Page 51 - Algebra 1

L E8S S O N Using Unit Analysis to Convert Measures
Warm Up
1. Vocabulary The amount of space a solid figure occupies is called
(SB 26)
Simplify.
the (area, volume).
__ __
2. 7 ·36 (SB 3) 12 49
4._2 ·_15 ·_6 (SB 3) 5 16 7
3.8·15 (SB 3) 9 36
5._12 ·_1 ·_39 (SB 3) 13 4 48
New Concepts
Unit analysis is a process for converting measures into different units. A unit ratio, or conversion factor, compares 2 measures that name the same amount.
12 in. 1 m 3 ft ___
1 ft 100 cm 1 yd
Since the amounts used in a unit ratio are equal to each other, a unit ratio is always equal to 1. Since the product of 1 and a number is that number, a unit ratio multiplied by a measure will always name the same amount.
Converting Units of Length
A cheetah ran at a rate of 105,600 yards per hour. How fast did the cheetah run in miles per hour?
Example
1
Hint
A mile is equal to 1760 yards.
SOLUTION Find a unit ratio and multiply.
105,600 yd = ? mi __
1 hour 1 hour 105,600 yd ? mi 1_mi = 1,760 yd
1 mi 1760 yd
Identify known and missing information.
Write the conversion. Equate units.
Write a unit ratio.
Write the multiplication sentence.
Canceloutcommonfactors.
Multiply.
Write the ratio of miles per hour.
105,600 yd · __
1 mi 1 hr 1760 yd
_60 =105,600yd ·
1 hr
= 60 mi _
1 mi _
1760 yd 1
105,600 yd = 60 mi __
1 hr
Online Connection www.SaxonMathResources.com
1 hr 1 hr
The cheetah ran at a rate of 60 miles per hour.
36 Saxon Algebra 1