Algebra 1 : How to find the part from the whole with percentage

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #52 : Whole And Part

What is ten percent of three?

Possible Answers:

\(\displaystyle -\frac{7}{10}\)

\(\displaystyle \frac{3}{10}\)

\(\displaystyle \frac{7}{10}\)

\(\displaystyle \frac{3}{5}\)

\(\displaystyle \frac{1}{3}\)

Correct answer:

\(\displaystyle \frac{3}{10}\)

Explanation:

Ten percent is ten out of 100 parts.

\(\displaystyle 10\% = \frac{10}{100}\)

Reduce the fraction to \(\displaystyle \frac{1}{10}\).

Multipy this fraction with three.

\(\displaystyle \frac{1}{10} \cdot 3 = \frac{3}{10}\)

The answer is:  \(\displaystyle \frac{3}{10}\)

Example Question #31 : How To Find The Part From The Whole With Percentage

What is 13% of 96 ?

Possible Answers:

\(\displaystyle 13\)

\(\displaystyle 12.48\)

\(\displaystyle 83\)

\(\displaystyle 15.75\)

\(\displaystyle 17.65\)

Correct answer:

\(\displaystyle 12.48\)

Explanation:

To find a percentage of a whole, we simply take the percentage and multiply it by the whole number.  In other words

\(\displaystyle 13\% \cdot 96\)

\(\displaystyle 0.13 \cdot 96\)

\(\displaystyle 12.48\)

Therefore, 13% of 96 is 12.48.

Example Question #54 : Whole And Part

What percentage of \(\displaystyle 4\) is \(\displaystyle 11\)?

Possible Answers:

\(\displaystyle 275\)

\(\displaystyle 3.6\)

\(\displaystyle 27.5\)

\(\displaystyle 2.75\)

\(\displaystyle 363\)

Correct answer:

\(\displaystyle 275\)

Explanation:

Set up the equation such that a percentage of \(\displaystyle 4\) is \(\displaystyle 11\).

A percentage is some number out of \(\displaystyle 100\).

\(\displaystyle (\frac{x}{100})(4) = 11\)

Multiply \(\displaystyle 100\) on both sides to eliminate the denominator.

\(\displaystyle 4x=1100\)

Divide by four on both sides.

\(\displaystyle \frac{4x}{4}=\frac{1100}{4}\)

Simplify both sides. The answer is,

\(\displaystyle x=275\)

Example Question #61 : Whole And Part

What number is forty percent of thirty five?

Possible Answers:

\(\displaystyle 14\)

\(\displaystyle 16\)

\(\displaystyle 38\)

\(\displaystyle 12\)

\(\displaystyle 46\)

Correct answer:

\(\displaystyle 14\)

Explanation:

A percentage is some number out of 100.  Set up an equation to find the missing number.

\(\displaystyle x=(\frac{40}{100}) \cdot 35\)

Simplify this equation.

\(\displaystyle x=(\frac{2}{5}) \cdot 35 = 2(7)=14\)

The answer is:  \(\displaystyle 14\)

Example Question #62 : Whole And Part

What is thirty percent of 90?

Possible Answers:

\(\displaystyle 27\)

\(\displaystyle 0.27\)

\(\displaystyle 3.3\)

\(\displaystyle 2.7\)

\(\displaystyle 33\)

Correct answer:

\(\displaystyle 27\)

Explanation:

Rewrite 30 percent into a fraction.

\(\displaystyle 30\% =\frac{30}{100} = \frac{3}{10}\)

Multiply this with 90.

\(\displaystyle \frac{3}{10} \cdot 90 = \frac{270}{10} = 27\)

The answer is \(\displaystyle 27\).

Example Question #63 : Whole And Part

What is 76% of 24?

Possible Answers:

\(\displaystyle 18.24\)

\(\displaystyle \frac{600}{19}\)

\(\displaystyle \frac{19}{600}\)

\(\displaystyle 1.824\)

Correct answer:

\(\displaystyle 18.24\)

Explanation:

To find the value, we must convert the percent to a fraction:

76%=\(\displaystyle \frac{76}{100}\).

Now, because "of" indicates multiplication, we multiply the fraction by the "whole":

\(\displaystyle \frac{76}{100}\cdot 24=\frac{1824}{100}=18.24\)

Example Question #64 : Whole And Part

What is 60 percent of 99?

Possible Answers:

\(\displaystyle \frac{178}{3}\)

\(\displaystyle \frac{301}{5}\)

\(\displaystyle \frac{297}{5}\)

\(\displaystyle \frac{271}{32}\)

\(\displaystyle \frac{129}{7}\)

Correct answer:

\(\displaystyle \frac{297}{5}\)

Explanation:

In order to determine the part, we will need to multiply the percent with the whole.

\(\displaystyle 60\% \cdot 99\)

Convert the percent to a fraction.  Remove the percentage sign and divide by 100.

\(\displaystyle \frac{60}{100} \cdot 99 =\frac{ 3}{5} \cdot 99\)

Multiply the numerator with 99.

The exact answer is:  \(\displaystyle \frac{297}{5}\)

Example Question #65 : Whole And Part

What is 40 percent of one-fourth?

Possible Answers:

\(\displaystyle \frac{1}{5}\)

\(\displaystyle \frac{1}{8}\)

\(\displaystyle \frac{1}{20}\)

\(\displaystyle \frac{1}{10}\)

\(\displaystyle \frac{1}{160}\)

Correct answer:

\(\displaystyle \frac{1}{10}\)

Explanation:

Rewrite the given percentage into a fraction.  A percentage is some number out of 100 parts.

\(\displaystyle 40\%=\frac{40}{100} = \frac{2}{5}\)

Multiply this fraction by one-fourth.

\(\displaystyle \frac{2}{5} \cdot \frac{1}{4} = \frac{2}{20} = \frac{1}{10}\)

The answer is:  \(\displaystyle \frac{1}{10}\)

Example Question #66 : Whole And Part

Find the number that is sixty percent of forty.

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 18\)

\(\displaystyle 14\)

\(\displaystyle 6\)

\(\displaystyle 28\)

Correct answer:

\(\displaystyle 24\)

Explanation:

Write sixty percent of forty as an expression.

\(\displaystyle 60\%\cdot 40\)

The percentage can be converted to a fraction by removing the percentage sign and divide by 100.

Rewrite the expression and simplify.

\(\displaystyle \frac{60}{100}\cdot 40 = \frac{3}{5}\cdot 40= 3\cdot 8\)

The answer is:  \(\displaystyle 24\)

Example Question #67 : Whole And Part

What is forty percent of eighty?

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 32\)

\(\displaystyle 36\)

\(\displaystyle 12\)

\(\displaystyle 40\)

Correct answer:

\(\displaystyle 32\)

Explanation:

A percent is some number out of 100 parts.  Rewrite 40 percent into a fraction.

\(\displaystyle 40\% = \frac{40}{100}\)

Write the expression for forty percent of eighty.

\(\displaystyle \frac{40}{100} \cdot 80\)

Simplify the expression.

\(\displaystyle \frac{40}{100} \cdot 80 = \frac{3200}{100} =32\)

The answer is:  \(\displaystyle 32\)

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