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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, percentstart fraction, 1, divided by, 2, end fraction0, point, 5
In conversation, we might say Ben ate 50, percent of the pizza, or start fraction, 1, divided by, 2, end fraction of the pizza, or 0, point, 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, percent to a simplified fraction.
15%=15100Write the percent as a fraction=15÷5100÷5Divide the top and bottom by 5=320Simplify\begin{aligned} 15\% &= \dfrac{{15}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{15 \div 5}{100 \div 5} &\small{\gray{\text{Divide the top and bottom by 5}}}\\\\\\\\ &= \dfrac{3}{20} &\small{\gray{\text{Simplify}}} \end{aligned}
We figured out that 15, percent is equivalent to start fraction, 3, divided by, 20, end fraction.
Problem 1A
Convert 44, percent to a simplified fraction.
  • Your answer should be
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4

Fractions to percents

Let's convert start fraction, 3, divided by, 5, end fraction to a percent. The key here is to turn start fraction, 3, divided by, 5, end fraction to a fraction with a denominator of 100. To do this, we need to know what times 5 gives us 100:
5, times, start color #11accd, question mark, end color #11accd, equals, 100
The number is 100, divided by, 5, equals, start color #11accd, 20, end color #11accd:
5, times, start color #11accd, 20, end color #11accd, equals, 100
Now we're ready to convert start fraction, 3, divided by, 5, end fraction to a percent:
35=3×205×20Multiply to get a denominator of 100=60100Simplify=60%Write as a percent\begin{aligned} \dfrac35 &= \dfrac{{3 \times \blueD{20}}}{5 \times \blueD{20}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{60}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 60\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that start fraction, 3, divided by, 5, end fraction is equivalent to 60, percent.
Problem 1B
Convert start fraction, 12, divided by, 25, end fraction to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent

Converting between percents and decimals

Percents to decimals

Let's convert 8, percent to a decimal:
8%=8100Write the percent as a fraction=0.088100is 8 hundredths\begin{aligned} 8\% &= \dfrac{{8}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.08 &\small{\gray{\dfrac{8}{100}\text{is 8 hundredths}}}\end{aligned}
We figured out that 8, percent is equivalent to 0, point, 08.

Practice:

Problem 2A
  • Current
Convert 4, percent to a decimal.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

Decimals to percents

Let's convert 0, point, 05 to a percent:
0.05=5100This is 5 hundredths=5%Write as a percent\begin{aligned} 0.05 &= \dfrac{{5}}{100} &\small{\gray{\text{This is 5 hundredths}}} \\\\\\\\ &= 5\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
We figured out that 0, point, 05 is equivalent to 5, percent.
Problem 2C
Convert 0, point, 14 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent

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
  • Current
Convert 0, point, 3 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent

Practice set:

Problem 3A
  • Current
Convert 0, point, 82 to a percent.
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
percent

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