Algebra 1 Common Core Student Edition, Grade 8-9

Pan
How do you choose
the conversion
factor?
Write a conversion factor
that has the desired units
in th e n u m e ra to r and
th e o rig in a l u nits in th e
denominator.

Plan

How can you

convert units?

Write the conversion

factor so th a t the

original units divide

out and leave only the

desired units.

G o t It? 1. If Store B lowers its price to $42 for 4 shirts, does th e solution to Problem 1

change? Explain.

To convert from one u n it to another, such as feet to inches, you m ultiply the original

unit by a conversion factor th a t p ro d u c es th e desired unit. A conversion factor is a ratio

of two equivalent m easures in different units. A conversion factor is always equal to 1,

such as See th e table on page 814 for som e co m m o n equivalent units of m easure.

Problem 2 Converting Units

What is the given amount converted to the given units?

C hoose a n d m ultiply by th e ap p ro p riate conversion factor. The ap p ro p riate factor will

allow you to divide out th e co m m o n units an d simplify.

□ 330 min; hours

330 m in lh

= 330jnki

60 m in

lh

Choose a

conversion factor.

Divide out

common units.

Simplify.

Q 15 kg; grams

1000 g

15 kg lk g

€

60mtrr

= 5.5 h

0 5 ft 3 in.; inches

5 ft 3 in. = 5 ft + 3 in.

_ 12 in. ,

= 5 if • 1 jy + 3 in.

= 60 in. + 3 in. = 63 in.

G o t It? 2. W hat is 1250 cm converted to m eters?

= 15J&T-

= 15,000 g

1000 g

1 -kT

In Problem 2, notice th a t th e u n its for each q uantity are in clu d ed in th e calculations

to help d eterm in e th e units for th e answ ers. This process is called unit analysis, or

dimensional analysis.

Converting Units Between Systems

Architecture The CN Tower in Toronto, Canada, is about 1815 ft tall. About how

many meters tall is the tower? Use the fact that l m » 3.28 ft.

M ultiply by th e ap p ro p riate conversion factor an d divide out co m m o n units.

1815 ft - 3^5 = lsistf- 3 ^ ~ 553 m

The CN Tower is a b o u t 553 m tall.

Check R ound 1815 to 1800 a n d 3.28 to 3. Then divide 1800 by 3. 1800 3 = 600, an d

600 is a b o u t 553. So, 553 m is a reasonable answer.

| Lesson 2- 6 Rat io s, Rat es, and Co nversio ns ~1 117

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