FRACTION, DECIMALS, AND PERCENTS CONVERSIONS,

WRITING AND SOLVING PROPORTIONS, AND

SOLVING SIMPLE PERCENT PROBLEMS

7th Grade Math

Ms. Richardson

FRACTION, DECIMAL, AND PERCENT CONVERSIONS To write a percent as a fraction You can write 16 percent as or 16% Your turn now: Write the percent as a fraction in

simplest form. 24% 2. 55% 3. 87% 4. 12%

10016

WRITE FRACTIONS AS PERCENTS To Write a fraction as a percent, rewrite

the fraction with a denominator of 100.Example 1: Write as a percent.

= 80%Your turn now: Write the fraction as a

percent5. 6. 7. 8.

54

10080

205204

2510

203

107

501

PERCENT AS A DECIMAL You can write a percent as a decimal and a

decimal as a percent by using a fraction as an intermediate step.

For example:

37% = = 37 ÷ 100 = 0.37 So, 37% = 0.37. Notice that 37% can be written as a decimal

by dropping the percent sign and moving he decimal point two places to the left.

A decimal can be written as percent by moving the decimal pint two places to the right and adding a percent sign.

10037

EXAMPLES Writing percents as decimals A. 48% = B. 9% = C. 75.5% = Writing decimals as percents A. 0.13 = B. 0.04 = C. 0.027 =

YOUR TURN NOW Write the percent as a decimal or

decimal as percent.1. 25%2. 1%3. 5.2%4. 0.0825. 0.066. 0.578

DECIMALS AS FRACTIONS To write a decimal as a fraction, use the

place value of the last digit of the decimal to determine the denominator.

For Example, to write 0.45 as a fraction, use the fact that 5 is in the hundredths’ place and write .

Write the decimal as a fraction in simplest form.

1. 0.40 2. 0.735

10045

WRITING FRACTIONS AS DECIMALS To write divide the numerator by the

denominator. For example: Write as a decimal

207

350

000

100

100

60

00720..

YOUR TURN NOW1. 2.

97

20017

WRITING AND SOLVING PROPORTIONS A proportion is an equation that states

that two ratios are equivalent.

For Example: The proportion is read “3 is to 5 as 6 is to 10.”

When one of the numbers in a proportion is unknown,, you can find the number by solving the proportion.

You can solve the proportion by:Using equivalent ratiosUsing algebraUsing cross products

106

53

SETTING UP THE PROPOTIONExample: A person burned about 150

calories while skateboarding for 30 minutes. About how many calories would the person burn while skateboarding for 50 minutes?

You will use a proportions to answer this question

To find the number C of calories the person would burn while skateboarding for 60 minute, solve the proportion

utesC

utescalories

minmin 6030150

SOLVE USING EQUIVALENT RATIOS 1. Ask yourself:What number can you

multiply 30 by to get 60?

×?2. Because 30 × 2 = 60, multiply the

numerator by 2 to find C.

×2

6030150 c

6030150 c

×2

THE ANSWERBecause 150 × 2 = 300, C = 300. So the

person would burn about 300 Calories while skateboarding for 60 minutes.

SOLVING PROPORTIONS USING ALGEBRA Solve the proportion

1st Write the original proportion

2nd Multiply each side by 25

3rd Simplify

4th Simplify the fraction The solution is 15

25106 x

25106 x

2525

106

25x

x10150

x15

SOLVING PROPORTIONS USING CROSS PRODUCTSIn the proportion , the products ofand are called cross products. Notice

that the cross products are equal.

64

32 62

43

2015

43

154203 6060

EXAMPLE Use the cross products property to solve

1st Write the original proportion2nd Cross Products Property3rd Divide each side by 2 4th Simplify

d3

92

d3

92

392 d

513239

22

.

d

d

YOUR TURN NOWUse equivalent ratios to solve the

proportion1. 2.

Use algebra to solve the proportion3. 4.

Use the Cross Product Property to solve the proportion

5.

2051 z

12927

c

49124 m

62

33h

1543 x

SETTING UP A PROPORTION There are different ways to sep up a

proportion. For Example:Yesterday you bought 8 bagels for $4.

Today you want only $5 bagels. How much will 5 bagels cost?

or

It could never be

bagelsxdollars

bagelsdollars

584

dollarsxdollars

bagelsbagels

485

bagelsdollars

dollarsbagels

YOUR TURN NOWSolve this problem by setting up a

proportionUse all 3 methods to solve the proportionExample: At maximum speed, the

elevators in the Empire State Building can pass 80 floors in 45 seconds. How many floors can the elevator pass in 9 seconds.

PERCENT PROBLEMSWe can solve problems involving percents

by: Setting up a proportion Using decimals Using fractions

TO SOLVE PERCENT PROBLEMS USING PROPORTIONS

The set up will always be the same“Is over of is equal to what percent over

100?”

The proportion method will work for all 3 types of questions you may be asked

1. What is 75% of 4?2. 3 is what percent of 4?3. 75% of what number is 3?

100percent

ofis

STEPS FOR SOLVING PERCENT PROBLEMS 1st Write the formula for the proportion2nd Fill in the information given in the

problem3rd assign a variable for the unknown4th solve for the variable using one of the

3 ways to solve a proportion Equivalent ratios Algebra Cross product property

100percent

ofis

EXAMPLE 1What percent of 24 is 18?

100%

ofis

What Percent

Of 24

Is 18?

EXAMPLE 2What number is 30% of 120?

What Number is

30% Of 120?

100%

ofis

EXAMPLE 3 12 is 80% of what number?

12 is 80% Of whatNumber?

100%

ofis

YOUR TURN NOW1. What number is 76% of 25?

2. What percent of 40 is 16?

3. 18 is 45% of what number?