Word Problems: Fractions

Fraction word problems are among the most common question types on the GED Mathematical Reasoning test. These problems require you to translate a real-world situation into a fraction calculation — addition, subtraction, multiplication, or division — and then solve it. With a clear strategy, even complex fraction word problems become manageable.

What Are Fraction Word Problems?

A fraction word problem describes a real-world scenario using fractions and asks you to find a missing quantity. The key skill is identifying which operation (add, subtract, multiply, or divide) is needed based on the wording of the problem. Clue words like “combined,” “total,” and “more than” suggest addition; “left over,” “less,” and “difference” suggest subtraction; “of” suggests multiplication; and “per” or “split equally” suggests division.

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Strategies for Fraction Word Problems

1. Addition and subtraction word problems

When combining or comparing fractional amounts, find a common denominator first, then add or subtract.

• A recipe calls for \(\color{blue}{\frac{1}{2}}\) cup of oil and \(\color{blue}{\frac{1}{4}}\) cup of water. How much liquid is needed?
  \(\color{blue}{\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}}\) cup.

2. Multiplication (“of”) word problems

The word “of” between two fractions (or a fraction and a whole number) means multiply.

• Maria used \(\color{blue}{\frac{2}{3}}\) of the \(\color{blue}{\frac{3}{4}}\) cup of sugar in the jar. How much did she use?
  \(\color{blue}{\frac{2}{3} \times \frac{3}{4} = \frac{6}{12} = \frac{1}{2}}\) cup.

3. Subtraction word problems

When a fraction is taken away or the remainder is asked for, subtract.

• A board is \(\color{blue}{\frac{3}{4}}\) meter long. A carpenter cuts \(\color{blue}{\frac{1}{6}}\) meter off. How much remains?
  \(\color{blue}{\frac{3}{4} – \frac{1}{6} = \frac{9}{12} – \frac{2}{12} = \frac{7}{12}}\) meter.

Step-by-Step Summary

1. Read the problem carefully and identify what is being asked.
2. Identify the operation: addition (combining), subtraction (difference/leftover), multiplication (of a fraction of something), division (splitting equally or finding how many fit).
3. Write a math sentence using the fractions given.
4. Solve: find common denominators for addition/subtraction; multiply/flip for division.
5. Simplify the answer and check that it makes sense in context.

Watch: Solving Fraction Word Problems (Video Lesson)

Math with Mr. J demonstrates how to set up and solve a variety of fraction word problems:

Fraction Word Problems – Worked Examples

Example 1: A painter has \(\color{blue}{\frac{3}{4}}\) of a gallon of paint. She uses \(\color{blue}{\frac{1}{4}}\) of a gallon. How much paint is left?

Subtract: \(\color{blue}{\frac{3}{4} – \frac{1}{4} = \frac{2}{4} = \frac{1}{2}}\) gallon remaining.

Example 2: A bag of rice weighs \(\color{blue}{\frac{5}{8}}\) of a kilogram. If \(\color{blue}{\frac{5}{8}}\) of it is used, how many kilograms were used?

Wait — re-read: \(\color{blue}{\frac{5}{8}}\) of \(\color{blue}{\frac{5}{8}}\) kg. Multiply: \(\color{blue}{\frac{5}{8} \times \frac{5}{8} = \frac{25}{64}}\) kg.

Example 3: A recipe needs \(\color{blue}{\frac{2}{3}}\) cup of butter and \(\color{blue}{\frac{1}{6}}\) cup of margarine. How much fat is used in total?

Add: LCD of 3 and 6 is 6. \(\color{blue}{\frac{2}{3} = \frac{4}{6}}\). So \(\color{blue}{\frac{4}{6} + \frac{1}{6} = \frac{5}{6}}\) cup.

Example 4: A hiker walked \(\color{blue}{\frac{5}{8}}\) of the 40-kilometer trail. How many kilometers did the hiker walk?

Multiply: \(\color{blue}{\frac{5}{8} \times 40 = \frac{200}{8} = 25}\) kilometers.

More Practice: Adding and Subtracting Fractions Word Problems (Video)

This Math with Mr. J video focuses specifically on adding and subtracting fractions in word problem contexts:

Exercises for Fraction Word Problems

1. A tank is \(\color{blue}{\frac{3}{4}}\) full. After filling, \(\color{blue}{\frac{1}{8}}\) more was added. What fraction of the tank is now filled?
2. A runner completed \(\color{blue}{\frac{2}{3}}\) of a 15-mile race. How many miles did she run?
3. A loaf of bread weighs \(\color{blue}{\frac{3}{4}}\) kg. After eating \(\color{blue}{\frac{1}{3}}\) of it, how much remains?
4. A student spent \(\color{blue}{\frac{2}{5}}\) of her 50-dollar budget on books. How much did she spend?
5. Two containers hold \(\color{blue}{\frac{5}{6}}\) liter and \(\color{blue}{\frac{1}{3}}\) liter. What is the total volume?
6. A recipe calls for \(\color{blue}{\frac{3}{4}}\) cup of flour, but you only want to make \(\color{blue}{\frac{2}{3}}\) of the recipe. How much flour do you need?

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Answers

1. \(\color{blue}{\frac{3}{4} + \frac{1}{8} = \frac{6}{8} + \frac{1}{8} = \frac{7}{8}}\)
2. \(\color{blue}{\frac{2}{3} \times 15 = 10}\) miles
3. \(\color{blue}{\frac{3}{4} \times (1 – \frac{1}{3}) = \frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}}\) kg
4. \(\color{blue}{\frac{2}{5} \times 50 = 20}\) dollars
5. \(\color{blue}{\frac{5}{6} + \frac{1}{3} = \frac{5}{6} + \frac{2}{6} = \frac{7}{6} = 1 \frac{1}{6}}\) liters
6. \(\color{blue}{\frac{3}{4} \times \frac{2}{3} = \frac{6}{12} = \frac{1}{2}}\) cup

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Frequently Asked Questions

How do I know whether to multiply or divide in a fraction word problem?

Multiply when you see “of” (finding a fraction of a quantity). Divide when you are splitting something into equal parts or finding how many times one fraction fits into another. For example, “how many \(\color{blue}{\frac{1}{4}}\)-cup servings are in 3 cups?” means \(\color{blue}{3 \div \frac{1}{4} = 12}\).

Do I always need a common denominator?

You need a common denominator only when adding or subtracting fractions. For multiplication and division, you do not need a common denominator — just multiply straight across, or multiply by the reciprocal for division.

How do fraction word problems appear on the GED test?

GED fraction word problems often involve cooking (recipes), construction (measurements), budgeting (portions of money), or distance (portions of a trip). Reading carefully to identify the operation is the most important skill.

Related Topics

• Simplifying Fractions
• Word Problems Involving Fractions of a Group
• Multiplying Mixed Numbers
• Dividing Mixed Numbers
• Convert Between Fractions and Decimals