2-2 Solving Equations by Multiplying or Dividingglhardy.pbworks.com/w/file/fetch/60912919/2-2 Teacher.pdf · 2-2 Solving Equations by Multiplying or Dividing 1. Students will solve

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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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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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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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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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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


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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


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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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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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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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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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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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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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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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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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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.

1 4

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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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Lesson Quiz: Part 1 Solve each equation.

1.

2.

3. 8y = 4

4. 126 = -9q

5.

6.

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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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2-2 Solving Equations by Multiplying or Dividingglhardy.pbworks.com/w/file/fetch/60912919/2-2 Teacher.pdf · 2-2 Solving Equations by Multiplying or Dividing 1. Students will solve