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Algebra 1 : Fractions and Percentage

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Example Question #1 :How To Find Fractional Percentages

Rewrite $21\tfrac{1}{3}\%$ as a fraction in lowest terms.

Possible Answers:

$\small \frac{32}{125}$

$\small \frac{21}{100}$

$\small \frac{2}{9}$

$\small \small \frac{23}{99}$

$\small \frac{16}{75}$

正确答案:

$\small \frac{16}{75}$

Explanation:

$\small \small 21\tfrac{1}{3}$ % $\small = \small \small \frac{21\frac{1}{3}}{100} = 21\frac{1}{3} \div 100 = \frac{64}{3} \div \frac{100}{1} = \frac{64}{3} \cdot \frac{1}{100}$

Cross-cancel by dividing 64 and 100 by 4:

$\small \small \frac{64}{3} \cdot \frac{1}{100} = \frac{16}{3} \cdot \frac{1}{25} = \frac{16}{75}$ ,

which is the fraction we want.

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Example Question #1 :How To Find Fractional Percentages

What is $\frac{1}{7} \%$ of 154,000 ?

Possible Answers:

22,000

2,200

2.2

220

正确答案:

220

Explanation:

$\frac{1}{7} \%$ of 154,000 can be calculated as follows.

First, we need to convert $\frac{1}{7} \%$ into a fraction that we can use in calculations. The percentage symbol tells us that the value is divided by 100 .

$\frac{1}{7}\% =\frac{\frac{1}{7}}{100}$

Now we can multiply our given value by this fraction to find our answer.

$\frac{\left (\frac{1}{7}) \right }{100}*154,000=\frac{\left (\frac{1}{7})*154,000 \right }{100}= \frac{22,000}{100}=220$

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Example Question #3 :How To Find Fractional Percentages

What is $\frac{1}{2}$ % of $\frac{1}{3}$ ?

Possible Answers:

$\frac{1}{1,500}$

$\frac{1}{600 }$

$\frac{1}{6}$

$\frac{1}{150}$

$\frac{1}{6,000}$

正确答案:

$\frac{1}{600 }$

Explanation:

Set up a proportion statement:

$\frac{\frac{1}{2}}{100} = \frac{N}{\frac{1}{3}}$

Cross-multiply and solve for:

$N \cdot 100 = \frac{1}{2} \cdot \frac{1}{3}$

$N \cdot 100 = \frac{1}{6}$

$N \cdot 100 \cdot \frac{1}{100} = \frac{1}{6} \cdot \frac{1}{100}$

$N = \frac{1}{600}$

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Example Question #4 :How To Find Fractional Percentages

$\frac{1}{5}$ is what percent of $1 \frac{2}{5}$ ?

Possible Answers:

$17 \frac{1}{2}$ %

$18 \frac{1}{4}$ %

$28 \frac{4}{7}$ %

$14 \frac{2}{7}$ %

$22 \frac{1}{5}$ %

正确答案:

$14 \frac{2}{7}$ %

Explanation:

Set up a proportion statement:

$\frac{P}{100} = \frac{\frac{1}{5}}{1 \frac{2}{5}}$

Simplify the right side and solve for:

$\frac{P}{100} = \frac{1}{5} \div 1 \frac{2}{5} = \frac{1}{5} \div \frac{7}{5} = \frac{1}{5} \cdot \frac{5}{7} = \frac{1}{7}$

$\frac{P}{100} \cdot 100 = \frac{1}{7}\cdot 100$

$P= \frac{100}{7} = 14 \frac{2}{7}$

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Example Question #5 :How To Find Fractional Percentages

What percent of 0.6 is 0.0003?

Possible Answers:

0.05 %

0.5 %

0.002 %

0.02 %

2 %

正确答案:

0.05 %

Explanation:

letbe the percent. Then

$P = \frac{ 0.0003}{0.6} \cdot100 = 0.05$

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Example Question #6 :How To Find Fractional Percentages

What is $1 \frac{1}{4}$ % of $1 \frac{1}{4}$ ?

