Solving Equations using Multiplication and Division

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Lesson 3-3

• Solving Equations using Multiplication and
  Division

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Transparency 3
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(No Transcript)
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Objectives

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

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Vocabulary

• Reciprocal multiplicative inverses (numbers
  when multiplied together equal 1)examples 2
  and ½ or 3 and ?Dividing by a
  number or multiplying by 1/number are equivalent
  actions

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Multiplication and Division PoE

• Properties 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

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Example 1
To check that 9 is the solution, substitute 9 for
s in the original equation.
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Example 2
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Example 2, a longer way
(-27) 9 Rewrite
each mixed number ------- k ----
as an improper fraction 8 5
(5?8) (-27) 9 (5?8)
Multiply both sides by -------------- k
--------------- common factor of (5?8)
8 5
5?(-27) k 9?8 Simplify
9?8 k -------------
Divide both sides by 5?(-27)
5?(-27)
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Example 3
Solve 11w 143 . Then check your solution.
To check, substitute 13 for w.
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Example 4
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Example 5
Space Travel What would be the weight (198 lbs
here on Earth) of Neil Armstrongs 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.
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Example 5 cont
Answer The weight of Neil Armstrongs suit and
life-support backpacks on Mars would be 66 pounds.
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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