Fraction Division Words

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Answer Key & Explanations

Fraction Division Words · Grade 6 · Worksheet 1

1. Aroha has 12 2/3 meters of fabric. She cuts it into pieces that are each 1 1/6 meters long. How many pieces of fabric does she get? Answer: 10 6/7 Solution: Convert mixed numbers to improper fractions. 12 2/3 = (12 × 3 + 2)/3 = (36 + 2)/3 = 38/3. 1 1/6 = (1 × 6 + 1)/6 = (6 + 1)/6 = 7/6.
   Full step-by-step solution

   Step 1: Convert mixed numbers to improper fractions. 12 2/3 = (12 × 3 + 2)/3 = (36 + 2)/3 = 38/3. 1 1/6 = (1 × 6 + 1)/6 = (6 + 1)/6 = 7/6. Step 2: Write the division problem: 38/3 ÷ 7/6. Step 3: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 7/6 is 6/7. So, 38/3 × 6/7. Step 4: Multiply the numerators: 38 × 6 = 228. Multiply the denominators: 3 × 7 = 21. This gives 228/21. Step 5: Simplify the fraction. Divide numerator and denominator by their greatest common factor, which is 3: 228 ÷ 3 = 76, 21 ÷ 3 = 7. So, 76/7. Step 6: Convert the improper fraction to a mixed number: 76 ÷ 7 = 10 with a remainder of 6, so 10 6/7. Final Answer: 10 6/7 pieces.

2. A construction company needs to pour concrete for a new sidewalk. The project requires 2 1/4 cubic meters of concrete, and each concrete truck can deliver 3/8 of a cubic meter per load. How many full truckloads of concrete are needed for the sidewalk? Answer: 6 Solution: Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 cubic meters Set up the division problem: (9/4) ÷ (3/8) To divide fractions, multiply by the reciprocal: (9/4) × (8/3) Multiply numerators: 9 × 8 = 72 Multiply denominators: 4 × 3 = 12 Simplify the fraction: 72/12 = 6…
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 cubic meters Step 2: Set up the division problem: (9/4) ÷ (3/8) Step 3: To divide fractions, multiply by the reciprocal: (9/4) × (8/3) Step 4: Multiply numerators: 9 × 8 = 72 Step 5: Multiply denominators: 4 × 3 = 12 Step 6: Simplify the fraction: 72/12 = 6 Step 7: Since the question asks for full truckloads, and 6 is a whole number, we have our answer. The construction company needs 6 full truckloads of concrete.

3. A construction crew is building a new bike path that requires 2 1/4 tons of asphalt per kilometer. If their asphalt truck can deliver 3/8 of a ton per load, how many full truckloads are needed to pave one kilometer of the bike path? Answer: 6 Solution: Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 tons Divide the total asphalt needed by the amount per truckload: (9/4) ÷ (3/8) When dividing fractions, multiply by the reciprocal: (9/4) × (8/3) Multiply numerators and denominators: (9 × 8)/(4 × 3) = 72/12 Simplify…
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 tons Step 2: Divide the total asphalt needed by the amount per truckload: (9/4) ÷ (3/8) Step 3: When dividing fractions, multiply by the reciprocal: (9/4) × (8/3) Step 4: Multiply numerators and denominators: (9 × 8)/(4 × 3) = 72/12 Step 5: Simplify the fraction: 72 ÷ 12 = 6 Step 6: Since the question asks for full truckloads, and 6 is a whole number, we have our answer. The construction crew needs 6 full truckloads to pave one kilometer of the bike path.

4. Liam has 5 1/3 cups of flour. He uses 2/3 cup of flour for each batch of cookies. How many batches of cookies can he make? Answer: 8 Solution: Convert the mixed number to an improper fraction. 5 1/3 = (5 × 3 + 1)/3 = (15 + 1)/3 = 16/3. Write the division problem: 16/3 ÷ 2/3.
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction. 5 1/3 = (5 × 3 + 1)/3 = (15 + 1)/3 = 16/3. Step 2: Write the division problem: 16/3 ÷ 2/3. Step 3: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. Step 4: Rewrite as multiplication: 16/3 × 3/2. Step 5: Multiply the numerators: 16 × 3 = 48. Step 6: Multiply the denominators: 3 × 2 = 6. Step 7: This gives 48/6. Step 8: Simplify: 48 ÷ 6 = 8. Final answer: Liam can make 8 batches of cookies.

5. 7/9 ÷ 5/11 = ? Answer: 77/45 Solution: Write the problem: 7/9 ÷ 5/11 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 5/11 is 11/5.
   Full step-by-step solution

   Step 1: Write the problem: 7/9 ÷ 5/11 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 5/11 is 11/5. Step 3: Rewrite: 7/9 × 11/5 Step 4: Multiply the numerators: 7 × 11 = 77 Step 5: Multiply the denominators: 9 × 5 = 45 Step 6: The result is 77/45. Check if it can be simplified: 77 and 45 have no common factors other than 1, so it is already in simplest form. Final answer: 77/45

6. A school is organizing a field trip and needs to transport 240 students. Each school bus can carry 5/8 of the total capacity of students that a regular bus holds. If a regular bus holds 48 students, how many school buses are needed to transport all the students? Answer: 8 Solution: Find how many students one school bus can carry. Each school bus carries 5/8 of a regular bus's capacity.
   Full step-by-step solution

   Step 1: Find how many students one school bus can carry. Each school bus carries 5/8 of a regular bus's capacity. Regular bus capacity = 48 students School bus capacity = (5/8) × 48 = (5 × 48)/8 = 240/8 = 30 students Step 2: Determine how many school buses are needed for 240 students. Number of buses = Total students ÷ Students per bus = 240 ÷ 30 = 8 The answer is 8.

7. 2/3 ÷ 4/5 = ? Answer: 5/6 Solution: We are dividing two fractions: 2/3 ÷ 4/5. Understand that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 4/5 is 5/4.
   Full step-by-step solution

   We are dividing two fractions: 2/3 ÷ 4/5. Step 1: Understand that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 4/5 is 5/4. Step 2: Rewrite the division as multiplication: 2/3 ÷ 4/5 = 2/3 × 5/4 Step 3: Multiply the numerators: 2 × 5 = 10 Step 4: Multiply the denominators: 3 × 4 = 12 Step 5: This gives the fraction 10/12 Step 6: Simplify 10/12 by dividing numerator and denominator by their greatest common factor, which is 2: 10 ÷ 2 = 5 12 ÷ 2 = 6 Step 7: The simplified fraction is 5/6. Final answer: 5/6

8. Matiu has a ribbon that is 8 yards long. Matiu cuts it into pieces that are each 4 yard long. How many pieces does Matiu get? Answer: 2 Solution: Total ribbon length: 8 yards. Each piece length: 4 yard. Number of pieces = 8 ÷ 4 = 8 × (1/4) = 2.
   Full step-by-step solution

   Step 1: Total ribbon length: 8 yards. Step 2: Each piece length: 4 yard. Step 3: Number of pieces = 8 ÷ 4 = 8 × (1/4) = 2. The answer is 2 pieces.

9. Tane has a ribbon that is 8 yards long. Tane cuts it into pieces that are each 2 yard long. How many pieces does Tane get? Answer: 4 Solution: Total ribbon length: 8 yards. Each piece length: 2 yard. Number of pieces = 8 ÷ 2 = 8 × (1/2) = 4.
   Full step-by-step solution

   Step 1: Total ribbon length: 8 yards. Step 2: Each piece length: 2 yard. Step 3: Number of pieces = 8 ÷ 2 = 8 × (1/2) = 4. The answer is 4 pieces.