RRPR - Fractions, Decimals, and Percents Lesson

Fractions, Decimals, and Percents 

We can designate equivalent amounts of a whole by using a fraction, a decimal number, or by using a percent.

All three shaded areas are equal. From these diagrams we see that 1/5 and 0.2 and 20 percent are three ways of saying the same thing. That is because 1/5, 0.2, and 20 percent are just equivalent fractions in disguise. 1/5 = 2/10 = 20/100 images of shaded blocks In the first figure, we have shaded one of the five equal parts to represent 1/5. The middle figure has ten equal parts, and we have shaded two of them to represent two tenths, which is 0.2. The last figure has been divided into one hundred equal parts; twenty of these parts have been shaded to represent 20 percent.

Let's practice.

  1. Find the decimal equivalent of 51/100.
    • Answer:  
    • To find the decimal equivalent of 51/100, we divide.   51/100 = 51 ÷ 100 =  0.51
  2. Find the percent equivalent of 51/100.
  • Answer:  
  • To change a decimal to a percent, we move the decimal point two places to the right.
  • .51 = 51 percent or 51%

Use the table below to understand how to use fractions, decimals and percents interchangeably:

Conversion

How to do it

Example

Decimals to Percents

Move the decimal two places to the right and add a % sign. 

.45=45% with arrows moving two places to the right

Decimals to Fractions

Use your place value information to write it over the appropriate denominator. (Tenths place will be over 10. Thousandths place would be over 1000.) Then reduce the fraction.

.45 (four as tenth, 5 as hundredth) = 45/100

Fractions to Decimals

Using a calculator or long division, divide the two numbers. You'll be asked to round to a specific decimal place. You should always round to at least the tenths place, but your instructions may ask you to round further.

45/100 = 100|45

Fractions to Percents

Convert to a decimal, then move the decimal two places to the right and add the % sign.

__.45 45/100=100|45.0=45%

Percents to Decimals

Move the decimal two places to the left and remove the % sign.

.45=45% with arrows moving two places to the left

Percents to Fractions

Change the percent to a decimal then use your place value information to write it over the appropriate denominator. (Tenths place will be over 10. Thousandths place would be over 1000.) Then reduce the fraction.

45% = .45 (4 is tenth, 5 is hundredth) = 45/100

 

Watch the Video Showcase below to learn more about conversions:

Now practice some conversions:

Proportions and Percents Homework Assignment

Download the "Proportions and Percents Homework Assignment" by clicking here. Be sure to work all of the practice problems on paper. You will use these problems and solutions to complete the "Investigating Rate, Ratio, and Proportional Reasoning Proportional Reasoning Homework Quiz 2." Remember you can always go back and review the lessons and videos for more help. Links to an external site. Links to an external site. Links to an external site.

Once you've done the practice work, you can click here for the first page of the answer key to check it. Links to an external site.

Here's the second page of the answer key. Links to an external site.

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