MATH

1. PERCENTS

2. 2
PERCENTS
 Indicates number of hundredths in a
whole
 Decimal fraction can be expressed as a
percent by moving decimal point two
places to right and inserting percent
symbol
 Express 0.375 as a percent:
 Move decimal point two places to right
 Insert percent symbol
0.375 = 37.5% Ans

3. 3
FRACTIONS TO PERCENTS
 To express a common fraction as a
percent:
 Divide the numerator by the denominator to
get the decimal fraction
 Convert the answer to a percent by moving the
decimal point two places to the right

4. 4
FRACTIONS TO PERCENTS
EXAMPLE
 Express each of the following as
percents
5
4
Ans
%
80
8
.
0
0
.
4
5 
20
125 25
.
6
00
.
125
20 = 625% Ans

5. 5
PERCENTS TO FRACTIONS
 Decimal Fractions:
 To express percent as decimal fraction:
 Drop percent symbol
 Move decimal point two places to left
 Express 25.4% as a decimal
25.4% = .254 Ans

6. 6
PERCENTS TO FRACTIONS
 Common Fractions:
 To express percents as common fractions:
 First convert percent to decimal fraction
 Express 64.5% as a common fraction
Ans
200
129
1000
645
645
.
%
5
.
64 



7. 7
PERCENT TERMS DEFINED
 All simple percent problems have three
parts:
 Rate is percent (%)
 Base represents whole or a quantity equal
to 100%
 Word “of” generally relates to the base
 Part (Percentage in Book) is part or
quantity of percent of base
 Word “is” generally relates to the percentage

8. 8
PERCENT TERMS DEFINED
 Identify base, rate, and percentage
What percent of 64 is 8?
 Problem is asking for rate (percent)
 64 represents whole and is identified by word
“of,” so it is the base
 8 represents part and is identified by word “is,”
so it is the percentage

9. 9
FINDING THE PERCENTAGE
 Proportion formula for all three types of
percentage problems:
Where
 B is the base or the starting/original value
 P is the percentage or part of the base
 R is the rate or percent
100
R
B
P


10. 10
FINDING THE PERCENTAGE
 Find 7.5% of 120?
 Rate: 7.5%
 Base: 120
 Problem is asking for
percentage (part)
 Multiply 120 x 75
 Divide the answer by 100
100
R
B
P

100
75
120

P
P = 9 Ans
Calculate using cross-
products and division.

11. 11
FINDING THE RATE
 What percent of 76 is 49.4?
 Rate: Find the rate
 Base: 76
 Percentage (part): 49.4
 Multiply 49.4 x 100
 Divide the answer by 76
100
R
B
P

100
76
4
.
49 R
 R = 65% Ans
Calculate using cross-
products and division.

12. 12
FINDING THE BASE
 17.5 is 12.5% of what amount?
 Percentage: 17.5
 Rate: 12.5% (.125 as a decimal)
 Problem is asking for base 100
R
B
P

B = 140 Ans
Calculate using cross-
products and division.
100
5
.
12
5
.
17

B

13. 13
Application Problem Examples
 A tank has a capacity of 300 gallons. It is 35%
full. How many gallons are in the tank?
 Part ->?? Base-> 300 Rate-> 35%
 105 gallons
100
35
300

P

14. 14
Application Problem Examples
 A tank has a capacity of 300 gallons. It is 35%
full. How many are needed to fill it?
 We found it had a 105 gallons in it in the last
part. So one way is to figure that and subtract
from 300….195 gallons to fill
 Another way is to see that percentages always
add up to 100% so the tank is 35% full or
65% empty…so change the rate.
195
,
100
65
300

 P
P

15. 15
PRACTICE PROBLEMS
1. Express each of the following as a percent.
2. Express each of the following as a decimal
fraction.
a. 1.46% b. 100%
c. 0.05%
3. Express each of the following as a common
fraction or mixed number.
a. 14.4% b. 2.5%
c. 138%
8
5
c.
35
14
b.
3
.
1
a.

16. 16
PRACTICE PROBLEMS (Cont)
Solve:
What is 12% of 150?
What percent of 234 is 86?
14.5 is 45% of what number?
What is 8 ¾% of 640?
What percent of 50 is 75?

17. 17
PRACTICE PROBLEMS (Cont)
Solve:
What is 125% of 75?
200 is 37 ½% of what
number?
What percent of 1375 is 350?
135 is 150% of what number?

18. 18
Applications
5. A carpenter has 1350 nails. He uses 23%
on a job and then uses 34% of the
remaining nails at his second job. How
many nails are left?
6. A mixture requires 20% of compound A,
30% of compound B, and 50% of
compound C. If there is 250 pounds of
compound B, how much should there be
of compound A?

19. 19
Solutions
1. Percents
a. 130%
b. 40%
c. 62.5%
2. Decimals
a. .0146
b. 1
c. .0005
3. Fractions
a. A
b. B
c. C
4. Problems
a. 18
b. 36.75%
c. 32.22
d. 56
e. 150%
f. 93.75
g. 533.33
h. 25.45%
i. 90
5. 686 nails
6. 166.67 pounds
125
18
40
1
50
19
1