World Problems Involving Fractions of a Group

Understanding fractions of a group is an essential GED Mathematical Reasoning skill. These problems ask you to find a fractional part of a whole set — for example, finding how many students out of a class, how many items in a batch, or how much of a quantity is represented. The method is straightforward: multiply the fraction by the total.

What Are Fractions of a Group?

When you find a fraction of a group, you are multiplying a fraction by a whole number to find a portion of that total. The word “of” in math always means multiply. So “\(\color{blue}{\frac{3}{4}}\) of 24” means \(\color{blue}{\frac{3}{4} \times 24}\). The result tells you how many items (or what amount) belong to that fractional portion of the group.

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How to Find a Fraction of a Group

Method 1: Multiply

Multiply the fraction by the total group size.

• \(\color{blue}{\frac{3}{4} \text{ of } 24 = \frac{3}{4} \times 24 = \frac{72}{4} = 18}\)
• \(\color{blue}{\frac{2}{5} \text{ of } 30 = \frac{2}{5} \times 30 = \frac{60}{5} = 12}\)

Method 2: Divide then multiply

Divide the total by the denominator (to find one equal part), then multiply by the numerator.

• \(\color{blue}{\frac{5}{6} \text{ of } 18}\): divide \(\color{blue}{18 \div 6 = 3}\) (one part), then \(\color{blue}{3 \times 5 = 15}\).
• \(\color{blue}{\frac{7}{8} \text{ of } 16}\): divide \(\color{blue}{16 \div 8 = 2}\) (one part), then \(\color{blue}{2 \times 7 = 14}\).

Step-by-Step Summary

1. Identify the total group size (the whole number).
2. Identify the fraction given.
3. Multiply the fraction by the total: \(\color{blue}{\text{ fraction } \times \text{ total }}\).
4. Simplify if needed.
5. Check: is your answer smaller than the total? (It should be, unless the fraction is greater than 1.)

Watch: Fractions of a Group Word Problems (Video Lesson)

Math with Mr. J explains how to find a fractional part of a group with worked examples and practice problems:

Fractions of a Group – Worked Examples

Example 1: A class has 24 students. Three-fourths of them passed the math test. How many students passed?

Find \(\color{blue}{\frac{3}{4}}\) of \(\color{blue}{24}\): \(\color{blue}{24 \div 4 = 6}\), then \(\color{blue}{6 \times 3 = 18}\) students passed.

Example 2: A farm has 30 animals. Two-fifths are cows. How many cows are on the farm?

Find \(\color{blue}{\frac{2}{5}}\) of \(\color{blue}{30}\): \(\color{blue}{30 \div 5 = 6}\), then \(\color{blue}{6 \times 2 = 12}\) cows.

Example 3: A bag contains 18 marbles. Five-sixths of them are red. How many are red?

Find \(\color{blue}{\frac{5}{6}}\) of \(\color{blue}{18}\): \(\color{blue}{18 \div 6 = 3}\), then \(\color{blue}{3 \times 5 = 15}\) red marbles.

Example 4: A box holds 16 apples. Seven-eighths of them are ripe. How many are ripe?

Find \(\color{blue}{\frac{7}{8}}\) of \(\color{blue}{16}\): \(\color{blue}{16 \div 8 = 2}\), then \(\color{blue}{2 \times 7 = 14}\) ripe apples.

More Practice: Word Problems About a Fraction of a Group (Video)

This lesson provides additional worked examples of fraction-of-a-group word problems at the GED level:

Exercises

1. A basket holds 20 oranges. Three-fourths are ripe. How many are ripe?
2. A school has 200 students. Two-fifths ride the bus. How many ride the bus?
3. A team won \(\color{blue}{\frac{2}{3}}\) of its 15 games. How many games did it win?
4. A jar has 40 coins. Five-eighths are pennies. How many are pennies?
5. A parking lot has 48 cars. One-sixth are red. How many red cars are there?
6. Of 45 questions on a quiz, a student answered \(\color{blue}{\frac{4}{5}}\) correctly. How many did she get right?

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Answers

1. \(\color{blue}{\frac{3}{4} \times 20 = 15}\)
2. \(\color{blue}{\frac{2}{5} \times 200 = 80}\)
3. \(\color{blue}{\frac{2}{3} \times 15 = 10}\)
4. \(\color{blue}{\frac{5}{8} \times 40 = 25}\)
5. \(\color{blue}{\frac{1}{6} \times 48 = 8}\)
6. \(\color{blue}{\frac{4}{5} \times 45 = 36}\)

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Frequently Asked Questions

What does “of” mean in a fraction word problem?

In mathematics, the word “of” between a fraction and a number means multiply. So “\(\color{blue}{\frac{2}{3}}\) of 15” is calculated as \(\color{blue}{\frac{2}{3} \times 15 = 10}\).

What if the answer is not a whole number?

In real-world group problems, the answer should usually be a whole number because you cannot have a fraction of a person or item. If the answer is not whole, re-read the problem — you may have the fraction or total wrong. On the GED, the numbers are carefully chosen to produce whole-number answers for count-type problems.

How is this different from “fraction of a whole”?

Both involve multiplying a fraction by a quantity. “Fraction of a group” specifically refers to a set of countable items (students, animals, objects), while “fraction of a whole” can involve measurements (cups, meters, dollars). The calculation method is identical.

Related Topics

• Word Problems Fractions
• Simplifying Fractions
• Multiplying Mixed Numbers
• Convert Between Fractions and Decimals
• Using a Fraction to Write Down a Ratio