Lesson 3 3 Solving Equations using Multiplication and

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Lesson 3 -3 Solving Equations using Multiplication and Division

Lesson 3 -3 Solving Equations using Multiplication and Division

Objectives • Solve equations by using multiplication • Solve equations by using division

Objectives • Solve equations by using multiplication • Solve equations by using division

Vocabulary • Reciprocal – multiplicative inverses (numbers when multiplied together equal 1) examples: 2

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 Po. E Properties of Equality (Po. E) are based on the

Multiplication and Division Po. E Properties of Equality (Po. E) 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 Po. E – 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 Po. E – 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. Original equation Multiply each side by

Example 1 Solve . Then check your solution. Original equation Multiply each side by 12. Answer: and To check that 9 is the solution, substitute 9 for s in the original equation.

Example 2 Solve . Then check your solution. Original equation Rewrite each mixed number

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. (-27) 9 -------

Example 2, a longer way Solve . Then check your solution. (-27) 9 ------- k = ---8 5 Rewrite each mixed number as an improper fraction (5 8) (-27) 9 (5 8) ------- k = -------8 5 5 (-27) k = 9 8 k = ------5 (-27) Answer: or Multiply both sides by common factor of (5 8) Simplify Divide both sides by 5 (-27) Check this result.

Example 3 Solve 11 w = 143. Then check your solution. Original equation Divide

Example 3 Solve 11 w = 143. Then check your solution. Original equation Divide each side by 11. Answer: To check, substitute 13 for w. and

Example 4 Solve . Original equation Divide each side by – 8. Answer: and

Example 4 Solve . Original equation Divide each side by – 8. Answer: and

Example 5 Space Travel What would be the weight (198 lbs here on Earth)

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. 3 198 w Original equation

Example 5 cont Original equation Multiply each side by . and Answer: The weight

Example 5 cont Original equation Multiply each side by . and Answer: The weight of Neil Armstrong’s suit and lifesupport backpacks on Mars would be 66 pounds.

Summary & Homework • Summary: – You can multiply both sides of an 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