Fraction Division Words

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Fraction Division Words · Grade 6 · Worksheet 2

1. Tane is building a traditional Māori fishing net. He has a piece of rope that is 7 1/3 meters long. He needs to cut the rope into pieces that are each 2/3 of a meter long to create the netting sections. How many complete pieces of rope can Tane cut? Answer: 11 Solution: Write the total rope length as an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3 meters. Divide the total length by the length of each piece: (22/3) ÷ (2/3).
   Full step-by-step solution

   Step 1: Write the total rope length as an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3 meters. Step 2: Divide the total length by the length of each piece: (22/3) ÷ (2/3). Step 3: To divide fractions, multiply by the reciprocal: (22/3) × (3/2). Step 4: Multiply the numerators: 22 × 3 = 66. Multiply the denominators: 3 × 2 = 6. This gives 66/6. Step 5: Simplify: 66 ÷ 6 = 11. Tane can cut 11 complete pieces of rope.

2. A school is organizing a field trip and needs to transport 180 students. Each school bus can carry 2/3 of the total capacity of students that a regular bus holds. If a regular bus holds 45 students, how many school buses are needed to transport all the students? Answer: 6 Solution: Find how many students one school bus can carry. A regular bus holds 45 students, and a school bus carries 2/3 of that. So, 2/3 × 45 = 90/3 = 30 students per school bus.
   Full step-by-step solution

   Step 1: Find how many students one school bus can carry. A regular bus holds 45 students, and a school bus carries 2/3 of that. So, 2/3 × 45 = 90/3 = 30 students per school bus. Step 2: Divide the total number of students by the capacity of one school bus to find how many buses are needed. 180 ÷ 30 = 6. Step 3: Since we can't have a fraction of a bus, and 6 is a whole number, we need 6 buses. The answer is 6.

3. Tane has 9 3/4 meters of ribbon. He cuts it into pieces that are each 1 1/2 meters long. How many pieces can he make? Answer: 6 1/2 Solution: Write the problem as a division: 9 3/4 ÷ 1 1/2. Convert both mixed numbers to improper fractions. 9 3/4 = (9 × 4 + 3)/4 = (36 + 3)/4 = 39/4 1 1/2 = (1 × 2 + 1)/2 = (2 + 1)/2 = 3/2 Rewrite the division: 39/4 ÷ 3/2.
   Full step-by-step solution

   Step 1: Write the problem as a division: 9 3/4 ÷ 1 1/2. Step 2: Convert both mixed numbers to improper fractions. 9 3/4 = (9 × 4 + 3)/4 = (36 + 3)/4 = 39/4 1 1/2 = (1 × 2 + 1)/2 = (2 + 1)/2 = 3/2 Step 3: Rewrite the division: 39/4 ÷ 3/2. Step 4: Multiply by the reciprocal of the second fraction: 39/4 × 2/3. Step 5: Multiply numerators: 39 × 2 = 78. Step 6: Multiply denominators: 4 × 3 = 12. Step 7: The result is 78/12. Step 8: Simplify by dividing numerator and denominator by their greatest common factor, 6: 78 ÷ 6 = 13, 12 ÷ 6 = 2. So 13/2. Step 9: Convert to a mixed number: 13/2 = 6 1/2. Final Answer: 6 1/2 pieces.

4. Emma has 7 1/2 cups of flour. She uses 3/4 cup of flour for each batch of cookies. How many batches of cookies can she make? Answer: 10 Solution: Convert the mixed number 7 1/2 to an improper fraction. 7 1/2 = (7 × 2 + 1)/2 = 15/2. Write the division problem: 15/2 ÷ 3/4.
   Full step-by-step solution

   Step 1: Convert the mixed number 7 1/2 to an improper fraction. 7 1/2 = (7 × 2 + 1)/2 = 15/2. Step 2: Write the division problem: 15/2 ÷ 3/4. Step 3: To divide fractions, multiply by the reciprocal of the divisor. The reciprocal of 3/4 is 4/3. Step 4: Rewrite as multiplication: 15/2 × 4/3. Step 5: Multiply the numerators: 15 × 4 = 60. Step 6: Multiply the denominators: 2 × 3 = 6. Step 7: Simplify: 60/6 = 10. Emma can make 10 batches of cookies.

