•m G o t It? Reasoning Is each statement in parts (a) and (b) true o r false?^ If it is^
false, give a counterexample. If true, use properties of real numbers to
show the expressions are equivalent.
a. F o r a ll r e a l n u m b e r s j a n d k, j • k = (k + 0 ) • j.
b. F o r a ll r e a l n u m b e r s m a n d n, m{n + 1) = mn + 1.
c. Is t h e s t a te m e n t i n p a r t (A) of Problem 4 false fo r every p a i r o f r e a l
num bers a and b? E xplain.Lesso n Ch eck
Do y o u k n o w H OW?
Name the property that each statement illustrates.
1. x+ 12 = 12 + x- 5 • (12 • x) = (5 • 12) • x
- Y o u b u y a s a n d w ic h f o r $ 2 .9 5 , a n a p p le f o r $ .4 5 , a n d a
bottle of juice for $1.05. W hat is the total cost? - Simplify
mat hematical
Do y o u UN DERSTAND? ISSfll PRACTICES- Vocabulary T e ll w h e t h e r t h e e x p re s s io n s i n e a c h p a ir
are equivalent.
a. 5x • 1 and 1 + 5x
b. 1 + ( 21 + 1 ) a n d 2 + 21 - J u s t i f y e a c h s t e p.
3 • (1 0 • 1 2) = 3 • (1 2 • 10)
= (3 • 12) • 10
= 36 • 10
= 360
^ Practice and Problem-Solving Exercises
MATHEMATICAL
PRACTICES,1 ^ 1 P ra c tic e Name the property that each statement illustrates.- 75 + 6 = 6 + 75 8. | • 1 = |
10.389 - 0 = 0 11. 2 7 • 7r = 7T • 27
Mental Math Simplify each expression.- 21 + 6 + 9 14. 10 • 2 • 19 • 5
1 6. 4 - 5 - 13 - 5 17.55.3 + 0.2 + 23.8 + 0.7 - Fishing Trip The sign at the rig h t shows the costs for a
d e e p -s e a f is h in g t r ip. H o w m u c h w i l l th e t o t a l c o s t b e f o r
1 adult, 2 c h ild re n , and 1 s e n io r c it iz e n t o g o o n a f is h in g
trip? Use m e n ta l m ath.
See Problem 1.- h + 0 = h
1 2. 9 • ( - 1 • x ) = 9 • (-jc)4* See Problem 2.- 0.1 + 3 .7 + 5.9
- 0.25 - 1 2 - 4
J26 Ch ap t er 1 Fo u n d at i o n s f o r A l g e b r a