Download Getting Ready Practice D Inverse Operations

Unit 3
Getting
Ready
Practice D
Inverse Operations
Inverse operations are operations that undo each other. Addition and
subtraction are inverse operations, and multiplication and division are inverse
operations. Inverse operations are used to write fact families, check answers,
and to solve equations.
EXAMPLE 1
Lisa begins with 9. She multiplies 9 by 3. She needs to use an inverse operation
on the result to end with 9. How can she do this?
Step 1:
Step 2:
9 × 3 = 27
27 ÷ 3 = 9
Multiply 9 × 3.
Use the inverse operation of multiplication, division, to undo
the multiplication.
Solution: Lisa can divide by 3 to undo 9 × 3.
You can think of inverse operations as opposites. For example, to undo a debt,
you pay money back. To undo a gain of yardage in football, you lose an equal
amount of yardage on the next play.
EXAMPLE 2
Nick has $25 more today than he did yesterday. How can Nick have
the same amount of money tomorrow as he did yesterday?
Step 1:
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Step 2:
m + 25
Write an algebraic expression to represent how much money
Nick has today compared to yesterday. Let m represent the
money Nick had yesterday.
Use the inverse operation of addition, subtraction, to
undo the gain.
m + 25 − 25 = m
Solution: Nick needs to spend $25 to have the same amount of money
tomorrow as he did yesterday.
You can use inverse operations to help you solve equations.
EXAMPLE 3
What is the value x in the equation x − 8 = 7?
Use the inverse operation of subtraction, addition, to find x.
Add 8 to both sides of the equation.
x−8=7
x−8+8=7+8
= 15
Solution: The value of x is 15.
Level 1, Unit 3 • Linear Patterns D-1
Unit 3
Getting
Ready
Practice D
Inverse Operations continued
Reciprocals are used when dividing by fractions. Two numbers are reciprocals if
their product is 1. For example __
​ 1 ​  and 2 are reciprocals because __
​ 1 ​  × __
​ 2 ​  = __
​ 2 ​  = 1.
2
2 1 2
A whole number has a unit fraction as its reciprocal. A unit fraction is a
fraction with a numerator of 1. Likewise, a unit fraction has a whole number as
its reciprocal.
EXAMPLE 4
What is the reciprocal of 6?
Step 1:
Write 6 as an improper fraction with a denominator of 1.
Step 2:
Switch the numerator and denominator.
6 = __
​ 6  ​
1
6
__
__
​ 1  ​
​    ​
1
6
Solution: The reciprocal of 6 is __
​ 1 ​ .
6
EXAMPLE 5
What is the reciprocal of __
​ 3 ​  ?
5
Switch the numerator and denominator.
__
​ 3 ​ 
5
__
​ 5  ​
3
Solution: The reciprocal of __
​ 3 ​  is __
​ 5 ​  .
5 3
1. subtracting 6
2. adding 12
3. multiplying by 3
4. dividing by 5
Write the reciprocal for each number.
1  ​
6. __
​ 5 ​  5. ​ __
3
8
8. Pick any number from 1 to 10. Multiply that number 6. Then add
4 to the product. Explain how you can use inverse operations in
two steps to get back to the original number. Give an example using
the number you chose.
D-2 Getting Ready Practice D Inverse Operations
7. __
​ 7 ​ 
4
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TRY THESE
Write how to undo each operation.