Word Problems | Open Textbooks

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In this lesson, you will apply your knowledge of equivalent fractions to solve real-world word problems. Learning to translate word problems into fraction equations is an essential skill.

Problem-Solving Strategy

Read carefully: Understand what the problem is asking.
Identify the fractions: Find the fractions mentioned in the problem.
Determine what to do: Do you need to find an equivalent fraction? Compare fractions? Simplify?
Solve: Use your fraction equivalence skills.
Check: Does your answer make sense in the context of the problem?

Examples

Work through these examples to see the concepts in action.

Example 1: Pizza Sharing

Maria ate 2/8 of a pizza. What fraction is this in simplest form?

Solution: 2/8 = 1/4 (divide both by 2). Maria ate 1/4 of the pizza.

Example 2: Recipe Adjustment

A recipe calls for 1/2 cup of flour. If you want to use a measuring cup marked in eighths, how many eighths do you need?

Solution: 1/2 = 4/8 (multiply both by 4). You need 4/8 cup of flour.

✏️ Practice

Test your understanding with these practice questions.

Practice Questions

0/4 correct

Question 1

If y = 3x represents a proportional relationship, what is the constant of proportionality?

A 1

B 3

C x

D y

Explanation: In y = kx, the constant of proportionality k is the coefficient of x. Here k = 3.

Question 2

A recipe uses 2 cups of flour for every 3 cups of sugar. If you use 6 cups of flour, how many cups of sugar do you need?

A 4 cups

B 9 cups

C 12 cups

D 8 cups

Explanation: Set up the proportion: 2/3 = 6/x. Cross multiply: 2x = 18, so x = 9 cups.

Question 3

Which equation represents a proportional relationship?

A y = 2x + 1

B y = 5x

C y = x²

D y = 3

Explanation: A proportional relationship has the form y = kx where k is a constant. Only y = 5x fits this form.

Question 4

The table shows x: 2, 4, 6 and y: 8, 16, 24. What is the constant of proportionality?

A 2

B 4

C 6

D 8

Explanation: Divide any y-value by its corresponding x-value: 8÷2 = 4, 16÷4 = 4, 24÷6 = 4. The constant is 4.

Check Your Understanding

Test yourself with these 10 quiz questions. Click on each question to reveal the answer.

Question 1: Jake ate 3/12 of a cake. Express this fraction in simplest form.

Answer: 1/4. The GCF of 3 and 12 is 3. Divide both by 3: 3/12 = 1/4

Question 2: A recipe needs 2/3 cup of sugar. Sarah only has a 1/6 cup measure. How many 1/6 cups equal 2/3 cup?

Answer: 4 cups. Since 2/3 = 4/6 (multiply both by 2), Sarah needs 4 of the 1/6 cup measures.

Question 3: Tom walked 4/10 of a mile. Express this distance in simplest form.

Answer: 2/5 mile. The GCF of 4 and 10 is 2. Divide both by 2: 4/10 = 2/5

Question 4: A garden is divided into 8 equal sections. If 6 sections have flowers, what fraction of the garden has flowers in simplest form?

Answer: 3/4. 6/8 simplifies to 3/4 (divide both by 2).

Question 5: Emma has 1/4 of a dollar. How many cents is this equivalent to out of 100 cents?

Answer: 25 cents. 1/4 = 25/100, so Emma has 25 cents.

Question 6: A class has 20 students. If 15 students passed a test, what fraction passed in simplest form?

Answer: 3/4. 15/20 = 3/4 (divide both by 5).

Question 7: A pizza is cut into 12 slices. Mike ate 4 slices. What fraction did he eat in simplest form?

Answer: 1/3. 4/12 = 1/3 (divide both by 4).

Question 8: Lisa read 2/5 of a book. If the book has 100 pages, how many pages did she read?

Answer: 40 pages. 2/5 = 40/100, so Lisa read 40 pages.

Question 9: A recipe calls for 3/4 cup of milk. Express this using a denominator of 16.

Answer: 12/16. Since 4 x 4 = 16, multiply both by 4: 3/4 = 12/16.

Question 10: A rope is 10/15 meters long. What is this length in simplest form?

Answer: 2/3 meters. The GCF of 10 and 15 is 5. Divide both by 5: 10/15 = 2/3.

Next Steps

Review any concepts that felt challenging
Move on to the next lesson when ready
Return to practice problems periodically for review