World Problems Involving Fractions of a Group

How to world problems involving fractions of a group, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

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?

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