What math symbols
give you clues about
the properties?
Parentheses, operation
symbols, and the
numbers 0 and 1
may indicate certain
properties.
How can you make
the addition easier?
Look for numbers having
decimal parts you can
add easily, such as 0.75
and 0.25.
Pr o p er t i es Properties of Real Numbers
Let a b e a n y r e a l n u m b e r.
Id e n tity Properties o f A d d itio n and M u ltip licatio n
T h e s u m o f a n y r e a l n u m b e r a n d 0 is t h e o r i g in a l n u m b e r. T h e p r o d u c t o f a n y r e a l
num ber and 1 is the original num ber.
Algebra Example
Addition a + 0 = a
Multiplication a • 1 = a5§ + 0 =
6 7 • 14
67Zero Property of M ultiplication
The product o f a and 0 is 0.Multiplication Property of -1
The product o f - 1 and a is -a.a • 0 = 0— 1 • a18 • 0 = 0-1 • 9 = -9Id en tifyin g Properties
What property is illustrated by each statement?
Q 4 2 • 0 = 0 Zero Property o f M ultiplication
0 (y + 2.5) + 28 = y + (2.5 + 28) Associative Property of Addition
0 lOx + 0 = lOx Identity Property of AdditionGo t I t? 1. W h a t p r o p e r t y is illu s t r a t e d b y e a c h s ta te m e n t?
a. 4x • 1 = 4x b. x + (V y + z) : + ( z + V y )Y o u c a n u s e p r o p e r t ie s t o h e lp y o u s o lv e s o m e p r o b le m s u s in g m e n t a l m a th.Using Properties for M ental Calculations
Movies A movie ticket costs $7.75. A drink costs $2.40. Popcorn costs $1.25. What is
the total cost for a ticket, a drink, and popcorn? Use mental math.
(7.75 + 2.40) + 1.25 = (2.40 + 7.75) + 1.25 Commutative Property of Addition
= 2.40 + (7.75 + 1.25) Associative Property of Addition
= 2 .4 0 + 9 Simplify inside parentheses.
= 11.40 Add.T h e t o t a l c o s t is $ 1 1 .4 0.Go t I t? 2. A c a n h o ld s 3 t e n n is b a lls. A b o x h o ld s 4 c a n s. A c a s e h o ld s 6 b o x e s. H o w
m a n y t e n n is b a lls a re i n 10 cases? U s e m e n t a l m a th.24 Ch ap t er 1 Fo u n d a t i o n s f o r A l g e b r a