The document explains percentages and how to calculate them. A percentage is defined as the number of parts out of 100. Common percentages are written as percentages (e.g. 50%) or decimals (e.g. 0.5). To calculate a percentage of a total amount, the percentage is converted to a fraction out of 100 and then multiplied by the total. This process is demonstrated through an example of calculating 45% of 60 pieces of candy.

1. Percentages

2. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .#
100

3. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100

4. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100
It’s useful think of % as
the ratio of pennies to 1$,
e.g. 1¢ is 1% of $1 (100 ¢).

5. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100
5% = 5 out of 100
5 percent = 5/100 = 1/20

6. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100
5% = 5 out of 100
5 percent = 5/100 = 1/20
10% = 10 out of 100
10 percent = 10/100 = 1/10

7. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100
5% = 5 out of 100
5 percent = 5/100 = 1/20
10% = 10 out of 100
10 percent = 10/100 = 1/10
25% = 25 out of 100
25 percent = 25/100 = 1/4

8. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100
5% = 5 out of 100
5 percent = 5/100 = 1/20
50% = 50 out of 100
= 50 percent = 50/100 = 1/2
10% = 10 out of 100
10 percent = 10/100 = 1/10
25% = 25 out of 100
25 percent = 25/100 = 1/4

9. Percentages
A percentage specified “how many out of per 100” and it’s written as #% or .
1% = 1 out of 100
1 percent = 1/100
#
100
5% = 5 out of 100
5 percent = 5/100 = 1/20
50% = 50 out of 100
= 50 percent = 50/100 = 1/2
10% = 10 out of 100
10 percent = 10/100 = 1/10
25% = 25 out of 100
25 percent = 25/100 = 1/4
100% = 100 out of 100
100 percent = 100/100 = 1.

10. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator.
Percentages

11. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator.
3
4 Divide $100 into
4 equal parts.
Percentages

12. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator.
3
4 Divide $100 into
4 equal parts.
100 ÷ 4 = 25 so each part is 25,
Percentages

13. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
hence 3 parts is 3 x $25 = $75.
Percentages

14. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75.
hence 3 parts is 3 x $25 = $75.
Percentages

15. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75.
hence 3 parts is 3 x $25 = $75.
Percentages

16. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols, 3
4
* 100
hence 3 parts is 3 x $25 = $75.
Percentages

17. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols, 3
4
* 100
25
hence 3 parts is 3 x $25 = $75.
Percentages

18. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols, 3
4
* 100 = 75.
25
hence 3 parts is 3 x $25 = $75.
Percentages

19. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
hence 3 parts is 3 x $25 = $75.
Percentages

20. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
hence 3 parts is 3 x $25 = $75.
Percentages
Example B. 45% of 60 pieces of candy are chocolates, how many is that?

21. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
45
10045% is
hence 3 parts is 3 x $25 = $75.
Percentages
Example B. 45% of 60 pieces of candy are chocolates, how many is that?

22. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
45
10045% is = 9
20
hence 3 parts is 3 x $25 = $75.
Percentages
÷5
÷5
Example B. 45% of 60 pieces of candy are chocolates, how many is that?

23. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
Example B. 45% of 60 pieces of candy are chocolates, how many is that?
45
10045% is = 9
20 so “45% of 60” is 9
20
* 60
hence 3 parts is 3 x $25 = $75.
Percentages
÷5
÷5

24. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
45
100
3
45% is = 9
20 so “45% of 60” is 9
20
* 60
hence 3 parts is 3 x $25 = $75.
Percentages
÷5
÷5
Example B. 45% of 60 pieces of candy are chocolates, how many is that?
divide 60 pieces into 20 groups
so each group consists of 3 pieces

25. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
divide 60 pieces into 20 groups
so each group consists of 3 pieces
and 9 groups make 27 pieces
45
100
3
45% is = 9
20 so “45% of 60” is 9
20
* 60 = 27
hence 3 parts is 3 x $25 = $75.
Percentages
÷5
÷5
Example B. 45% of 60 pieces of candy are chocolates, how many is that?

26. Example A. What is ¾ of $100?
The expression “a fractional of the total..” means to divide the total into equal
parts indicated by the denominator, then retrieve the number of parts indicated
by the numerator. We record this process with a division then a multiplication.
3
4 Divide $100 into
4 equal parts.
Take 3 parts.
100 ÷ 4 = 25 so each part is 25,
So ¾ of $100 is $75. In symbols,
The same steps of calculation apply for calculating “the #% of a total” and
in such a problem, simplify the percent to a reduced fraction first.
3
4
* 100 = 75.
25
So 27 pieces are chocolates.
45
100
3
45% is = 9
20 so “45% of 60” is 9
20
* 60 = 27
hence 3 parts is 3 x $25 = $75.
Percentages
÷5
÷5
Example B. 45% of 60 pieces of candy are chocolates, how many is that?
divide 60 pieces into 20 groups
so each group consists of 3 pieces
and 9 groups make 27 pieces

27. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
Percentages

28. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
Percentages

29. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
5
1005% =
Percentages
= 1
20

30. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.

31. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.

32. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.
25
10025% = = 1
4
: one quarter is 1/4 of a dollar and 4 quarters is $1.

33. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.
25
10025% = = 1
4
: one quarter is 1/4 of a dollar and 4 quarters is $1.
50
10050% = = 1
2
: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,

34. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.
25
10025% = = 1
4
: one quarter is 1/4 of a dollar and 4 quarters is $1.
50
10050% = = 1
2
: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,
100
100
and 100% = = 1, 200
100
200% = = 2, etc..

35. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
It’s useful to think of percentages of multiples of 5 as counting nickels where
one nickel is $1/20.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.
25
10025% = = 1
4
: one quarter is 1/4 of a dollar and 4 quarters is $1.
50
10050% = = 1
2
: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,
100
100
and 100% = = 1, 200
100
200% = = 2, etc..

36. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
It’s useful to think of percentages of multiples of 5 as counting nickels where
one nickel is $1/20. For example, 35% = 7/20 because there are 7 nickels in
35 cents, or that 85% = 17/20 because there are 17 nickels in 85 cents.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.
25
10025% = = 1
4
: one quarter is 1/4 of a dollar and 4 quarters is $1.
50
10050% = = 1
2
: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,
100
100
and 100% = = 1, 200
100
200% = = 2, etc..

37. Following is a list of important simplified percentage, they are familiar because
they are related to our coins: nickels, dimes, quarters, and the 50–cent pieces.
It’s useful to think of percentages of multiples of 5 as counting nickels where
one nickel is $1/20. For example, 35% = 7/20 because there are 7 nickels in
35 cents, or that 85% = 17/20 because there are 17 nickels in 85 cents.
5
1005% =
Percentages
= 1
20
: one nickel is 1/20 of a dollar and 20 nickels is $1.
10
10010% = = 1
10
: one dime is 1/10 of a dollar and 10 dimes is $1.
25
10025% = = 1
4
: one quarter is 1/4 of a dollar and 4 quarters is $1.
50
10050% = = 1
2
: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,
100
100
and 100% = = 1, 200
100
200% = = 2, etc..
Other useful approximate percentages in fractions are
33% ≈ 1/3 and that 66% ≈ 2/3.

38. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.

39. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
a. 60% of 120 people enjoyed the movie, how many people is that?

40. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = 60
100 = 3
5

41. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 =3
5
60
100 = 3
5 , so 60% of 120 people is

42. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24

43. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
Hence 72 people like the movie.

44. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
b. Of the people enjoyed it, 75% are men, how many men enjoyed the movie?
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
Hence 72 people like the movie.

45. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
b. Of the people enjoyed it, 75% are men, how many men enjoyed the movie?
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
Hence 72 people like the movie.
There are 72 people that like the movie.

46. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
b. Of the people enjoyed it, 75% are men, how many men enjoyed the movie?
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
75% = x 723
4
, so 75% of 72 people is75
100 = 3
4
Hence 72 people like the movie.
There are 72 people that like the movie.

47. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
b. Of the people enjoyed it, 75% are men, how many men enjoyed the movie?
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
75% = x 723
4
, so 75% of 72 people is75
100 = 3
4
18
= 54.
Hence 72 people like the movie.
There are 72 people that like the movie.

48. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
b. Of the people enjoyed it, 75% are men, how many men enjoyed the movie?
a. 60% of 120 people enjoyed the movie, how many people is that?
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
75% = x 723
4
, so 75% of 72 people is75
100 = 3
4
18
= 54.
Hence 72 people like the movie.
There are 72 people that like the movie.
Therefore there are 54 men who enjoyed the movie “As the Paint Dries”.

49. Percentages
We may use percentages to indicate the “concentration” of specific groups in a
larger population.
Example C. 120 people who watched the movie “As the Paint Dries” are
surveyed to see if they enjoyed it.
b. Of the people enjoyed it, 75% are men, how many men enjoyed the movie?
a. 60% of 120 people enjoyed the movie, how many people is that?
“The amount of adjustments” are often given as percentages such as the
discount rates or tax rates etc..
60% = x 120 = 72.3
5
, so 60% of 120 people is60
100 = 3
5
24
75% = x 723
4
, so 75% of 72 people is75
100 = 3
4
18
= 54.
Hence 72 people like the movie.
There are 72 people that like the movie.
Therefore there are 54 men who enjoyed the movie “As the Paint Dries”.

50. Percentages
Example D. A $45 nose–ring is on sale at a 15% discount rate.
How much is the discounted price?

51. Percentages
Example D. A $45 nose–ring is on sale at a 15% discount rate.
How much is the discounted price?
15% = 15
100 = 3
20

52. Percentages
Example D. A $45 nose–ring is on sale at a 15% discount rate.
How much is the discounted price?
15% =
x 453
20
, so the amount of discount “15% of $45” is15
100 = 3
20

53. Percentages
Example D. A $45 nose–ring is on sale at a 15% discount rate.
How much is the discounted price?
15% =
x 45 =3
20
, so the amount of discount “15% of $45” is15
100 = 3
20
4
9
27
4

54. Percentages
Example D. A $45 nose–ring is on sale at a 15% discount rate.
How much is the discounted price?
15% =
x 45 =3
20
, so the amount of discount “15% of $45” is15
100 = 3
20
4
9
27
4
= 6 3
4
= $6.75

55. Percentages
Example D. A $45 nose–ring is on sale at a 15% discount rate.
How much is the discounted price?
15% =
x 45 =3
20
, so the amount of discount “15% of $45” is15
100 = 3
20
4
Hence the marked–down price of the nose–ring is
45 – 6.75 = $38.25.
9
27
4
= 6 3
4
= $6.75