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.
boy students 10
A ratio

compares two
girl students 12
quantities by
5
division!

6
You can write a ratio in different ways.
5

5 to 6
5:6
6
The order of the numbers in a ratio is very important.
The first number in a ratio always names the quantity
mentioned first.
An equation that states that two ratios are equal is a
proportion.
88
a c
1 4

where b and d  0

b d
2 8
Cross Product Property
If two ratios are equal then their cross products are
also equal.
Determine whether each pair of ratios forms a
proportion. Write yes or no (must show support work).
0.56  0.56
0 .4 0 .7

0 .8 1 .4
yes
Determine whether each pair of ratios forms a
proportion. Write yes or no (must show support work).
Example 1
168  192
6 24

8 28
Example 2
no
no
0.50  0.75
0.25 1.25

0.6
2
When a proportion involves a variable, solving for the
variable is called solving the proportion.
Solve the proportion.
Write the cross products.
Multiply.
Solve
Do the
arithmetic work
off to the side
or make a
separate column
for this work!
10 5

y 24
10  24  y5
240  5y
5
5
48  y
Check
10 5

y 24
10


5
24
240  240
Solve the proportion.
Write the cross products.
Multiply.
Solve
You can not cross cancel
through an equal sign.
5
10
/ 5
y 24
/
12
5  12  y5
60  5y
5 5
12  y
Check
10 5

y 24
10 5

24
240  60
Solve the proportion. If necessary, round to the nearest
hundredth.
Example 4
Example 3
Example 5
x 4

9 6
x6  9  4
6x  36
6 6
x6
1.5 .07

y
.14
1.5.14   y.07
.210  .07 y
.07 .07
3y
3 . 2 2 .6

4
n
3.2n  42.6
3.2n  10.4
3.2 3.2
n  3.25
x 4
You can simplify a fraction

Do
9 the
6 arithmetic
before you use cross products.
work
off
to
the
x 2
 or make a
side
9
3
separate column
 18this work!
3xfor
3.07 .3210  7 21.0
x6
Solve the proportion.
Example 6
5 x 1

12
4
54   12x  1
20  12x  12
 12
 12
8  12x
12 12
2
x
3
Example 7
Example 8
r2 5

7
7
r  27  75
3 x 2

7
6
36  7x  2
7r  14  35
 14  14
7r  21
7
7
r3
18  7 x  14
 14
 14
32  7x
7
7
32
x
7
Write a proportion for the problem. Then solve.
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.
miles
hours
140 m

4
2 .5
1404   2.5m
560  2.5m
2.5 2.5
224  m
Mrs. Jones will travel 224 miles in 4 hours.
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.
miles
hours
140 224

2 .5
h
140h  2.5224
140h  560
140 140
h4
Mrs. Jones will travel 224 miles in 4 hours.
Write a proportion for each problem. Then solve.
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?
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?
dollars 92 d

Write a word ratio.
hours 4 6
926  4d
Sentence.
Do the arithmetic
work off to the
side or make a
separate column
for this work!
552  4d
4
4
138  d
The mechanic will charge
$138 for 6 hours of work.
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.?
g
gallons 3

Write word ratio.
sq. ft. 1,350 1,800
31,800  1,350g
5,400  1,350g
1,350 1,350
4g
Mr. Green will need 4 gallons of paint.
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?
players
48 1,440
Write word ratio.

6
c
cheerleaders
48c  61,440
48c  8,640
48
48
c  180
There are 180 cheerleaders.
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?
p
pages 12

minutes 4.5 60
1260  4.5p
720  4.5p
4.5 4.5
160  p
Sue will read 160 pages.
2-A11 Pages 109-110 #9-33,41-48.