Download Properties of Real Numbers

Properties of
Real Numbers
1-2
Vocabulary
Review
1. Circle the pairs of numbers that are opposites.
7 and 17
24 and 4
5 and 25
1.2 and 2.1
4 and u 4 u
2. Write the opposite of each number.
u 23 u
1
217
1
2
!16
0
Vocabulary Builder
Real Numbers
real numbers (noun) reel NUM burz
1
, 8, 0,
3 6
1.55, and 4
Definition: The set of real numbers includes all rational and
irrational numbers.
Related Words: natural numbers, whole numbers, integers, rational numbers,
irrational numbers
Use Your Vocabulary
3. Circle the real numbers.
23
!5
!21
0
7
8
!21
0
7
8
4. Circle the real numbers that are integers.
23
!5
5. How does the set of real numbers differ from the set of integers?
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Chapter 1
6
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
5,
Problem 1 Classifying a Variable
Got It? Your school is sponsoring a charity race. If each participant made a
donation d of $15.50 to a local charity, which subset of real numbers best describes
the amount of money raised?
6. Circle the values below that could represent the number of participants making
a donation.
!5
3
8
0
2.7
10
150
7. Circle the set of numbers that best describes the numbers you chose in Exercise 6.
counting numbers
rational numbers
real numbers
whole numbers
Problem 2 Graphing Numbers on the Number Line
Got It? What is the graph of the numbers !3, 21.4, and 13 ?
8. Find the integers each number is between.
Use a calculator and round to one decimal place:
Because !3 <
, !3 is between 1 and 2.
Think of the fraction form: 21.4 < 21.4 <
so 21.4 is between
and
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Think: 13 is between
and
,
.
.
9. How can you estimate !3 without using a calculator?
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10. Graph the numbers !3, 21.4, and 13 on the number line.
3
2
1
0
1
2
3
Problem 3 Ordering Real Numbers
Got It? How do !26 and 6.25 compare? Use S or R.
11. Find a perfect square close to 26.
2
5
12. Find a square root of a perfect square close to 6.25.
"
5
7
Lesson 1-2
13. Use , or . twice to compare your answers to Exercises 11 and 12.
"
"
6.25
14. Now write . or , to compare !26 and 6.25.
!26
6.25
Key Concept Properties of Real Numbers
Let a, b, and c represent real numbers.
Property
Addition
Multiplication
Closure
a b is a real number.
ab is a real number.
Commutative
abba
ab ba
Associative
(a b) c a (b c)
(ab)c a(bc)
Identity
a 0 a, 0 a a
0 is the additive identity
a ∙ 1 1, 1 ∙ a a
1 is the multiplicative identity
Inverse
a (a) 0
1 1, a 0
a ∙
a
a(b c) ab bc
Distributive
Column A
Column B
2(3x 1 7) 5 (3x 1 7)(2)
Inverse Property of Addition
(x 1 y) 1 5 5 x 1 (y 1 5)
Commutative Property of Multiplication
x105x
Associative Property of Addition
x?15x
Distributive Property
8 1 (28) 5 0
Identity Property of Multiplication
5(2x 1 1) 5 5 ? 2x 1 5 ? 1
Identity Property of Addition
Problem 4 Identifying Properties of Real Numbers
Got It? Which property does the equation 3(g 1 h) 1 2g 5 (3g 1 3h) 1 2g
illustrate?
16. Circle the operations used in the equation.
division
addition
multiplication
subtraction
17. Circle the algebraic equation that models 3(g 1 h) 5 3g 1 3h.
hg 5 gh
h1g5g1h
a(g 1 h) 5 ag 1 ah
a 1 (g 2 h) 5 (g 2 h) 1 a
18. The equation 3(g 2 h) 1 2g 5 3g 2 3h 1 2g illustrates the 9 Property.
Chapter 1
8
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
15. Draw a line from the expression in Column A to the property that it illustrates
in Column B.
Lesson Check • Do you UNDERSTAND?
Reasoning There are grouping symbols in the equation (5 1 w) 1 8 5
(w 1 5) 1 8, but it does not illustrate the Associative Property of Addition. Explain.
19. Circle the equation below that illustrates the Associative Property of Addition.
a1b1c5b1a1c
a 1 (b 1 c) 5 ab 1 ac
(a 1 b) 1 c 5 a 1 (b 1 c)
20. The Associative Property of Addition is a rule about the order / grouping of the
terms of an addition statement.
21. Write the terms grouped on each side of the equation.
Left side:
and
Right side:
and
22. Now explain why (5 1 w) 1 8 5 (w 1 5) 1 8 does NOT illustrate the Associative
Property of Addition.
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23. Circle the property that the equation illustrates.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
Closure Property of Addition
Commutative Property of Addition
Inverse Property of Addition
Distributive Property
Math Success
Check off the vocabulary words that you understand.
additive inverse
multiplicative inverse
opposite
reciprocal
squares
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Lesson 1-2