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Percent Percent of a number Multiplication and division Simplifying fractions Mixed number to improper fraction Equivalent fractionsHere you will learn about converting fractions to percentages.

Students will first learn about converting fractions to percentages in 6th grade math as part of their work with ratios and proportional relationships and will expand that knowledge to solving problems finding the whole given a part and the percent, or finding a part given the whole and the percent.

This will later be used to find the percent increase/decrease in 7th grade.

Converting a **fraction to a percent** is representing the fraction as a percentage without changing its value.

For example,

\begin{aligned} \cfrac{1}{4}&=25 \% \\\\ \cfrac{9}{20}&=45 \% \\\\ \cfrac{1}{3}&=33.3 \% \\\\ \cfrac{4}{5}&=80 \% \end{aligned}

How does this apply to 6th grade math and 7th grade math?

**Grade 6: Ratios and Proportional Relationships (6.RP.A.3a)**Use ratio and rate reasoning to solve real-world and mathematical problems, for example, by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

**Grade 7: The Number System (7.NS.A.2d)**

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0 s or eventually repeats.

In order to convert from a fraction to a percent:

**Determine if the denominator is a factor or multiple of**\bf{100}**.**

If** it is **follow these steps:

2**Convert the fraction so the denominator is ** \bf{100} **.**

3**Write the numerator as a percentage by using the percent symbol (** \bf{\%} **) because it is now βout of ** \bf{100} **β.**

4**Clearly state the answer showing the βfractionβ = βpercentageβ.**

If the denominator **is not **a factor or multiple of 100 follow these steps:

2**Divide the numerator by the denominator.**

3**Multiply by ** \bf{100} ** to convert to a percentage (in cases with a decimal number, this involves moving the decimal point two spaces to the right of the decimal).**

4**Clearly state the answer showing the βfractionβ = βpercentageβ.**

Use this quiz to check your grade 4 to 6 studentsβ understanding of converting fractions, decimals and percents. 10+ questions with answers covering a range of 4th, 5th and 6th grade converting fractions, decimals and percents topics to identify areas of strength and support!

DOWNLOAD FREEUse this quiz to check your grade 4 to 6 studentsβ understanding of converting fractions, decimals and percents. 10+ questions with answers covering a range of 4th, 5th and 6th grade converting fractions, decimals and percents topics to identify areas of strength and support!

DOWNLOAD FREEConvert \, \cfrac{3}{4} \, to a percent.

**See if the denominator is a factor or multiple of**\bf{100}**.**

4 is a factor of 100 \; ( because 4 \times 25=100) .

2**Convert the fraction so the denominator is** \bf{100} **.**

4 needs to be multiplied by 25 to make 100, so we are going to multiply the denominator **and numerator** by 25 (this ensures they are equivalent fractions).

\cfrac{3}{4}

\cfrac{3 \, \times \, 25}{4 \, \times \, 25}

\cfrac{75}{100}

3**Write the numerator as a percent. **

\cfrac{75}{100}=75\% \; because \% means out of 100.

4**Clearly state the answer showing the βfractionβ = βpercentβ.**

\cfrac{3}{4}=75\%

Convert \, \cfrac{60}{200} \, to a percent.

**See if the denominator is a factor or multiple of ** \bf{100} **.**

200 is a multiple of 100 because 200 \div 2 = 100.

**Convert the fraction so the denominator is** \bf{100} **.**

200 needs to be divided by 2 to make 100, so we are going to divide the denominator **and numerator** by 2.

Note that we are not dividing by the greatest common factor (GCF) here because the intention is to make the denominator 100, not to simplify the fraction to the lowest terms.

\cfrac{60}{200}

\cfrac{60 \, \div \, 2}{200 \, \div \, 2}

\cfrac{30}{100}

Because we are converting to a percent, we only need to simplify the fraction so that the denominator is 100. The fraction is not in its simplest form.

**Write the numerator as a percent.**

\cfrac{30}{100}=30\% \; because \% means out of 100.

**Clearly state the answer showing the βfractionβ = βpercentβ.**

\cfrac{60}{200}=30\%

Convert \, \cfrac{25}{20} \, to a percent.

**See if the denominator is a factor or multiple of ** \bf{100} **.**

20 is a multiple of 100 because 20 \times 5 = 100.

**Convert the fraction so the denominator is** \bf{100} **.**

20 needs to be multiplied by 5 to make 100, so we are going to multiply the denominator **and numerator** by 5.

\cfrac{25}{20}

\cfrac{25 \, \times \, 5}{20 \, \times \, 5}

\cfrac{125}{100}

**Write the numerator as a percent.**

\cfrac{125}{100}=125\% \; because \% means out of 100.

**Clearly state the answer showing the βfractionβ = βpercentβ.**

\cfrac{25}{20}=125\%

Convert \, \cfrac{5}{8} \, to a percent.

**Determine if the denominator is a factor or multiple of ** \bf{100} **.**

8 is not a factor or multiple of 100.

**Divide the numerator by the denominator.**

\cfrac{5}{8}

5 \div 8

Therefore,

\cfrac{5}{8}=0.625

**Multiply by ** \bf{100} ** to convert to a percent.**

0.625 \times 100

62.5\%

**Clearly state the answer showing the βfractionβ = βpercentβ.**

\cfrac{5}{8}=62.5\%

Convert \, \cfrac{2}{9} \, to a percent.

