NAME
DATE
PERIOD
Study Guide a n d Intervention
Properties
of N u m b e r s
identity and Equality Properties T h eidentity
a n d equaUty properties i nt h e chart
below can help y o u solve algebraic equations a n d evaluate m a t h e m a t i c a l expressions.
Additive Identity
For any number a , a + 0 = a .
Additive Inverse
For any number a, a + ( - a ) = 0.
Multiplicative Identity
For any number a, a • 1 = a.
IMultiplicative Property of 0
For any number a, a • 0 = 0.
Multiplicative inverse
For every number
Property
b
where a, b * 0, there is exactly one number •§- such that
a -
Reflexive Property
For any number a , a — a .
Symmetric Property
For any numbers a and b , if a = t>, then b = a .
Transitive Property
For any numbers a, b , and c, if a = b and b - c , then a = c.
Substitution Property
if a = b, then a may be replaced by b in any expression.
Evaluate 24 • 1 - 8 + 5(9 -r 3 - 3). Name the property used in each step.
2 4 • 1 - 8 + 5 ( 9 4- 3 - 3 ) = 2 4 • 1 - 8 + 5 ( 3 - 3 ) Substitution; 9 ^ - 3 = 3
Substitution; 3 - 3 = 0
= 2 4 • 1 - 8 + 5(0)
Multiplicative Identity; 24 • 1 = 24
= 2 4- 8 + 5(0)
Multiplicative Property of Zero; 5(0) = 0
= 2 4 - 8+ 0
Substitution; 24 - 8 = 16
= 16+ 0
Additive Identity; 16 + 0 = 16
= 16
Exercises
Evaluate each expression. Name the property used i n each step.
1.2
a
2.16 • 1 - 9 + 2(16 -f 3 - 5)
2-
4.18 • 1 - 3 • 2 + 2(6 + 3 - 2)
V
3.2(3 • 6 • 1 - 14) - 4 • A
Chapter 1
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Glencoe Algebra 1
NAME
DATE
PERIOD
Study Guide a n d Intervention
(continued)
Properties
of N u m b e r s
Commutative and Associative Properties
T h e C o m m u t a t i v e a n d Associative
Properties c a n be used t o simphfy expressions. T h e C o m m u t a t i v e Properties state t h a t t h e
order i n w h i c h y o u a d d o r m u l t i p l y n u m b e r s does n o t change t h e i r s u m o r product. T h e
Associative Properties state that t h e w a y y o u group three ormore numbers w h e n adding or
m u l t i p l 3 d n g does n o t change t h e i r s u m o r product.
Commutative Properties
For any numbers a and b , a + b = b + a and
Associative Properties
For any numbers a, to, and c, (a + fa) + c = a + (to + c ) and (ato)c = a(toc).
Evaluate 6 • 2 • 3 • 5
using properties of ntimbers. Name the
property used in each step.
6 ' 2 ' 3 ' 5 = 6-3*2*5
Commutative Property
• 5)
b - b • a.
Evaluate
8.2 + 2.5 + 2.5 + 1.8 using properties of
numbers. Name the property used in
each step.
8.2 + 2 . 5 + 2 . 5 + 1.8
=
(6 • 3)(2
=
18-10
Multiply.
=
8.2
=
180
Multiply
=
(8.2
Associative Property
+
1.8
+
+
1.8)
2.5
+
+
(2.5
2.5
Commutative Prop.
+
Associative Prop.
2.5)
= 10 + 5
= 15
T h e product is180.
Add.
Add.
T h e s u m is 15.
Exercises
Evaluate each expression using properties of numbers. Name the property used in
each step.
1.12 + 1 0 + 8 + 5
2.16 + 8 + 2 2 + 1 2
3.10 • 7 • 2 . 5
4. 4 • 8 • 5 • 3
5.12 + 2 0 + 1 0 + 5
6. 2 6 + 8 + 4 + 2 2
7.3| + 4 + 2 | - + 3
8. ^ • 1 2 • 4 • 2
4
9. 3 . 5 + 2 . 4 + 3 . 6 + 4 . 2
10. 4 1 + 5 +
I
13.|- 1 8 • 2 5
+ 3
'I
11. 0 . 5 • 2 . 8 - 4
12. 2 . 5 + 2 . 4 + 2 . 5 + 3 . 6
14. 3 2 • -i- • ^ • 1 0
15.1-7 1 6 - 1
5
16. 3 . 5 + 8 + 2 . 5 + 2
Ciiapter 1
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17.18 - 8 • i •
6
1
18.-| - 1 0 - 1 6 • -|
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DATE
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PERIOD
Properties o f Numbers
S c a n t h e t e x t i n t h e lesson. W r i t e t w o facts y o u learned
a b o u t p r o p e r t i e s o f n u m b e r s as y o u s c a n n e d t h e t e x t .
What You'U Learn
11
wil i o o ^
1.
2.
Active Vocabulary
Review Vocabulary D e f i n e variables i n y o u r o w n w o r d s .
(Lesson 1-1)
New Vocabulary F i l l i n e a c h b l a n k w i t h t h e c o r r e c t t e r m o r
phrase.
equivalent expressions
T w o n i u n b e r s w h o s e p r o d u c t i s 1 a r e c a l l e d multiplicative
inverses o r
reciprocals
Expressions that represent the same n u m b e r are
Additive Identity
T h e n u m b e r 1 is k n o w n as t h e
Olfiph
Multiplicative Identity
T h e n u m b e r 0 is k n o w n as t h e
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Vocabulary Link Identity i s a w o r d t h a t i s u s e d i n e v e r y d a y
E n g U s h . F i n d t h e d e f i n i t i o n of identity u s i n g a d i c t i o n a r y .
Explain how its English definition can help you understand
its m e a n i n g i n m a t h e m a t i c s , specifically w h e n r e f e r r i n g to
additive and multiplicative identities.
7
Glencoe Algebra 1
PERIOD .
DATE
NAME
(continued)
iVlaii» Idea
Properties of Equality
and Identity
Details
FUl in the blanks with the property used i n each step.
5 ( 9 + 3 ) - ( 9 - 8 ) - ^ + ( - 5 + 5)
t)U
= 5(12) • (1)
= 5(12). (1)
60
+0
-5+5=0
60
= 60 . ( l ) . - i - + 0
60
= 60
60
+ 0
inu^
g d d m
5 ( 1 2 ) = 6 0 ^(MbshhMm
60 • 1 = 6 0
pm^- •
^
= 1+ 0
= 1
Use Commutative and
Associate Properties
1 +0
Use the Associative Property to write two equivalent
expressions. Use the numbers 4, 6, and 9.
Use the numbers and a
set of parentheses t o
write an addition
expression.
= 19
= 19
s.
1^
I Helping
M M L I i i t d HYou
M t a H iRemember
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L o o k u p t h e m e a n i n g o f t h e w o r d commute i n
t h e d i c t i o n a r y . F i n d a n e v e r y d a y m e a n i n g t h a t is close t o t h e m a t h e m a t i c a l m e a n i n g
a n d explain h o w i t can help y o u r e m e m b e r t h e m a t h e m a t i c a l meaning.
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Chapter 1
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Algebra 1