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6th grade

Course: 6th grade > Unit 3

Lesson 4: Equivalent representations of percent problems
Math
6th grade
Rates and percentages
Equivalent representations of percent problems
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Converting between percents, fractions, & decimals

Google Classroom
For example, learn how 50%, 1/2, and 0.5 are all equivalent.
Percents, fractions, and decimals are all just different ways of writing numbers. For example, each of the following are equivalent:
PercentFractionDecimal
50%120.5
In conversation, we might say Ben ate 50% of the pizza, or 12 of the pizza, or 0.5 of the pizza. All three of these phrases mean the exact same thing.
In this article, we'll learn how to convert between percents, fractions, and decimals.

Converting between percents and fractions

Percents to fractions

Let's look at an example converting 15% to a simplified fraction.
15%=15100Write the percent as a fraction=15÷5100÷5Divide the top and bottom by 5=320Simplify
We figured out that 15% is equivalent to 320.
Problem 1A
Convert 44% to a simplified fraction.
  • Your answer should be
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4

Fractions to percents

Let's convert 35 to a percent. The key here is to turn 35 to a fraction with a denominator of 100. To do this, we need to know what times 5 gives us 100:
5×?=100
The number is 100÷5=20:
5×20=100
Now we're ready to convert 35 to a percent:
35=3×205×20Multiply to get a denominator of 100=60100Simplify=60%Write as a percent
We figured out that 35 is equivalent to 60%.
Problem 1B
Convert 1225 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

Converting between percents and decimals

Percents to decimals

Let's convert 8% to a decimal:
8%=8100Write the percent as a fraction=0.088100is 8 hundredths
We figured out that 8% is equivalent to 0.08.

Practice:

Problem 2A
Convert 4% to a decimal.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Decimals to percents

Let's convert 0.05 to a percent:
0.05=5100This is 5 hundredths=5%Write as a percent
We figured out that 0.05 is equivalent to 5%.
Problem 2C
Convert 0.14 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

Converting from a decimal to a percent can be tricky when the decimal is in tenths. Let's see if you can figure it out!

Practice:

Problem 2D
Convert 0.3 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

Practice set:

Problem 3A
Convert 0.82 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
%

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