**Determine if the denominator is a factor or multiple of ** \bf{100} **.**

9 is not a factor or multiple of 100 \; ( because 9 cannot be multiplied by an integer to make 100).

**Divide the numerator by the denominator.**

\cfrac{2}{9}

2 \div 9

You can use your written method for division here. This example will show the βlong division methodβ.

Therefore,

\cfrac{2}{9}=0.22222...=0.\overline{2}

**Multiply by ** \bf{100} ** to convert to a percent.**

0.\overline{2} \times 100 = 22.\overline{2}\%

**Clearly state the answer showing the βfractionβ = βpercentβ.**

\cfrac{2}{9}=22.\overline{2}\%

Convert 4 \, \cfrac{5}{16} \, to a percent.

** Added step – convert to an improper fraction first**.

4\, \cfrac{5}{16}=\cfrac{69}{16}

**Determine if the denominator is a factor or multiple of ** \bf{100} **.**

16 is not a factor or multiple of 100 \; ( because 16 cannot be multiplied by an integer to make 100).

**Divide the numerator by the denominator.**

\cfrac{69}{16}

69 \div 16

You can use your written method for division here. This example will show the βlong division methodβ.

Therefore,

\cfrac{69}{16}=4.3125

**Multiply by ** \bf{100} ** to convert to a percent.**

4.3125 \times 100

431.25\%

**Clearly state the answer showing the βfractionβ = βpercentβ.**

\cfrac{69}{16}=431.25\%

- Use visual models such as hundreds grids or pie charts to illustrate the equivalence of fractions and percents and to demonstrate how both forms are ways to represent a part of a whole or a rate.

- Use real world contexts to demonstrate how fractions can be thought of as percentages.

- Worksheets for converting fractions to percentages have their place, but make sure that students have a conceptual understanding of the relationship between percentages and fractions.

**Mistakes with written division**

Often, mistakes are made when implementing a form of written division. For example, a common mistake with long division is mixing up the number being divided (dividend) by the number you are dividing by (divisor). The numerator is the dividend and therefore goes underneath the division symbol.

**Not multiplying by**\bf{100}**to make a percentage**

The percent sign means the number is given out of 100; therefore, we need to multiply the result of the division (the quotient) by 100 when writing it as a percentage.

Example,

\cfrac{3}{4}=0.75=75\%

**Not noticing a repeating decimal**

Sometimes a repeating decimal is not immediately obvious. For example,

\cfrac{1}{7}=0.142857142857142857...

Therefore,

\cfrac{1}{7}= 0.\overline{142857}\

1. Convert \, \cfrac{1}{10} \, to a percent.

1\%

10\%

0.1\%

0.01\%

Start by making an equivalent fraction with a denominator of 100.

\cfrac{1}{10} \, is equal to \, \cfrac{10}{100} \, by multiplying the numerator and denominator by 10.

Write the numerator as a percent with the percent symbol (\%).

This gives you 10\%.

2. Convert \, \cfrac{4}{10} \, to a percent.

40\%

4\%

0.4\%

2.5\%

Start by making an equivalent fraction with a denominator of 100.

\cfrac{4}{10} \, is equal to \, \cfrac{40}{100} \, by multiplying the numerator and denominator by 10.

Write the numerator as a percent with the percent symbol (\%).

This gives you 40\%.

3. Convert \, \cfrac{11}{10} \, to a percent.

90.9\%

1.1\%

\cfrac{11}{10} \, \%

110\%

Start by making an equivalent fraction with a denominator of 100.

\cfrac{11}{10} \, is equal to \, \cfrac{110}{100} \, by multiplying the numerator and denominator by 10.

Write the numerator as a percent with the percent symbol (\%).

This gives you 110\%.

4. Convert \, \cfrac{6}{1000} \, to a percent.

0.6

166.6\%

6 \%

0.6 \%

Start by making an equivalent fraction with a denominator of 100.

\cfrac{6}{1000} \, is equal to \, \cfrac{0.6}{100} \, by dividing the numerator and denominator by 10.

Write the numerator as a percent with the percent symbol (\%).

This gives you 0.6\%.

5. Convert \, \cfrac{601}{20} \, to a percent.

30.05\%

3005\%

3.327787 \%

601 \%

Start by making an equivalent fraction with a denominator of 100.

\cfrac{601}{20} \, is equal to \, \cfrac{3005}{100} \, by multiplying the numerator and denominator by 5.

Write the numerator as a percent with the percent symbol (\%).

This gives you 3005\%.

6. Convert \, \cfrac{15}{16} \, to a percent.

0.9375\%

93.75\%

1.06 \%

937.5 \%

Start by dividing your numerator by your denominator.

15 \div 16=0.9375

Multiply your quotient by 100 and write this product as a percentage.

This gives you 93.75\%.

Yes, this method will always work. However, it may be simpler to first check to see if the denominator is a factor or multiple of 100 to make an equivalent fraction with a denominator of 100.

If you have a repeating decimal, you can write the strand of digits that repeat (or just one digit if that digit repeats) and put a line over it that means it will repeat infinitely. If you do not have a repeating decimal, you can either round the number to the nearest tenth or hundredth place and write it as a percentage.

You can still divide the numerator by this factor, you will just not have a whole number as the answer. You can still express the numerator as a percentage with a decimal number.

- Percent
- Compound measures
- Arithmetic
- Properties of equality
- Decimals

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