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Solving Equations by Multiplying or Dividing
Warm Up Simplify each expression.
1. (–7)(2.8)
2. 0.96 ÷ 6
3. (–9)(–9)
4.
5.
6.
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Solving Equations by Multiplying or Dividing
1. Students will solve and check equations using multiplication
2. Students will solve and check equations using division
3. Students will solve and check equations with fractions by dividing or multiplying by the reciprocal
4. Students will identify important information from an application problem and use that information to set up and solve an equation.
Learning Goals
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Solving Equations by Multiplying or Dividing
Inverse Operations
Operation Inverse Operation
Multiplication Division
Division Multiplication
Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable.
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Solving Equations by Multiplying or Dividing
WORDS
Addition Property of Equality You can add the same number to both sides of an equation, and the statement will still be true.
NUMBERS
3 = 3 3 + 2 = 3 + 2 5 = 5
ALGEBRA a = b a + c = b + c
Properties of Equality
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Solving Equations by Multiplying or Dividing
WORDS
Subtraction Property of Equality You can subtract the same number from both sides of an equation, and the statement will still be true.
NUMBERS
7 = 7 7 – 5 = 7 – 5 2 = 2
ALGEBRA a = b a – c = b – c
Properties of Equality
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Solving Equations by Multiplying or Dividing
WORDS
Multiplication Property of Equality You can multiply both sides of an equation by the same number, and the statement will still be true.
NUMBERS
6 = 6 6(3) = 6(3) 18 = 18
ALGEBRA a = b ac = bc
Properties of Equality
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Solving Equations by Multiplying or Dividing
Properties of Equality Division Property of Equality You can divide both sides of an equation by the same nonzero number, and the statement will still be true.
WORDS
a = b (c ≠ 0)
8 = 8
2 = 2
ALGEBRA
NUMBERS 8 4
8 4
=
a c
a c =
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Solving Equations by Multiplying or Dividing
Solve the equation. Check your answers
Example 1A: Solving Equations by Using Multiplication
–8 = j 3 = 2.8 n
6 = 10 p
5
–13 = y 3
= 7 c 8
B. C.
D. E.
A.
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Solving Equations by Multiplying or Dividing
Solve the equation. Check your answers Example 1a: Solving Equations by Using Multiplication
b. c.
d. e.
a. −9 = j2
n4= 3.1 p
10= 5
10 = y−3
c6= 9
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Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer. Example 2A: Solving Equations by Using Division
9y = 108 –4.8 = –6v 16 = 4c
0.5y = –10 15k = 75
B. C.
D. E.
A.
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Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer. Example 2a: Solving Equations by Using Division
12y = 108 –6.4 = –4v 49 = 7c
0.4y = –8 25k = 125
b. c.
d. e.
a.
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Solving Equations by Multiplying or Dividing
Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.
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Solving Equations by Multiplying or Dividing
Solve the equation. Check your answers Example 3A: Solving Equations That Contain Fractions
B. C.
D. E.
A. 56w = −20 3
16=18z −
14=15b
4 j6=23
16w =102
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Solving Equations by Multiplying or Dividing
Solve the equation. Check your answers Example 3a: Solving Equations That Contain Fractions
b. c.
d. e.
a. 34w = −18 5
18=19z −
13=17b
5 j10
=12
13w = 54
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Solving Equations by Multiplying or Dividing
Example 4: Application Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year.
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Solving Equations by Multiplying or Dividing
The distance in miles from the airport that a plane should begin descending, divided by 3, equals the plane's height above the ground in thousands of feet. A plane began descending 45 miles from the airport. Use the equation to find how high the plane was flying when the descent began.
Example 4: Application
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Solving Equations by Multiplying or Dividing
Lesson Quiz: Part 1 Solve each equation.
1.
2.
3. 8y = 4
4. 126 = -9q
5.
6.
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Solving Equations by Multiplying or Dividing
Lesson Quiz: Part 2
7. A person's weight on Venus is about his or her weight on Earth. Write and solve an equation to find how much a person weighs on Earth if he or she weighs 108 pounds on Venus.
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