Algebra 1 Common Core Student Edition, Grade 8-9

G o t It? 5. a. A bicyclist rides 5 m i out a n d th e n rides back. His speed re tu rn in g is

re d u ced 20% b ecau se it is raining. Let r be his speed in m iles p e r h o u r

riding out. W hat is an expression th a t rep resen ts his total tim e in hours

riding o u t an d back?

b. Reasoning In Problem 5, su p p o se m rep resen ts th e n u m b e r of miles p er

gallon of gasoline th e truck gets w h en it holds no cargo. W hat expression

represents th e n u m b e r of m iles p er gallon of gasoline th e truck gets w hen

fully loaded? Explain.

Lesso n Ch eck

Do you k n o w HO W?

Add or subtract.

1 4 +^7

2.

x — 7

9

x — 7

5

2y + 4 2y + 4

3 — + —' 6 b2 8 b3

4. A ru n n e r practices ru n n in g 2 m i up a slope an d
   2 mi down. She ru n s dow n th e slope 50% faster
   th a n she ru n s u p it. Let r be th e ru n n e r's speed, in
   miles p er hour, w hen ru n n in g up the slope. W hat
   expression represents the tim e she sp en d s running?

_ r / 3 | MATHEMATICAL

D o y o u U N D E R S T A N D? PRACTICES

5. W riting Suppose your friend was absent today. How
   w ould you explain to your friend how to ad d and
   subtract rational expressions?


6. Compare and Contrast How is finding th e LCD of
   two rational expressions sim ilar to finding th e LCD of
   two num erical fractions? How is it different?


7. Reasoning Your friend says she can always find a
   common denominator for two rational expressions
   by finding th e p ro d u c t of th e denom inators.
   a. Is your friend correct? Explain.
   b. Will your friend’s m eth o d always give you the
   LCD? Explain.

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

Practice Add or subtract.

Q _ §__|_ _4_

■ 2m 2m

11 5c , c - 28

1 1 ■ 2c + 7 2c + 7

2y + 1 y + 2

9. 9

14.

y —i y - i

12.

15.

c — 5 c — 5

1 4

2 -b 2-b

3n + 2 _ n — 6

n + 4 n + 4

Find the LCD of each pair of expressions.

17.^1 ±^
2 ’ x 2

21.

18.

22.

b 2b

6’ 9

2. a — b

ab' b2c

MATHEMATICAL

PRACTICES

19.

23.

10.

13.

16.

^ See Problems 1 and 2.

3 b

1.3.

z ’ 7 z

3 m 3 n

m + n’ m - n

b-3 b-3

n |________ 2

n2 + 4rc + 4 n2 + 4n + 4

21 _______________ 3

2t2 — t — 3 2 t 2 — t — 3

See Problems 3 and 4.

20 .8 12

24.

5 b ' 7b3c

1 3

k' k2 - 2

I

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Lesson 11-4 Adding and Subtracting Rational Expressions

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