3 = 5 y + 9 = 7 13 = m – 6
f + 4 =

12. Solving Equations by Multiplying or Dividing
Division Property of Equality
For any numbers a, b, and c, where c < > 0, if a = b, then a/c = b/c.

13. Solving Equations by Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.

14. Solving Equations by Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/8 = 96/8 Divide each side by 8.

15. Solving Equations by Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/8 = 96/8 Divide each side by 8.
y = 12

16. Solving Equations by Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/8 = 96/8 Divide each side by 8.
y = 12
Check: 8y = 96 Replace y with 12.

17. Solving Equations by Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/8 = 96/8 Divide each side by 8.
y = 12
Check: 8y = 96 Replace y with 12.
8(12) ? 96

18. Solving Equations by Multiplying or Dividing
Example
Solve 8y = 96. Check your solution.
8y/8 = 96/8 Divide each side by 8.
y = 12
Check: 8y = 96 Replace y with 12.
8(12) ? 96
96 = 96 The solution is 12.

19. Solving Equations by Multiplying or Dividing
Multiplication Property of Equality
For any numbers a, b, and c, if a = b, then ac = bc.

20. Solving Equations by Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.

21. Solving Equations by Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12 Multiply each side by –6

22. Solving Equations by Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12 Multiply each side by –6
y = -72

23. Solving Equations by Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12 Multiply each side by –6
y = -72
Check: y/-6 = 12 Replace y with -72

24. Solving Equations by Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12 Multiply each side by –6
y = -72
Check: y/-6 = 12 Replace y with -72
-72/-6 ? 12

25. Solving Equations by Multiplying or Dividing
Example 2
Solve y/-6 = 12. Check your solution.
-6 * y/-6 = -6 * 12 Multiply each side by –6
y = -72
Check: y/-6 = 12 Replace y with –72.
-72/-6 ? 12
12 = 12 The solution is –72.

26. Solving Equations by Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be?

27. Solving Equations by Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.

28. Solving Equations by Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
105 = 5*L Write an equation.

29. Solving Equations by Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
105 = 5*L Write an equation.
105/5 = 5*L/5 Divide each side by 5.

30. Solving Equations by Multiplying or Dividing
Application:
Tom has a piece of rope that is 105 feet long. He wants to cut the rope into 5 equal pieces. How long will each piece be?
Let L represent the length of each piece.
105 = 5*L Write an equation.
105/5 = 5*L/5 Divide each side by 5.
21 = L The solution is 21.