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.

Free tool: try the problems from this lesson in our Fraction Calculator.

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. \(\color{blue}{\frac{4}{5} \times 45 = 36}\)

Frequently Asked Questions

What is a fraction of a group?

A fraction of a group is a part of a whole set of objects or people, not part of a single shape. For example, if 3 out of 4 marbles in a bag are red, then 3/4 of the group is red. In a group of 24 marbles, that would be 18 red marbles, because 3/4 × 24 = 18.

How do you find a fraction of a group?

Multiply the fraction by the number of items in the group, because the word “of” means multiply. Another way is to divide the total by the denominator to find one equal part, then multiply by the numerator. For 5/6 of 18, divide 18 ÷ 6 = 3, then multiply 3 × 5 = 15.

How do you solve fractions of a group word problems?

First find the total in the group, then find the fraction the question asks about, and multiply. Example: a class has 30 students and 2/5 of them walk to school. Divide 30 ÷ 5 = 6, then 6 × 2 = 12 students walk. Always reread the question, since some problems ask for the part that is left, here 30 − 12 = 18.

What is a group size in fractions?

The group size is the total number of items in the set you are taking a fraction of. It plays the role of the whole. In “7/8 of 16 cupcakes,” the group size is 16. Dividing the group size by the denominator gives the size of one equal part: 16 ÷ 8 = 2, so 7/8 of the group is 2 × 7 = 14 cupcakes.

How do you do fractions of a group with objects?

Arrange the objects into as many equal groups as the denominator, then count the objects in the number of groups shown by the numerator. To find 2/3 of 12 counters, split them into 3 equal groups of 4. Two of those groups hold 8 counters, so 2/3 of 12 is 8. Drawing circles around equal groups works well for younger students.

Related Topics

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