33 percentages

Percentages

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

100

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

1% = 1 out of 1001 percent = 1/100

#100

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

1% = 1 out of 1001 percent = 1/100

#100

It’s useful think of % as the ratio of pennies to 1$, e.g. 1¢ is 1% of $1 (100 ¢).

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

1% = 1 out of 1001 percent = 1/100

#100

5% = 5 out of 1005 percent = 5/100 = 1/20

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

1% = 1 out of 1001 percent = 1/100

#100

5% = 5 out of 1005 percent = 5/100 = 1/20

10% = 10 out of 10010 percent = 10/100 = 1/10

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

1% = 1 out of 1001 percent = 1/100

#100

5% = 5 out of 1005 percent = 5/100 = 1/20

10% = 10 out of 10010 percent = 10/100 = 1/10

25% = 25 out of 10025 percent = 25/100 = 1/4

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

1% = 1 out of 1001 percent = 1/100

#100

5% = 5 out of 1005 percent = 5/100 = 1/20

50% = 50 out of 100 = 50 percent = 50/100 = 1/2

10% = 10 out of 10010 percent = 10/100 = 1/10

25% = 25 out of 10025 percent = 25/100 = 1/4

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

1% = 1 out of 1001 percent = 1/100

#100

5% = 5 out of 1005 percent = 5/100 = 1/20

50% = 50 out of 100 = 50 percent = 50/100 = 1/2

10% = 10 out of 10010 percent = 10/100 = 1/10

25% = 25 out of 10025 percent = 25/100 = 1/4

100% = 100 out of 100100 percent = 100/100 = 1.

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

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.

34 Divide $100 into

4 equal parts.

Percentages

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.

34 Divide $100 into

4 equal parts.

100 ÷ 4 = 25 so each part is 25,

Percentages

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.

34 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

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.

34 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

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.

34 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

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.

34 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, 34 * 100

hence 3 parts is 3 x $25 = $75.

Percentages

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.

34 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, 34 * 100

25hence 3 parts is 3 x $25 = $75.

Percentages

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.

34 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, 34 * 100 = 75.

25hence 3 parts is 3 x $25 = $75.

Percentages

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25hence 3 parts is 3 x $25 = $75.

Percentages

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25hence 3 parts is 3 x $25 = $75.

Percentages

Example B. 45% of 60 pieces of candy are chocolates, how many is that?

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25

4510045% is

hence 3 parts is 3 x $25 = $75.

Percentages

Example B. 45% of 60 pieces of candy are chocolates, how many is that?

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25

4510045% 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?

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25

Example B. 45% of 60 pieces of candy are chocolates, how many is that?

4510045% is = 9

20 so “45% of 60” is 920

* 60

hence 3 parts is 3 x $25 = $75.

Percentages

÷5

÷5

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25

45100

345% is = 9

20 so “45% of 60” is 920

* 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

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25

divide 60 pieces into 20 groups so each group consists of 3 pieces and 9 groups make 27 pieces

45100

345% is = 9

20 so “45% of 60” is 920

* 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?

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.

34 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” andin such a problem, simplify the percent to a reduced fraction first.

34 * 100 = 75.

25

So 27 pieces are chocolates.

45100

345% is = 9

20 so “45% of 60” is 920

* 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

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

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

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.

51005% =

Percentages

= 120

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

2510025% = = 1

4: one quarter is 1/4 of a dollar and 4 quarters is $1.

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

2510025% = = 1

4: one quarter is 1/4 of a dollar and 4 quarters is $1.

5010050% = = 1

2: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

2510025% = = 1

4: one quarter is 1/4 of a dollar and 4 quarters is $1.

5010050% = = 1

2: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,

100100and 100% = = 1, 200

100200% = = 2, etc..

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

2510025% = = 1

4: one quarter is 1/4 of a dollar and 4 quarters is $1.

5010050% = = 1

2: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,

100100and 100% = = 1, 200

100200% = = 2, etc..

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

2510025% = = 1

4: one quarter is 1/4 of a dollar and 4 quarters is $1.

5010050% = = 1

2: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,

100100and 100% = = 1, 200

100200% = = 2, etc..

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.

51005% =

Percentages

= 120

: one nickel is 1/20 of a dollar and 20 nickels is $1.

1010010% = = 1

10: one dime is 1/10 of a dollar and 10 dimes is $1.

2510025% = = 1

4: one quarter is 1/4 of a dollar and 4 quarters is $1.

5010050% = = 1

2: one 50–cent piece is 1/2 of a dollar and 2 of them is $1,

100100and 100% = = 1, 200

100200% = = 2, etc..

Other useful approximate percentages in fractions are33% ≈ 1/3 and that 66% ≈ 2/3.

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

PercentagesWe 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?

PercentagesWe 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% = 60100 = 3

5

PercentagesWe 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 =35

60100 = 3

5 , so 60% of 120 people is

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

Hence 72 people like the movie.

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

Hence 72 people like the movie.

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

Hence 72 people like the movie.

There are 72 people that like the movie.

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

75% = x 7234, so 75% of 72 people is 75

100 = 34

Hence 72 people like the movie.

There are 72 people that like the movie.

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

75% = x 7234, so 75% of 72 people is 75

100 = 34

18= 54.

Hence 72 people like the movie.

There are 72 people that like the movie.

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

75% = x 7234, so 75% of 72 people is 75

100 = 34

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”.

PercentagesWe 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 = 72.35, so 60% of 120 people is60

100 = 35

24

75% = x 7234, so 75% of 72 people is 75

100 = 34

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”.

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

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

15% = 15100 = 3

20

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

15% =

x 45320

, so the amount of discount “15% of $45” is15100 = 3

20

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

15% =

x 45 =320

, so the amount of discount “15% of $45” is15100 = 3

20

4

9274

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

15% =

x 45 =320

, so the amount of discount “15% of $45” is15100 = 3

20

4

9274

= 6 34 = $6.75

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

15% =

x 45 =320

, so the amount of discount “15% of $45” is15100 = 3

20

4

Hence the marked–down price of the nose–ring is 45 – 6.75 = $38.25.

9274

= 6 34 = $6.75