Possible Answers:

$15\frac{5}{8}$

$\frac{1}{64}$

$\frac{1}{640}$

$1\frac{9}{16}$

$\frac{1}{6,400}$

正确答案:

$\frac{1}{64}$

Explanation:

Set up the proportion statement:

$\frac{N}{1\frac{1}{4}} = \frac{1\frac{1}{4}}{100}$

Cross-multply and solve for:

$100 N=1 {\frac{1}{4}} \cdot 1{\frac{1}{4}} = {\frac{5}{4}} \cdot {\frac{5}{4}}$

$100 N= {\frac{25}{16}}$

$\frac{1}{100} \cdot 100 N=\frac{1}{100} \cdot {\frac{25}{16}}$

$N =\frac{1}{100} \cdot {\frac{25}{16}}= \frac{1}{4} \cdot {\frac{1}{16}}= \frac{1}{64}$

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Example Question #7 :How To Find Fractional Percentages

What is $\frac{1}{4}$ % of $\frac{1}{4}$ ?

Possible Answers:

$\frac{1}{1,600}$

1,600

$\frac{1}{16}$

正确答案:

$\frac{1}{1,600}$

Explanation:

Set up the proportion statement:

$\frac{N}{\frac{1}{4}} = \frac{\frac{1}{4}}{100}$

Cross-multply and solve for:

$100 N= {\frac{1}{4}} \cdot {\frac{1}{4}}$

$100 N= {\frac{1}{16}}$

$\frac{1}{100} \cdot 100 N=\frac{1}{100} \cdot {\frac{1}{16}}$

$N = \frac{1}{1,600}$

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Example Question #1 :How To Find Fractional Percentages

What is $\frac{2}{3}\%$ of $\frac{2}{5}$ ?

Possible Answers:

$\frac{1}{600}$

$\frac{3}{5,000}$

$\frac{2}{75}$

$\frac{1}{375}$

$\frac{3}{500}$

正确答案:

$\frac{1}{375}$

Explanation:

Set up a proportion:

$\frac{\frac{2}{3}}{100} = \frac{N}{\frac{2}{5}}$

Cross-multiply and solve for:

$N \cdot 100 = \frac{2}{3} \cdot \frac{2}{5}$

$N \cdot 100 = \frac{4}{15}$

$N \cdot 100 \cdot \frac{1}{100} = \frac{4}{15} \cdot \frac{1}{100}$

$N = \frac{4}{1,500} = \frac{1}{375}$

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Example Question #9 :How To Find Fractional Percentages

What is $\small \small \frac{3}{5}\%$ of 450 ?

Possible Answers:

$\small 270$

$\small 750$

$\small 27$

$\small 2.7$

$\small 1.33$

正确答案:

$\small 2.7$

Explanation:

There are a few ways we can approach this problem. We know that $\small \frac{3}{5}\%$ is $\small \frac{\frac{3}{5}}{100 }$ , or $\small \frac{3}{5}*\frac{1}{100}$ .

We also know that for percentages, "of" means multiply, so we can set up a multiplication problem:

$\small \small \frac{3}{5}*\frac{1}{100}*450$

Simplifying gives

$\small \small \frac{1350}{500}=2.7$ .

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Example Question #10 :How To Find Fractional Percentages

What is $\frac{1}{2}\%$ of 300,000 ?

Possible Answers:

5000

15000

2500

75000

1500

正确答案:

1500

Explanation:

Remember that the word "of" means multiply. One way to solve this is to first divide the percentage by 100.

$\frac{\frac{1}{2}}{100}$

This is the division of two fractions and can be done by multiplying the first fraction by the reciprocal of the second fraction. Remember to treat 100 as the fraction $\frac{100}{1}$

The multiplication should look like this

$\frac{1}{2}\cdot \frac{1}{100}$

Now multiply across the numerator and denominator

$\frac{1}{200}$

Now that the fractional percentage has been converted to a regular fraction we can multiply this by the 300,000 to get the answer

$\frac{1}{200}\cdot \frac{300000}{1}$

$\frac{300000}{200}$

1500

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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 #1 :How To Find Fractional Percentages

Example Question #1 :How To Find Fractional Percentages

Example Question #3 :How To Find Fractional Percentages

Example Question #4 :How To Find Fractional Percentages

Example Question #5 :How To Find Fractional Percentages

Example Question #6 :How To Find Fractional Percentages

Example Question #7 :How To Find Fractional Percentages

Example Question #1 :How To Find Fractional Percentages

Example Question #9 :How To Find Fractional Percentages

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