3.2 Multiplication Property of Equality

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

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.

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

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

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

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

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.

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

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.

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

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

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

Try these on your own...