1 - 1 V a r i a b l e s a n d E x p r e s s i o n s
qppQuick Review
A variable is a s y m b o l, u s u a lly a le tte r , t h a t r e p r e s e n ts
values o f a variable quantity. For exam ple, d o fte n
represents distance. A n algebraic expression is a
m a t h e m a t ic a l p h r a s e t h a t i n c lu d e s o n e o r m o r e v a r ia b le s.
A numerical expression is a m a t h e m a t ic a l p h r a s e
in v o lv in g n u m b e r s a n d o p e r a t io n s y m b o ls , b u t n o v a r ia b le s.
Example
What is an algebraic expression for the word phrase 3 l ess
than half a number xl
You can represent “h a lf a num ber x” as §. T h e n s u b t r a c t 3 to
get f-3.
Exercises
Write an algebraic expression for each word phrase.6. the product of a number w and 737
7. th e d if f e r e n c e o f a n u m b e r q a n d 8- the sum of a num ber x a n d 84
- 9 m o r e t h a n th e p r o d u c t o f 51 a n d a n u m b e r t
- 14 less than the q u o tie n t o f 63 and a num b e r h
11. a n u m b e r b le s s th e q u o t i e n t o f a n u m b e r k a n d 5
Write a word phrase for each algebraic expression.- 12 + fl 13. r — 31
- 19t 15. b - 3
- 7c- 3
- £-6
17. 2 + |
19. 21d+13
1 - 2 O r d e r o f O p e r a t i o n s a n d E v a l u a t i n g E x p r e s s i o n s
Quick Review
To evaluate an algebraic expression, first substitute a given
n u m b e r f o r e a c h v a r ia b le. T h e n s i m p li f y t h e n u m e r ic a l
expression using the order of operations.
- D o o p e r a t io n ( s ) in s id e g r o u p in g s y m b o ls.
- Simplify powers.
- M u l t i p l y a n d d iv id e f r o m le f t t o r ig h t.
- A d d a n d s u b t r a c t f r o m le f t t o r ig h t.
Example
A student studies with a tutor for 1 hour each week
and studies alone for h hours each week. What is an
expression for the total hours spent studying each week?
Evaluate the expression for h = 5.
The expression is h + 1. T o e v a lu a te th e e x p r e s s io n f o r
h - 5, substitute 5 for h: (5) + 1 = 6.
Exercises
Simplify each expression.- 92 21. 53
- 7' 24. (^24 - 6)2
22- ( I f
- (3 3 - 4) + 5 2
Evaluate each expression for c = 3 and d— 5. - d3 + 15 27. (2 + d)2 - 32
- cd2 + 4 29. (3c 2 - 3d)2 - 21
- The expression 6 s 2 represents the surface area o f a
c u b e w i t h e d g e s o f le n g t h s.
a. W hat is the cube's surface area when s = 6?
b. Reasoning E x p la in h o w a c u b e ’s s u rfa c e a re a
c h a n g e s i f y o u d iv id e s b y 2 in th e expression 6 s2. - A ra c e c a r tr a v e ls a t 2 0 5 m i / h. H o w f a r d o e s th e c a r
tra ve l in 3 h?
c
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