2-6 Ratios and Proportions
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Transcript of 2-6 Ratios and Proportions
2-6 Ratios and Proportions
Algebra 1 Glencoe McGraw-Hill Linda Stamper
A ratio is a comparison of two quantities measured in the same unit.
1210
students girlstudents boy
You can write a ratio in different ways.65
The order of the numbers in a ratio is very important. The first number in a ratio always names the quantity mentioned first.
5 to 6 5 : 6 65
A ratio compares
two quantities
by division!
An equation that states that two ratios are equal is a proportion.
0dandb where dc
ba
Cross Product PropertyIf two ratios are equal then their cross products are
also equal.
84
21
8 8
Determine whether each pair of ratios forms a proportion. Write yes or no (must show support work).
4.17.0
8.04.0
56.0 56.0
yes
2824
86
168 192
Determine whether each pair of ratios forms a proportion. Write yes or no (must show support work).
225.1
6.025.0
50.0 75.0
no
Example 1
Example 2
no
Solve the proportion.245
y10Write the cross products.
2410Multiply.
y5240 Solve
y48
Check
245
y10
24510
240
5y
5 5 240Do the
arithmetic work off to the side or
make a separate
column for this work!
48
When a proportion involves a variable, solving for the variable is called solving the proportion.
Solve the proportion.245
y10Write the cross products.
Multiply.Solve
You can not cross cancel through an equal sign.
//
5
125y125 y560
y12
245
y10
24510
60240
Check
5 5 12
Example 3
64
9x
6x36x6
6 6 6x
49
Solve the proportion. If necessary, round to the nearest hundredth.
You can simplify a fraction before you use cross products.
64
9x
32
9x
x3 3 3
6x
18
Example 4
14.07.
y5.1
07.y14.5.1
y07.210. 07 . 07 .
y3
Do the arithmetic work off to the side or make a separate column for this
work! 0.217210.07.
Example 5
n6.2
42.3
6.24n2.3
4.10n2.3 .23 .23
25.3n
Example 6
41x
125
4512x1220
21 21 x3
2
1x12
Solve the proportion. Example
775
72r
5772r
3514r7 14 14
3r
Example 8
62x
73
2x763
14x718
7 7 x7
32
1212x128 21r7
1414x732
7 7
Mrs. Jones travels 140 miles in 2.5 hours. At this rate, how far will she travel in 4 hours?
Start with a word ratio. 5.2
140
m5.24140
m5.2560
hoursmiles
Mrs. Jones will travel 224 miles in 4 hours.
4
.52 .52 m224
m
Write a proportion for the problem. Then solve.
Mrs. Jones travels 140 miles in 2.5 hours. At this rate, how long will it take her to travel 224 miles?
Write word ratio. 5.2140
2245.2h140
560h140
hoursmiles
Mrs. Jones will travel 224 miles in 4 hours.
h
401 401 4h
224
Example 9 A mechanic charged $92 for 4 hours of work. At this rate, how much will be charged for 6 hours?Example 10 Mr. Green used 3 gallons of paint to cover 1,350 sq ft. At this rate, how much paint will be needed to cover 1,800 sq. ft.?Example 11 The ratio of football players to cheerleaders in the NFL is 48 to 6. If there are 1,440 football players, how many cheerleaders are there?Example 12 Sue, the speed reader, can read 12 pages in 4.5 minutes. At that rate, how many pages will she read in 60 minutes?
Write a proportion for each problem. Then solve.
Example 9 The mechanic will charge $138 for 6 hours of work.Example 10 Mr. Green will need 4 gallons of paint.Example 11 There are 180 cheerleaders.Example 12 Sue will read 160 pages.
Example 9 A mechanic charged $92 for 4 hours of work. At this rate, how much will be charged for 6 hours?
492
d4692
d4552
hoursdollars
The mechanic will charge $138 for 6 hours of work.
6d
4 4 d138
Do the arithmetic work off to the side
or make a separate
column for this work!
Write a word ratio.
Sentence.
Example 10 Mr. Green used 3 gallons of paint to cover 1,350 sq ft. At this rate, how much paint will be needed to cover 1,800 sq. ft.?Write word ratio. 350,1
3
g350,1800,13
g350,1400,5
.ft .sqgallons
Mr. Green will need 4 gallons of paint.
800,1g
,3501 ,3501 g4
Example 11 The ratio of football players to cheerleaders in the NFL is 48 to 6. If there are 1,440 football players, how many cheerleaders are there?Write word ratio. 6
48
440,16c48
640,8c48
rscheerleadeplayers
There are 180 cheerleaders.
c440,1
84 84 180c
Example 12 Sue, the speed reader, can read 12 pages in 4.5 minutes. At that rate, how many pages will she read in 60 minutes?
5.412
p5.46012
p5.4720
minutespages
Sue will read 160 pages.
60p
.54 .54 p160
2-A11 Pages 109-110 #9-33,41-48.