FRACTIONSDECIMALSPERCENTS

Shelby Blackwood

The student will be able to convert fractions, decimals,

and percentages.

This lesson will meet the following standards for Oklahoma 6th grade

mathematics curriculum:

PASS – Strand 2N, Standard 2.1 Number Sense: Convert compare, and order decimals, fractions, and percents using a variety of methods.

Common Core – RP.3c Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole given a part and the percent. Shelby

Blackwood

Decimals, fractions, and percentages are just

different ways of showing the same value.

The following presentation will show you different procedures to convert these

numbers.Shelby Blackwood

*Source: www.mathisfun.com

How to change fractions to decimalsMethod 1-Use a proportion

Step 1 – Rename the fraction as an equivalent fraction with 100 as the denominator. We can multiply 5 by 20 to get 100. You must multiply the numerator by 20 also.

1 x 20 20 5 x 20 100

=

Shelby Blackwood

Method 1-Use a proportion

(continued)

Step 2 – 20/100 is 20 divided by 100. A quick way to divide by 100 is to move the decimal two places from the right. Write the numerator with two decimal places from the right.

So, 1/5 = .20 or .2 as a decimal!

= .2020100

= .20

Shelby Blackwood

Easy, right? But there’s a problem.

What do you do when you have a fraction, such as 1/7, that has a

denominator that is not a factor of 100?

You would use the long division method.

It will always work!Shelby Blackwood

How to change fractions to decimals

Step 1 – First, you should realize that 1/7 is the same thing as 1 divided by 7. In order to change this fraction to a decimal, you will use division. Follow the algorithm on the next slide.

Shelby Blackwood

Method 2- Use a long division algorithm

17

Step 1 –7 will not go into 1, so add a decimal and a 0 to the right of the 1

.0 Step 2 –Bring the decimal straight up

.

Step 3 –Divide 7 into 10. It goes 1 time, so place a 1 above the 0

1

Step 4 –Multiply 1 times 7 and subtract it from 10.

7 3

Step 5 –You get 3. Seven will not go into 3, so you can add another 0 and bring it down. Shelby

Blackwood

0

0

Step 6 –Now divide 7 into 30. It will go 4 times, so place a 4 next to the one. 17 .0

.1

7 3

0

0

4

Step 7 – 7 times 4 is 28, so place the 28 under the 30 and subtract. You get 2.

2 82

Step 8 –Add another 0 to the dividend and bring it down.

0

0 Step 9 – Divide 7 into 20. It will go 2 times, so place a 2 next to the 4 and multiply 2 times 7. Place 14 under the 20 and subtract. You get 6.

1 4

2

6Shelby Blackwood

Step 10 –You can stop here. This is a non-terminating, non-repeating decimal and would go on forever. 17 .0

.1

7 3

0

0

4

2 82

0

01 4

2

6

Step 11 –Since it is a non-terminating, non-repeating decimal, we will round it to two decimal places to get an approximate value.

Shelby Blackwood

The result would be .14, so 1/7 is

approximately .14 as a decimal.

How to change fractions to a percent

Step 1 – After changing 1/5 to a decimal, .20, you will multiply by 100 to change it to a percent.

.20 x 100 = 20%shortcut: when multiplying by 100, you move the decimal two places to the right

1/5 = .20 = 20%Shelby Blackwood

Resource Page

Follow these links for more help changing fractions to decimals and

percents.http://www.youtube.com/watch?v=VlqhVldVces

http://www.mathplayground.com/howto_perfracdec.html

http://www.quia.com/cb/34887.html

When you are ready to practice what you’ve learned, follow this link to play a

Jeopardy! game using fractions, decimals, and percents.

Shelby Blackwood

Why Convert Decimals to Percents

One use for decimals is in working with percents, which are commonplace in everyday life: •Discounts on Sale Items•Counting Money, ETC.

The word  percent  means  per one hundred.

The symbol % is used for percent.

The % symbol can be traded for a factor of 100.A factor of 100 can be traded for a % symbol.This simple idea is the key to success with percents.

Jessica Thompson

How to Change Decimals to Percents

Jessica Thompson

From Decimal To Percent  

move the decimal point 2 places to the right, and add the "%" sign.

To convert from decimal to percent: multiply by 100, and add a "%" sign.

The easiest way to multiply by 100 is to move the decimal point 2 places to the right. So:

Converting Decimals to Percents is as Easy as Sliding the Decimal 2 Places to

the Right and Adding a % SignIt must be noted that “Sliding the Decimal” is only allowed

because it is the same as multiplying the original number by 100.

