Algebra 1 Common Core Student Edition, Grade 8-9

2-6 Rat ios, Rat es, and Conversions

Quick Review

A ratio betw een n u m b ers m easu red in different units

is called a rate. A conversion factor is a ratio of two

equivalent m easures in different units such as gg lh

an d is always equal to 1. To convert from one u n it to

another, m ultiply the original u n it by a conversion factor

th at has th e original units in th e d en o m in ato r an d the

desired units in th e num erator.

Example

A painting is 17.5 in. wide. W hat is its w idth in centim eters?

Recall th at 1 in. = 2.54 cm.

17.5irt: • = 44.45 cm

The p ainting is 44.45 cm wide.

Exercises

Convert the given amount to the given unit.

37. 6 | ft; in. 38. 4lb7oz;oz


38. 135 s; m in 40. 2.25 mi; yd


39. Production A b re ad slicer ru n s 20 h p er day for
    30 days an d slices 144,000 loaves of bread. How
    m any loaves p e r h o u r are sliced?


40. Pets A gerbil eats a b o u t \ oz of food p e r day. About
    how m any p o u n d s of food can a gerbil eat in a year?


41. Sports If a baseball travels at 90 m i/h , how m any
    seconds does it take to travel 60 ft?

2-7 and 2-8 So l v i n g Pr o p o r t i o n s a n d U si n g Si m i l a r Fi g u r e s

r

Quick Review

The cr oss p r o d u ct s of a p ro p o rtio n are equal.

If | = | , w here b + 0 an d d # 0, th e n ad = be.

If two figures are sim ilar, th e n corresponding angles

are congruent an d corresponding side lengths are in

proportion. You can use p roportions to find m issing side

lengths in sim ilar figures an d for indirect m easurem ent.

Example

A tree casts a shadow 10 m long. At the sam e time, a

signpost next to th e tree casts a shadow 4 m long. The

signpost is 2.5 m tall. How tall is th e tree?

x

10

2 A

' 4

4x = 10(2.5)

4x= 25

X = 6.25

W rite a p ro p o rtio n.

Cross Products Property

Simplify.

Divide each side by 4.

Exercises

Solve each proportion.

44.

46.

48.

3 _ 9

7 - x

6 _ a

15 4

b + 3 b-3

6

45 — = - 10 5

47 -3_ = ^ 9-7 t

49.2c - 3 7c + 4

50. M odels An airplane has a w ingspan of 25 ft and
    a length of 20 ft. You are designing a m odel of the
    airp lan e w ith a w ingspan of 15 in. W hat will the
    length of your m odel be?


51. Project ions You project a draw ing 7 in. w ide and
    4^ in. tall onto a wall. The p rojected im age is 27 in.
    tall. How w ide is th e projected image?

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