Download Multiplying and Dividing Real Numbers

1-6
Multiplying and
Dividing Real Numbers
Vocabulary
Review
1. How is a product different from a quotient?
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2. Circle the product of 12 and 4. Underline the quotient of 12 and 4.
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Vocabulary Builder
Related Term: multiplicative inverse
Definition: Two numbers are reciprocals if their product is 1.
Main Idea: To write the reciprocal of a fraction, switch the numerator and
denominator of the fraction.
5 7
8
2
Examples: 45 and 4 , 28 and 27 , 5 and 15 , 112 and 3
Use Your Vocabulary
3. Draw a line from each expression in Column A to its reciprocal in Column B.
Column A
Column B
3
4
1
2
25
22
212
3
4
3
4
7
14
5
23
Chapter 1
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3
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reciprocals
b
a
and , where
a
b
a lj0 and b lj0
reciprocal (noun) rih SIP ruh kul
Key Concept Multiplying and Dividing Real Numbers
The product or quotient of two real numbers
with different signs is negative.
The product or quotient of two real numbers
with the same sign is positive.
The quotient of 0 and any nonzero real
number is 0.
The quotient of any real number and 0 is
undefined.
ART
4. Write negative, positive, undefined, or zero for each result.
28(22)
5(29)
FPO
049
940
5. Write 4 or (24) to make each equation true.
6?
5 24
6?
5 224
24 4
5 26
24 4
56
Problem 1 Multiplying Real Numbers
Got It? What is each product?
6(215)
7 3
210 Q 5 R
12(0.2)
(24) 2
7 3
6. In 6(215) and 210 Q 5 R , the signs of the numbers are the same / different .
7
3
So, the product of 6 and (215) and the product of 210 and 5 will be positive / negative .
7. Multiply.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
6(215) 5
7 3
210 Q 5 R 5
8. In 12(0.2) and (24)(24) , the signs of the numbers are the same / different .
9. Multiply.
12(0.2) 5
(24) 2 5 (24) (24) 5
Problem 2 Simplifying Square Root Expressions
Got It? What is the simplified form of !100?
10. Circle the equation that uses the positive square root of 100.
2 ? 50 5 100
4 ? 25 5 100
10 ? 10 5 100
11. Will the simplified form of !100 be positive or negative? Explain.
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12. The simplified form of !100 is
.
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Lesson 1-6
Problem 3 Dividing Real Numbers
Got It? You make five withdrawals of equal amounts from your bank account. The
total amount you withdraw is $360. What is the change in your account balance each
time you make a withdrawal?
13. Complete the model.
total amount
divided by
withdrawn
Relate
Write
number of
change in account
is
withdrawals
balance each time
â
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14. The change in the account balance per withdrawal is 2$
.
Property Inverse Property of Multiplication
For every nonzero real number a, there is a multiplicative inverse a1 such that a Q a1 R 5 1.
a
b
The reciprocal of a nonzero number of the form b is a . The product of a number and its
reciprocal is 1, so the reciprocal of a number is its multiplicative inverse.
Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction. In
a
c
a
d
Problem 4 Dividing Fractions
Got It? What is the value of 34 4 Q 252 R ?
Underline the correct word to complete each sentence.
15. The expression shows multiplication / division .
16. To divide fractions, multiply the first / second fraction by the reciprocal of the
first / second fraction.
17. Simplify the expression below.
3
5
3
4 4 Q 22 R 5 4 ? ° 2
52
¢
5
Multiply by the reciprocal of 22 .
Multiply.
20
5
Simplify.
Got It? Reasoning Is 34 4 Q 252 R equivalent to 2 Q 34 4 52 R ? Explain.
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18. Dividing a number by 2 is equivalent to multiplying the number by
Chapter 1
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.
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general, b 4 d 5 b ? c for b, c, and d 2 0.
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5
19. Simplify 2Q 4 4 2 R .
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5
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20. Is 4 4 Q2 2 R equivalent to 2Q 4 4 2 R ? Explain.
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Lesson Check • Do you UNDERSTAND?
Reasoning Use a number line to explain why 215 4 3 5 25.
21. In words, 215 4 3 means dividing 215 into
equal groups.
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22. To model 215 4 3 on a number line, start at 215. Then use arrows to show three
equal groups. The first equal group is shown.
Ľ15 Ľ14 Ľ13 Ľ12 Ľ11 Ľ10
Ľ9
Ľ8
Ľ7
Ľ6
Ľ5
Ľ4
Ľ3
Ľ2
Ľ1
0
23. What do the three arrows showing the equal groups represent?
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24. Divide: 215 4 3 5
.
Math Success
Check off the vocabulary words that you understand.
Inverse Property of Multiplication
multiplicative inverse
reciprocal
Rate how well you can multiply and divide real numbers.
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review
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get it!
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Lesson 1-6