WWW.KHANACADEMY.COM Web Linkhttp://s3.amazonaws.com/KA-youtube-converted/

5z568fLBQyQ.mp4/5z568fLBQyQ.mp4

EXAMPLES:

0.25 = 25%3.75 = 375%7.0683 = 706.83%

Here's the idea that makes this work:

0.25 = 25/100 = 25 x 1/100 = .25%

Notice that the 1/100 gets traded in for the percent symbol.

Jessica Thompson

http://www.aaastudy.com/dec71dx2.htm

Websites to Practice Converting Decimals to Percents

http://www.math-play.com/Decimals-and-Percents/Decimals-and-Percents.html

http://s3.amazonaws.com/KA-youtube-converted/5z568fLBQyQ.mp4/5z568fLBQyQ.mp4

Video Link to Khan Academy to Learn How to Convert Decimals to Percents

Jessica Thompson

How to Change Decimals to Fractions

Jessica Thompson

Step 1: Write down the decimal divided by 1, like this: decimal/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify/Reduce the fraction

To Convert a Decimal to a Fraction Follow These Steps:

Example: Express 0.75 as a fraction

Step 1: Write down 0.75 divided by 1:

0.75 1

Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):

× 100

0.75 =

75 1 100

× 100

(Do you see how it turns the top number into a whole number?)

Jessica Thompson

Step 3: Simplify the fraction (this took me two steps):

÷5 ÷ 5

75

= 15

= 3

100 20 4

÷5 ÷ 5

Answer = 3/4

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction

Jessica Thompson

Jessica Thompson

Example: Express 0.333 as a fraction

Step 1: Write down:

0.333 1

Step 2: Multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

333 1,000

Step 3: Simplify Fraction:

Can't get any simpler!

Answer = 333/1,000

Jessica Thompson

Websites to Practice Converting Decimals to Fractions

Video Link to Khan Academy to Learn How to Convert Decimals to Percents

http://www.mathplayground.com/percent04.html

http://www.aaastudy.com/fra71bx2.htm

http://www.khanacademy.org/math/arithmetic/decimals/v/converting-decimals-to-fractions-1--ex-1

Converting Percents to

Fractions and Decimals

Jill Porter

Things to remember when converting a percent to a fraction

• The % Sign means (Per 100) Ex. 25% is 25/100

• When converting a percent to a fraction fractions must always be reduced to lowest terms.

25 /25 = 1 100 /25 = 4

• So the reduced version of 25/100 is 1/4

Jill Porter

Example Problems

15% 15 /5 = 3 27% _ 27100 / 5 = 20 100

NOTE nothing will go 22% 22 /2 = 11 into both 27 and 100 100 /2 = 50 evenly so 27/100 is

lowest terms

60% 60 /20 = 3 75% _75 /25 = 3 100/20 = 5 100 /25 = 4

Jill Porter

Working with Percentages that include decimals

• When you have a Percent that includes a decimal you must get rid of the decimal before you can convert the percent into a fraction.

• Move decimal to the right until it is at the end of the number.

• If there is one decimal place this would be the same as multiplying by 10

• Remember if you multiply the numerator by 10 you must multiply the denominator by 10 as well

Jill Porter

Example Problems

5.5% 5.5 X 10 = __55 /5 = 11 100.0 X 10 = 1000 /5 = 200

25.5% 25.5 X 10 = 255 /5 =_ 51 100.0 X 10 = 1000/5 = 200

85.5% 85.5 X 10 = 855 /5 = 171 100.0 X 10 =1000/5 = 200

Jill Porter

Things to Remember When Converting Percents to Decimals

• Percent means per 100• So to change a number from a percent

into a decimal just remove the percent sign and divide by 100

37% 37/100 = 0.37• Simply move the decimal two places to

the left • Repeat same process even if the

percent has a decimal in it such as 8.5%

Jill Porter

Example Problems

5% 5/100 = 0.05 15.3% 15.3/100 = 0.153

25% 25/100 = 0.25 50.7% 50.7/100 = 0.507

Practice moving decimal places 2 spaces to the left

77% 77. = 0.77 83% 83. = 0.83 115% 115. = 1.15

Jill Porter

Resource page

For extra explanations and practice you can visit http://www.youtube.com/watch?v=04eEAxkc4bk

http://www.math-salamanders.com/convert-percent-to-fraction.html

Jill Porter