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Algebra 1 : Fractions and Percentage

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3101 : Algebra 1

Convert $25.66\%$ into a reduced fraction.

Possible Answers:

$\frac{1283}{5000}$

$\frac{2566}{10000}$

$\frac{25.66}{100}$

$\frac{1283}{50000}$

$\frac{1283}{500}$

Correct answer:

$\frac{1283}{5000}$

Explanation:

First, take the decimal and divide over 100 .

We have

$\frac{25.66}{100}$ .

Then, shift the decimal two places to the right which means we add two s to the denominator.

We have $\frac{2566}{10000}$ .

Then if we divide top and bottom by ,

$\frac{2566}{10000}=\frac{1283\cdot 2}{5000\cdot 2}=\frac{1283}{5000}$

final answer will become $\frac{1283}{5000}$ .

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Example Question #12 : How To Find A Fraction From A Percentage

Convert $24\frac{4}{5}\%$ as a reduced fraction.

Possible Answers:

$23\frac{4}{}5$

$\frac{31}{125}$

$\frac{248}{1000}$

$\frac{24.8}{100}$

$\frac{119}{5}$

Correct answer:

$\frac{31}{125}$

Explanation:

First, let's convert the fraction into a decimal. By dividing into we get 0.8 .

Then, we take the new value and place it over 100 .

We have

$\frac{24.8}{100}$ .

Then, shift the decimal one place to the right which means we add one to the denominator.

We have $\frac{248}{1000}$ .

Then if we divide top and bottom by ,

$\frac{248}{1000}=\frac{31\cdot 8}{125\cdot 8}=\frac{31}{125}$

final answer will become $\frac{31}{125}$ .

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Example Question #71 : Fractions And Percentage

Convert $0.01\%$ to a reduced fraction.

Possible Answers:

$\frac{1}{100}$

$\frac{1}{10000}$

$\frac{1}{1000000}$

$\frac{1}{10}$

$\frac{1}{1000}$

Correct answer:

$\frac{1}{10000}$

Explanation:

First, take the decimal and divide over 100 .

We have

$\frac{0.01}{100}$ .

Then, shift the decimal two places to the right which means we add two s to the denominator.

We have $\frac{1}{10000}$ .

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Example Question #74 : Fractions And Percentage

Convert $165.7\%$ to a reduced fraction.

Possible Answers:

$\frac{1657}{1000}$

$\frac{165.7}{100}$

$\frac{16570}{1000}$

$\frac{1.657}{1000}$

$\frac{1657}{10000}$

Correct answer:

$\frac{1657}{1000}$

Explanation:

First, take the decimal and divide over 100 .

We have

$\frac{165.7}{100}$ .

Then, shift the decimal one places to the right which means we add one to the denominator.

We have $\frac{1657}{1000}$ .

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Example Question #75 : Fractions And Percentage

Convert $33.\overline{333}\%$ into a reduced fraction.

Possible Answers:

$\frac{333333}{1000000}$

$\frac{33333}{100000}$

$\frac{333}{1000}$

$\frac{3333}{10000}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

The bar on top means repeating decimals. Let's convert the percent to a decimal. We shift the decimal two places to the left.

The value is then $.33\overline{333}$ . Let's say $.33\overline{333}$ is .

If we multiply both sides by , we get 3.333=10x .

If we subtract both equations, we get 3=9x .

$x=\frac{3}{9}=\frac{1}{3}$

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Example Question #76 : Fractions And Percentage

Convert $9.09\%$ into a reduced fraction.

Possible Answers:

$\frac{909}{1000}$

$\frac{1}{13}$

$\frac{1}{11}$

$\frac{2}{11}$

$\frac{1}{9}$

Correct answer:

$\frac{1}{11}$

Explanation:

The bar on top means repeating decimals. Let's convert the percent to a decimal. We shift the decimal two places to the left.

The value is then $.09\overline{090}$ . Let's say $.09\overline{090}$ is .

If we multiply both sides by 100 , we get 9.0909=100x .

If we subtract both equations, we get 9=99x .

$x=\frac{9}{99}=\frac{1}{11}$

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Example Question #77 : Fractions And Percentage

Convert $12.3\overline{123}\%$ to a reduced fraction.

Possible Answers:

$\frac{123}{999}$

$\frac{123}{333}$

$\frac{41}{999}$

$\frac{43}{237}$

$\frac{41}{333}$

Correct answer:

$\frac{41}{333}$

Explanation:

The bar on top means repeating decimals. Let's convert the percent to a decimal. We shift the decimal two places to the left.

The value is then $.123\overline{123}$ . Let's say $.123\overline{123}$ is .

If we multiply both sides by 1000 , we get 123.123=1000x .

If we subtract both equations, we get 123=999x .

$x=\frac{123}{999}=\frac{41}{333}$

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Example Question #78 : Fractions And Percentage

$\small 35\%$ in the form of a fraction is $\small \square$ .

Possible Answers:

$\small \frac{3}{5}$

$\small \frac{7}{20}$

3.5

$\small \frac{3.5}{100}$

$\small \frac{3500}{10}$

Correct answer:

$\small \frac{7}{20}$

Explanation:

Percentages are equivalent to parts of a whole, or part of $\small 100$ . $\small 35\%$ then is equivalent to $\small \frac{35}{100}$ just like $\small 10\%$ is equivalent to $\small \frac{10}{100}$ , and $\small 60\%$ is equivalent to $\small \frac{60}{100}$ . An easy way to remember percentage to fraction conversions is to simply write the percentage over one hundred. Any percentage can be placed over one hundred and then reduced.

Further more, we are able to reduce this fraction by finding common factors in both the numerator and the denominator.

$\small \frac{35}{100}=\frac{5\cdot 7}{5\cdot 20}$

By canceling out the five in the numerator and the denominator we get our reduced fraction form and final answer of,

$\frac{7}{20}$ .

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Example Question #72 : Fractions And Percentage

Convert $\small 47\%$ into a fraction.

Possible Answers:

$\frac{4.7}{100}$

$\frac{.47}{10}$

$\frac{47}{100}$

This percentage cannot be converted to a fraction.

$\small \frac{470}{1}$

Correct answer:

$\frac{47}{100}$

Explanation:

When converting percentages into fractions, the easiest way to go about it is to simply place the percentage given over one hundred.

So for this example, the percentage is $\small 47\%$ , meaning the it can be rewritten as $\small \frac{47}{100}$ .

Since $\small 47$ is a prime number, this fraction is already in its simplest form.

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Example Question #22 : How To Find A Fraction From A Percentage

What is the most-simplified fractional equivalent of $\small 22 \%$ ?

Possible Answers:

$\small \frac{11}{50}$

$\small \frac{22}{100}$

$\small \frac{1}{11}$

$\small \frac{1}{25}$

$\small \frac{1}{22}$

Correct answer:

$\small \frac{11}{50}$

Explanation:

"Percent" literally means "out of 100," so 22% is equivalent to $\small \frac{22}{100}$ . We can simplify this becasue both the numerator and the denominator are divisible by 2. Divide top and bottom by 2 to get $\small \frac{11}{50}$ .

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Algebra 1 : Fractions and Percentage

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3101 : Algebra 1

Example Question #12 : How To Find A Fraction From A Percentage

Example Question #71 : Fractions And Percentage

Example Question #74 : Fractions And Percentage

Example Question #75 : Fractions And Percentage

Example Question #76 : Fractions And Percentage

Example Question #77 : Fractions And Percentage

Example Question #78 : Fractions And Percentage

Example Question #72 : Fractions And Percentage

Example Question #22 : How To Find A Fraction From A Percentage

All Algebra 1 Resources

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