Lesson 3-3

Solving Equations using Multiplication and Division

Objectives

• Solve equations by using multiplication

• Solve equations by using division

Vocabulary

• Reciprocal – multiplicative inverses (numbers when multiplied together equal 1)

examples: 2 and ½ or 3 and ⅓

Dividing by a number or multiplying by 1/number are equivalent actions

Multiplication and Division PoEProperties of Equality (PoE) are based on the concept

that as long as you do the same thing to both sides of an equation, then you have not changed anything.

• Multiplication PoE– For any numbers a, b, and c, if a = b, then ac = bc

– You can multiply both sides of an equation by the same thing without changing the equation

• Division PoE– For any numbers a, b, and c with c ≠ 0, if a = b, then a/c = b/c

– You can divide both sides of an equation by the same thing without changing the equation

• Multiplication and division are reciprocal actions

Example 1

Solve . Then check your solution.

To check that 9 is the solution, substitute 9 for s in the original equation.

Original equation

Answer: and

Multiply each side by 12.

Example 2

Solve . Then check your solution.

Original equation

Rewrite each mixed number as in improper fraction.

Multiply each side by ,

the reciprocal of .

Answer: or Check this result.

Example 2, a longer way

Solve . Then check your solution.

Answer: or Check this result.

(58) (-27) 9 (58) Multiply both sides by-------------- k = --------------- common factor of (58) 8 5

5(-27) k = 98 Simplify

(-27) 9 Rewrite each mixed number------- k = ---- as an improper fraction 8 5

98k = ------------- Divide both sides by 5(-27) 5(-27)

Example 3

Solve 11w = 143 . Then check your solution.

Original equation

Answer: and

To check, substitute 13 for w.

Divide each side by 11.

Example 4

Solve .

Original equation

andAnswer:

Divide each side by –8.

Example 5

Space Travel What would be the weight (198 lbs here on Earth) of Neil Armstrong’s suit and life-support backpack on Mars if three times the Mars weight equals the Earth weight?

Words Three times the weight on Mars equals the weight on Earth.

Variables Let w = the weight on Mars.

Three times the weight on Mars equals the weight on Earth.

Original equation

3 w 198

Example 5 cont

Answer: The weight of Neil Armstrong’s suit and life-support backpacks on Mars would be 66 pounds.

and

Multiply each side by .

Original equation

Summary & Homework

• Summary:– You can multiply both sides of an equation by the

same thing without changing the equation– You can divide both sides of an equation by the

same thing without changing the equation

– Multiplication and division are reciprocal actions

• Homework: – pg 138; 14-40 even