1. 3.2 Multiplication Property of Equality

2. Property of Equality
You can multiply or divide BOTH sides of an equation by any number and the equation will still hold true.

3. An easy example: (don’t copy)
Would you ever put deodorant under just one arm?
Would you ever put nail polish on just one hand?
Would you ever wear just one sock?
We all know that 3 = 3.
Does 3(4) = 3? NO!
But 3(4) = 3(4).
The equation is still true if we multiply both sides by 4.

4. To get the variable by itself, which number needs to be moved?
Solve. -5t = 60
To get the variable by itself, which number needs to be moved? -5
To move the -5, you have to do the opposite operation. What operation will we use?
division

5. Solve -5t = 60
-5 -5
t = -12
-5(-12) = 60
Draw “the river” to separate the equation into 2 sides
Divide both sides by -5
Simplify
Check your answer

6. 2 Examples:
2) -6x = 18
1) 4x = 24

7. Solve 15 = 6n 6 6 2.5 = n 15 = 6(2.5) Draw “the river”
6 6
2.5 = n
15 = 6(2.5)
Draw “the river”
Divide both sides by 6
Simplify
Check your answer

8. 4) Solve You don’t like fractions? Let’s get rid of them! 
“Clear the fraction”
by multiplying both sides of the equation by the denominator.

9. Solve 4 · · 4 x = -48 Draw “the river”
Clear the fraction – multiply both sides by 4
Simplify
Check your answer
4 · · 4
x = -48

10. What do we do with negative fractions?
Recall that
The two negatives will cancel each other out.
The two fives will cancel each other out.
Solve
Multiply both sides by -5.

11. Solve = 18 3 · = 18 · 3 2x = 54 2 2 x = 27 Draw “the river”
3 · = 18 · 3
2x = 54
x = 27
Draw “the river”
Clear the fraction – multiply both sides by 3
Simplify
Divide both sides by 2
Check your answer

12. Which step clears the fraction in
Multiply by 3
Multiply by 5
Multiply by -12
Multiply by -5
Answer Now

13. 7) Solve
b = -56
b = -14
b = 14
b = 56
Answer Now

14. Try these on your own...