Grade 6 Fractions: Word Problems

Real-world fraction problems

What You'll Learn

Divide fractions by fractions to answer "how many groups?" and "how much in one whole?" (6.NS.A.1)
Find a missing side of a rectangle from its fractional area and length (6.NS.A.1)
Choose the operation in mixed-number story problems

📖Two kinds of division stories

"How many 3/4-cup servings are in 2/3 cup?" asks how many groups: 2/3 ÷ 3/4. "3/4 of a bag weighs 2/3 pound — how much is the full bag?" asks how much is in one whole: also 2/3 ÷ 3/4.

✏️Servings of yogurt

How many 3/4-cup servings are in 2/3 cup of yogurt? 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9, so there is 8/9 of a serving.

💡Check with multiplication

Check a quotient by multiplying back: 8/9 × 3/4 = 24/36 = 2/3. Write answers in simplest form. An answer bigger than 1 can be an improper fraction (35/12) or a mixed number (2 11/12); online, type it as a fraction.

Worked examples

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

Example 1
A painter used 1/4 gallon of paint to cover 5/6 of a wall. How many gallons will it take to paint the whole wall?
1. Write the story as a number sentence: 1/4 ÷ 5/6.
2. Keep the first fraction, change ÷ to ×, and flip the second: 5/6 becomes 6/5.
3. 1/4 ÷ 5/6 = 1/4 × 6/5.
4. Multiply the numerators: 1 × 6 = 6. Multiply the denominators: 4 × 5 = 20.
5. That gives 6/20.
6. The greatest number that divides both 6 and 20 is 2.
7. Divide the top and bottom by 2: 6 ÷ 2 = 3 and 20 ÷ 2 = 10, so 6/20 = 3/10.
8. So 1/4 ÷ 5/6 = 3/10.
Answer: 3/10
Example 2
Sam walks 9/10 mile in 4/5 hour. At that speed, how many miles does Sam walk in one hour?
1. Write the story as a number sentence: 9/10 ÷ 4/5.
2. Keep the first fraction, change ÷ to ×, and flip the second: 4/5 becomes 5/4.
3. 9/10 ÷ 4/5 = 9/10 × 5/4.
4. Multiply the numerators: 9 × 5 = 45. Multiply the denominators: 10 × 4 = 40.
5. That gives 45/40.
6. The greatest number that divides both 45 and 40 is 5.
7. Divide the top and bottom by 5: 45 ÷ 5 = 9 and 40 ÷ 5 = 8, so 45/40 = 9/8.
8. So 9/10 ÷ 4/5 = 9/8.
Answer: 9/8
Example 3
Each scoop holds 1/2 pound of birdseed. Diego has 2 1/10 pounds of birdseed. How many scoops' worth of birdseed does Diego have?
1. Write 2 1/10 as an improper fraction: 2 × 10 + 1 = 21, so 2 1/10 = 21/10.
2. Write the story as a number sentence: 21/10 ÷ 1/2.
3. Keep the first fraction, change ÷ to ×, and flip the second: 1/2 becomes 2/1.
4. 21/10 ÷ 1/2 = 21/10 × 2/1.
5. Multiply the numerators: 21 × 2 = 42. Multiply the denominators: 10 × 1 = 10.
6. That gives 42/10.
7. The greatest number that divides both 42 and 10 is 2.
8. Divide the top and bottom by 2: 42 ÷ 2 = 21 and 10 ÷ 2 = 5, so 42/10 = 21/5.
9. So 21/10 ÷ 1/2 = 21/5.
Answer: 21/5