Word Problems: Fractions

How to word problems: fractions, 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.

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?

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

Frequently Asked Questions

How do you solve word problems involving fractions?

Read the problem twice, find what is being asked, then use clue words to choose the operation: total or combined means add, left over or difference means subtract, of means multiply, and split equally or per means divide. Write the expression, solve it, simplify, and check that the answer makes sense in the story.

How do you solve multiplying fractions word problems?

Look for the word of, which usually signals multiplication. Multiply the numerators, multiply the denominators, and simplify. For example, if 3/5 of a class of 30 students walk to school, then 3/5 × 30 = 90/5 = 18 students walk. If two fractions are involved, such as 1/2 of 2/3 of a cake, multiply 1/2 × 2/3 = 2/6 = 1/3.

How do you solve dividing fractions word problems?

Division problems ask how many groups fit or how much is in each share. Rewrite the division by multiplying by the reciprocal of the divisor. For example, how many 3/4-cup servings are in 6 cups of rice? 6 ÷ 3/4 = 6 × 4/3 = 24/3 = 8 servings. Checking with multiplication, 8 × 3/4 = 6, confirms it.

How do you solve word problems with fractions and whole numbers?

Write the whole number as a fraction over 1, then work as usual. For example, a 12-foot board is cut into pieces 2/3 foot long. How many pieces? 12/1 ÷ 2/3 = 12/1 × 3/2 = 36/2 = 18 pieces. When finding a fraction of a whole number, divide by the denominator first and then multiply by the numerator to keep numbers small.

How do you solve fraction addition and subtraction word problems?

Find a common denominator, add or subtract the numerators, and simplify. Suppose Jake hiked 2 1/3 miles in the morning and 1 3/4 miles in the afternoon. Using twelfths, 2 4/12 + 1 9/12 = 3 13/12 = 4 1/12 miles in total. For a subtraction story, such as how much farther he hiked in the morning, subtract the two amounts instead: 7/12 mile.

How do you find fractions of amounts in word problems?

Divide the amount by the denominator to find one part, then multiply by the numerator. To find 5/8 of $64, divide 64 ÷ 8 = 8, then 8 × 5 = $40. This works for money, time, distance and people. On a GED question you can also enter 5 ÷ 8 × 64 on the calculator to check.

Related Topics

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