Ratios as fractions of a whole drills

Express a part relative to its whole as a fraction or percent - from a part-to-part ratio or from a given part and total.

Free, timed SHSAT practice sets on ratios as fractions of a whole— every question includes a full worked explanation, and there's no account required.

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How to turn a ratio into a fraction of the whole

A part-to-part ratio compares two groups. A fraction of the whole compares one group to the total. To get the total, add the parts.

Common traps:

Worked examples

Example 1.
A school orchestra has violins and cellos in the ratio 4:7. What fraction of the instruments are violins?
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Answer:
B

Total instruments \(= 4 + 7 = 11\). Fraction that are violins \(= 4/11\), which is already in lowest terms. (Writing the part-to-part ratio 4:7 as a fraction gives 4/7. Finding the fraction that are cellos gives 7/11. Putting the total on top gives 11/4.)

Example 2.
A flower shop has roses and tulips in the ratio 7:3. What percent of the flowers are roses?
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Answer:
D

Total flowers \(= 7 + 3 = 10\). Percent that are roses \(= (7 \div 10) \times 100 = 70\%\). (Dividing by 3 (the other part) instead of the total 10 gives the wrong answer about 233.33%. Finding the percent that are tulips instead gives 30%. Forgetting to multiply by 100 gives 0.7%.)

Example 3.
A sports bin has 120 balls, and 56 of them are basketballs. What percent of the balls are basketballs? Round to the nearest hundredth of a percent.
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Answer:
A

Percent \(= (56 \div 120) \times 100 \approx 46.67\%\). (Dividing by the 64 that are NOT basketballs instead of the total 120 gives 87.5%. Finding the percent that are NOT basketballs gives about 53.33%. Forgetting to multiply by 100 gives about 0.47%.)