Grade 5 Fractions: Word Problems

Solve fraction word problems

What You'll Learn

Add and subtract fractions and mixed numbers with unlike denominators in story problems (5.NF.A.2)
Find a fraction of a fraction or of a mixed number in a real-world problem (5.NF.B.6)
Share a unit fraction equally among a whole number of people (5.NF.B.7)

📖Read, then choose the operation

Combining amounts ("in all", "altogether") means add. Finding what is left or how much farther means subtract. Taking a fraction OF an amount means multiply. Sharing equally means divide: sharing 1/3 among 4 people is 1/3 ÷ 4, the same as 1/4 of 1/3 = 1/12.

✏️Fraction of a fraction

A garden covers 2/3 acre and 3/4 of it is tomatoes. 3/4 × 2/3 = 6/12 = 1/2, so 1/2 acre is tomatoes.

💡Simplest form

Simplify every answer. An answer bigger than 1 can be an improper fraction (15/8) or a mixed number (1 7/8 cups); online, type it as a fraction.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Omar has 1/2 of a pan of lasagna left. Omar's family eats 1/3 of what is left. What fraction of the whole pan does the family eat?
1. Write the story as a number sentence: 1/3 × 1/2.
2. Multiply the numerators: 1 × 1 = 1.
3. Multiply the denominators: 3 × 2 = 6.
4. So 1/3 × 1/2 = 1/6.
Answer: 1/6
Example 2
A recipe calls for 1 3/8 cups of flour. Maya makes only 1/3 of the recipe. How much flour does Maya need?
1. Write 1 3/8 as an improper fraction: 1 × 8 + 3 = 11, so 1 3/8 = 11/8.
2. Write the story as a number sentence: 11/8 × 1/3.
3. Multiply the numerators: 11 × 1 = 11.
4. Multiply the denominators: 8 × 3 = 24.
5. So 11/8 × 1/3 = 11/24.
Answer: 11/24
Example 3
A rope is 3 1/6 yards long. Aisha uses 3/4 of the rope to tie up a tent. How many yards of rope does Aisha use?
1. Write 3 1/6 as an improper fraction: 3 × 6 + 1 = 19, so 3 1/6 = 19/6.
2. Write the story as a number sentence: 19/6 × 3/4.
3. Multiply the numerators: 19 × 3 = 57.
4. Multiply the denominators: 6 × 4 = 24.
5. 19/6 × 3/4 = 57/24.
6. The greatest number that divides both 57 and 24 is 3.
7. Divide the top and bottom by 3: 57 ÷ 3 = 19 and 24 ÷ 3 = 8, so 57/24 = 19/8.
8. So 19/6 × 3/4 = 19/8.
Answer: 19/8