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Objective

Solve equations by using the Division and Multiplication Properties of Equality

Review Vocabulary

Identity Property (X)

The product of a number and 1 is that same number

7 · 1 = 7

X · 1 = X

Example 1 Solve a Multiplication Equation

Example 2 Solve a Division Equation

Example 3 Use an Equation to Solve a Problem

Solve

Write the equation.

7z = -49

7z = -49

7 7

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Ask: What is being done to the variable?

The variable is being multiplied by 7

Do the inverse on both sides of the equal sign

Bring down 7z = - 49

Divide 7z by 7

Divide - 49 by 7

Combine like terms

Solve

Answer: z = -7

7z = -49

7 7

1

z

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Divide 7 by 7

Divide 49 by 7

Bring down z =

1z =1z = 7

Opposite signs in division makes a negative answer

1z = - 7Remember: The identity property of Multiplication states anything multiplied by 1 does not change

Multiply 1 z z = -7

Bring down = - 7

Answer: a = - 8

Solve

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Write the equation.

Solve

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Ask: What is being done to the variable?

The variable is being divided by 9

Do the inverse on both sides of the equal sign

Bring down

Multiply by 9

9

Bring down = - 6

= - 6

Multiply by 9

9

Solve

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9 = - 6 9

Combine like terms

Remember: If the same number is in the numerator as in the denominator they can be divided into each other to make 1

Divide 9 by 91

Bring down the c =

1c =

Multiply 6 9

1c = - 54

Opposite signs in division makes a negative answer

1c = 54

Answer: c = –54

Solve

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c

Multiply 1 c

c = - 54

1c = - 54

Bring down = - 54

Solve

Answer: x = - 50

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SURVEYING English mathematician Edmund Gunter lived around 1600. He invented the chain, which was used to measure land for maps and deeds. One chain equals 66 feet. If the south side of a property measures 330 feet, how many chains long is it?

Words

Variable

More Needed Information

One chain equals 66 feet.

Let the number of chains

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330 feet Measurement of property

SURVEYING English mathematician Edmund Gunter lived around 1600. He invented the chain, which was used to measure land for maps and deeds. One chain equals 66 feet. If the south side of a property measures 330 feet, how many chains long is it?

Words

Variable

More Needed Information

One chain equals 66 feet.

Let the number of chains

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Measurement of property is 330 feet

Write the equation.

c66c66c = 330

Solve the equation

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66c = 330Ask: What is being done to the variable?

The variable is being multiplied by 66

Do the inverse on both sides of the equal sign

Bring down 66c = 330

66c = 330

Divide 66c by 66

66

Divide 330 by 66

66

Answer: c = 5 chains

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66c = 33066 66

Combine like terms

Remember: If the same number is in the numerator as in the denominator they can be divided into each other to make 1

Divide 66 by 6611c =

Bring down the c =

Divide 330 by 66

1c = 5

Multiply 1 c

c c = 5

Bring down = 5

HORSES Most horses are measured in hands. One hand equals 4 inches. If a horse measures 60 inches, how many hands is it?

Answer: x = 15 hands

*

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Assignment

Lesson 1:9Solving Multiplication &

Division14 - 35 All

  Equations