chapter 6staff · 2017. 8. 16. · start by dividing the denominator into the numerator. at this...

Chapter 6

Percents and their Applications

What is a percent?

A percent is 1 one hundredth of a number.

For instance, a penny is 1/100 of a dollar.

Each one hundredth is 1%

A nickel is 5/100 of a dollar or 5%

A dime is 10/100 of a dollar or 10%

No. of fraction % of decimal currency

pennies of dollar a dollar number (cents)

50 50/100 50% .50 $.50

25 25/100 25% .25 $.25

10 10/100 10% .10 $.10

5 5/100 5% .05 $.05

1 1/100 1% .01 $.01

Notice the difference between these two sets of numbers.

Visualize the alphabet to determine which way to move the decimal

point when converting from decimals to percent and from percent to

decimals

a b c D e f g h i j k l m n o P q r s t u v w x y z

Left Right

Toward D Toward P

.xx xx.

Decimal to Percent (from D toward P) – move the decimal

point two places to the right

Percent to Decimal (from P toward D) – move the decimal

point two places to the left

D for

Decimal

P for

Percent

Converting Decimals to Percents

.75 75%

5.00 500%

Move decimal point 2 places to the right, and add zeros if

necessary. Add a percent symbol at the end of the number.

.01 1%

a b c D e f g h i j k l m n o P q r s t u v w x y z

Converting a fraction to a decimal number, to a percent,

and then rounding to the hundredth place

513

13 5.000000

.384615

=

38.4615% 38.46%=

Converting Percents to Decimals, example 1

35% .35

2.50250%

Drop the percent symbol. Move decimal point 2

places to the left, add zeros if necessary

8% .08

a b c D e f g h i j k l m n o P q r s t u v w x y z

Converting Percents to Decimals-- Example 2

Drop the percent symbol

Move the decimal point 2 places to left.

.8% .8 .00.8 .008

A B C D

In this case we had to add zeros to fill in the empty

places to the left of the 8.

a b c D e f g h i j k l m n o P q r s t u v w x y z

Converting Fractional Percents to Decimals

12

1.00 2 .00.5

.005

% .5

A fractional percent is a part (fraction) of a percent.

Start by dividing the denominator into the numerator.

At this point, the number is

still a percent and has to

be converted to a decimal.

Converting Proper Fractions to Percents

1.00 10 10%.10.1

10

Remember, converting from a decimal number to a

percent means moving the decimal point two places to

the right. (D to P) Then add the percent sign (%).

Fraction ► Decimal ► Percent

Converting a Whole Percent to a Fraction

76% 76 x 11 100

76100

1925

Divide 4 into the numerator and the denominator

to reduce this fraction to lowest terms.

Converting a Mixed Percent

(also called a Decimal Percent) to a Fraction

12½ %

252

25 x

1 = 252 100 200

1

8

Drop % symbol, and change the mixed

percent to an improper fraction.

Multiply improper fraction by 1/100

Reduce to lowest terms.

Application of Percents - Portion Formula

Portion (P) = Base (B) x Rate (R)

Portion “is”

Base “of” Rate “%”

Base: 100% - whole. Usually given after the word of – but not always $100 – Bonus check

Rate: Usually expressed as a percent but could also be a decimal or fraction. 20% taxes

Portion: A number – not a percent and not the whole $20 taxes

X

Center line stands for

division.

To find the portion, multiply the rate x base

To find the rate, divide portion by base

To find base, divide portion by rate Very

Useful

McDonalds has two major categories of sales—

drive-through and eat-in. Both are portions of

total McDonalds sales. The following business

math problems have to do with these portions

of the total sales.

Solving for PortionSales to McDonalds drive-thru customers are

60% of total sales. Total sales are $1,600,000.

What are the drive-thru sales?

Portion = Base x Rate

P = $1,600,000 x .60

P = $960,000

base

rate

portion

960,000

.60 1,600,000

portion

rate base

Solving for Rate

Sales to McDonalds drive-thru customers are $960,000.

Total sales are $1,600,000. What Percent of customers

eat in the restaurant?

Rate = PortionBase

R = $640,000$1,600,000

R = 40%

$1,600,000

- 960,000

640,000

drive-thruEat in

total

rate

÷base

portion

? 1,600,000

640,000

Solving for Base

Sales to McDonalds drive-thru customers are 60% of total sales.

Sales to eat-in customers are $640,000. What are total sales?

Base = PortionRate

B = $640,000.40

B = $1,600,000

eat in salesPercent of

customers that

eat-in (1.00 - .60)

Rate of Decrease (rates are percent)

15 oz.

bunch

Rate = PortionBase

Rate = 1215

Amount of Decrease

(Portion)

Original Weight (Base)

.80 or 80% decrease

3 oz.

bunch

Original New

The actual decrease in size

(portion) is 15 oz. – 3 oz. = 12 oz.

What percent is 12 (the decrease)

of 15 (the original size)?

Rate of Percent Increase

$1,000

Rate = PortionBase

Rate = $1,500$1,000 Original sales

(Base)

1.5 or 150%Increase

$2,500

Original New

Amount of

Increase (Portion)

Percent of

Increase (Rate)

The actual increase (portion) is

2,500 – 1,000 = 1,500

What percent is 1,500 (the

increase) of 1,000 (the original

size)? You are seeking the rate.