Download Writing Percents as a Decimal or Fraction Convert from a percent to

6.1 – Ratio and Proportion
Ratio: is the quotient of two numbers or quantities.
The ratio of a number a to a number b
can be written several ways.
a
a :b
a to b
b
Write the ratio of 3 parts of oil to 7 parts of gasoline.
3
7
Write the ratio of 40 minutes to 1 hour.
40
4


60
6
2
3
6.1 – Ratio and Proportion
Write the ratio of 1.68 to 4.8.
1.68 100

100
4.8
168

480
7

20
10 meters
6 meters
8 meters
Using the dimensions of the triangle, write (1) the ratio of the
smallest side to the longest side and (2) the ratio of the longest side to
the perimeter.
(1)
6  3
10
5
(2)
10
10
5


24
10  8  6
12
6.1 – Ratio and Proportion
Proportion: is an equation setting two ratios equal.
a c

b d
The method of cross products is used to solve proportions.
a c

b d

ad  bc
Solve for x.
3 63

8
x

3 x  63  8

21
63 8
x
3 1
x  168
6.1 – Ratio and Proportion
Solve for x.
2x  1 x  3


7
5
52 x  1  7 x  3
10 x  5  7 x  21
 7x
 7x
3 x  5  21
5
5
3 x  26
3 x  26

3
3
26
x
3
6.1 – Ratio and Proportion
Mixing 5 ounces of isopropyl alcohol per 16 gallons of gasoline can
increase the amount of octane. How many gallons of gasoline can be
treated with an 8 ounce bottle of isopropyl alcohol?
Set up the proportion.
5 ounces
8 ounces

16 gallons
x gallons
5 x  16  8
5 x 128

5
5
x  25.6 gallons
6.1 – Ratio and Proportion
On construction scaled drawings, 1 inch corresponds to 4 feet in the
1
field. How long is a wall if its length on the plans is 4 inches?
4
1 17
4 
4
4
Set up the proportion.
17
inches
1 inch
 4
4 feet
x feet
17
x  4
4
x  17 feet
6.2 – Percents, Decimals and Fractions
Percent: A method to describe a portion. It is based on “per
hundred” and % is used to denote a percent.
Of 100 students in a club, 27 of them are freshmen. What percent of
the students are freshman?
27

100
27%
Thirty-one out of one hundred executives are in their forties. What
percent are in their forties?
31

100
31%
6.2 – Percents, Decimals and Fractions
Writing Percents as a Decimal or Fraction
Convert from a percent to a decimal: drop the % sign and multiply
by 0.01.
49%  49  0.01 
0.49
82% 
0.82
175%  175 0.01  1.75
1.5%  0.015
3.5%  3.5  0.01  0.035
600%  6
0.46%  0.46  0.01  0.0046
6.2 – Percents, Decimals and Fractions
Writing Percents as a Decimal or Fraction
Convert from a percent to a fraction: drop the % sign and multiply
by 1/100.
1
49%  49 
100

49
100
1
175%  175

100
175
100

7
4
1
3 .5
35
7

3.5%  3.5 


100
100
1000
200
0.46%  0.46 
1
0.46
46
23



100
100
10000
5000
6.2 – Percents, Decimals and Fractions
Writing Decimals or Fractions as Percents
Convert from a decimal or fraction to a percent: multiply by 100%
and simplify if necessary.
0.14
0.14 (100%)
14%
1.75
1.75(100%)
175%
0.057
0.057 (100%)
0.5
0.5 (100%)
5.7%
50%
6.2 – Percents, Decimals and Fractions
Writing Decimals or Fractions as Percents
Convert from a decimal or fraction to a percent: multiply by 100%
and simplify if necessary.
3
25
3
300
 100% 
%

25
25
9
40
90
900
9
%
% 
 100% 

4
40
40
1
5
2
11
1100
%
  100% 
2
2
12%
550%
22.5%
6.2 – Percents, Decimals and Fractions
Writing Decimals or Fractions as Percents
Write 3/17 as a percent. Round the answer to the nearest hundredth
percent.
3
17
3
300
 100% 
%

17
17
17.647%
17.65%
Provincetown’s budget for waste disposal increased by 1¾ times
from last year’s budget. What percent increase is this?
3 7
1 
4 4
700
7
%
  100% 
4
4
175%