ACT Math : How to find the ratio of a fraction

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #31 : Proportion / Ratio / Rate

A pie is made up of  \(\displaystyle \frac{1}{9}\) crust, \(\displaystyle \frac{1}{3}\) apples, and \(\displaystyle \frac{1}{4}\) sugar, and the rest is jelly. What is the ratio of crust to jelly?

Possible Answers:

\(\displaystyle 1:4\)

\(\displaystyle 11:36\)

\(\displaystyle 3:10\)

\(\displaystyle 4:11\)

\(\displaystyle 11:3\)

Correct answer:

\(\displaystyle 4:11\)

Explanation:

A pie is made up of  \(\displaystyle \frac{1}{9}\) crust, \(\displaystyle \frac{1}{3}\) apples, \(\displaystyle \frac{1}{4}\) sugar, and the rest is jelly. What is the ratio of crust to jelly?

To compute this ratio, you must first ascertain how much of the pie is jelly. This is:

\(\displaystyle 1-\frac{1}{4}-\frac{1}{3}-\frac{1}{9}\)

Begin by using the common denominator \(\displaystyle 36\):

\(\displaystyle 1-\frac{1}{4}-\frac{1}{3}-\frac{1}{9}=\frac{36}{36}-\frac{9}{36}-\frac{12}{36}-\frac{4}{36}\)

\(\displaystyle \frac{36}{36}-\frac{9}{36}-\frac{12}{36}-\frac{4}{36}=\frac{11}{36}\)

So, the ratio of crust to jelly is:

\(\displaystyle \frac{1}{9}:\frac{11}{36}\)

This can be written as the fraction:

\(\displaystyle \frac{\frac{1}{9}}{\frac{11}{36}}=\frac{1}{9}*\frac{36}{11}=\frac{4}{11}\), or \(\displaystyle 4:11\)

Example Question #1 : How To Find The Ratio Of A Fraction

In a solution, \(\displaystyle \frac{1}{3}\) of the fluid is water, \(\displaystyle \frac{1}{5}\) is wine, and \(\displaystyle \frac{7}{15}\) is lemon juice. What is the ratio of lemon juice to water?

Possible Answers:

\(\displaystyle 7:8\)

\(\displaystyle 3:5\)

\(\displaystyle 5:7\)

\(\displaystyle 7:5\)

\(\displaystyle 7:3\)

Correct answer:

\(\displaystyle 7:5\)

Explanation:

This problem is really an easy fraction division. You should first divide the lemon juice amount by the water amount:

\(\displaystyle \frac{lemon\:juice}{water}=\frac{\frac{7}{15}}{\frac{1}{3}}\)

Remember, to divide fractions, you multiply by the reciprocal:

\(\displaystyle \frac{\frac{7}{15}}{\frac{1}{3}} = \frac{7}{15}*3=\frac{7}{5}\)

This is the same as saying: 

\(\displaystyle 7:5\)

Example Question #1131 : Gre Quantitative Reasoning

If \(\displaystyle x=\frac{11}{100}\) and \(\displaystyle y=\frac{15}{8}\), what is the ratio of \(\displaystyle x\) to \(\displaystyle y\)?

Possible Answers:

\(\displaystyle 45 : 191\)

\(\displaystyle 121 : 800\)

\(\displaystyle 165:800\)

\(\displaystyle 15:200\)

\(\displaystyle 22:375\)

Correct answer:

\(\displaystyle 22:375\)

Explanation:

To find a ratio like this, you simply need to make the fraction that represents the division of the two values by each other. Therefore, we have:

\(\displaystyle x:y=\frac{\frac{11}{100}}{\frac{15}{8}}\)

Recall that division of fractions requires you to multiply by the reciprocal:

\(\displaystyle \frac{\frac{11}{100}}{\frac{15}{8}} = \frac{11}{100}*\frac{8}{15}=\frac{11}{25}*\frac{2}{15}\)

which is the same as:

\(\displaystyle \frac{22}{375}\)

This is the same as the ratio:

\(\displaystyle 22:375\)

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