5. 2/3 ÷ 3/4 = ? Answer: 8/9 Solution: To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal. Write down the problem. 2/3 ÷ 3/4 Change the division sign to a multiplication sign and flip the second fraction (find its reciprocal).
   Full step-by-step solution

   To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal. Step 1: Write down the problem. 2/3 ÷ 3/4 Step 2: Change the division sign to a multiplication sign and flip the second fraction (find its reciprocal). The reciprocal of 3/4 is 4/3. So the problem becomes: 2/3 × 4/3 Step 3: Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerators: 2 × 4 = 8 Denominators: 3 × 3 = 9 This gives us: 8/9 Step 4: Check if the fraction can be simplified. The fraction 8/9 has no common factors other than 1, so it is already in simplest form. Therefore, the final answer is 8/9.

6. A construction company needs to pave a 2,850-meter long road. Each day they can pave 3/4 of a kilometer. How many days will it take them to complete the entire road? (Remember: 1 kilometer = 1000 meters) Answer: 3.8 Solution: The road length is 2,850 meters. Each day they pave 3/4 of a kilometer. We know 1 kilometer = 1000 meters.
   Full step-by-step solution

   Let's go step-by-step. **Step 1: Understand the problem** The road length is 2,850 meters. Each day they pave 3/4 of a kilometer. We know 1 kilometer = 1000 meters. **Step 2: Convert daily paving length to meters** 3/4 kilometer = 3/4 × 1000 meters = 0.75 × 1000 = 750 meters per day. **Step 3: Find total days needed** Total road length = 2850 meters Daily paving = 750 meters Days = Total length ÷ Daily paving Days = 2850 ÷ 750 **Step 4: Perform the division** 2850 ÷ 750 = 2850 / 750 Simplify: divide numerator and denominator by 150: 2850 ÷ 150 = 19 750 ÷ 150 = 5 So 2850 / 750 = 19 / 5 = 3.8 **Step 5: Interpret the result** 3.8 days means 3 full days and 0.8 of the fourth day. **Final Answer:** 3.8

7. Aroha has 7 1/3 cups of flour. She uses 2/3 cup of flour for each batch of cookies. How many batches of cookies can she make? Answer: 11 Solution: Convert the mixed number 7 1/3 to an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3. Write the division problem: 22/3 ÷ 2/3.
   Full step-by-step solution

   Step 1: Convert the mixed number 7 1/3 to an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3. Step 2: Write the division problem: 22/3 ÷ 2/3. Step 3: To divide fractions, multiply by the reciprocal of the divisor. The reciprocal of 2/3 is 3/2. Step 4: 22/3 × 3/2 = (22 × 3) / (3 × 2) = 66/6. Step 5: Simplify 66/6 by dividing numerator and denominator by 6: 66 ÷ 6 = 11, 6 ÷ 6 = 1, so 66/6 = 11/1 = 11. Final answer: Aroha can make 11 batches of cookies.

8. A rectangular garden is drawn on a coordinate plane with vertices at (2, 1), (14, 1), (14, 9), and (2, 9). The gardener wants to create a triangular vegetable patch using the diagonal from (2, 1) to (14, 9) and the side from (2, 1) to (2, 9). What is the area of this triangular vegetable patch in square units? Answer: 48 Solution: Find the dimensions of the rectangle. The length is from x=2 to x=14, so 14 - 2 = 12 units. The width is from y=1 to y=9, so 9 - 1 = 8 units.
   Full step-by-step solution

   Step 1: Find the dimensions of the rectangle. The length is from x=2 to x=14, so 14 - 2 = 12 units. The width is from y=1 to y=9, so 9 - 1 = 8 units. Step 2: The triangular vegetable patch has vertices at (2,1), (14,9), and (2,9). This triangle uses the left side of the rectangle as one side and the diagonal as another side. Step 3: The base of the triangle is the left side from (2,1) to (2,9), which has length 8 units. Step 4: The height of the triangle is the horizontal distance from the base to the opposite vertex at (14,9), which is 14 - 2 = 12 units. Step 5: Calculate the area using the formula: Area = 1/2 × base × height Area = 1/2 × 8 × 12 Area = 1/2 × 96 Area = 48 square units The answer is 48.

9. Aroha has 10 2/3 meters of fabric. She cuts it into pieces that are each 2/3 meter long. How many pieces does she get? Answer: 16 Solution: Write the total length as an improper fraction. 10 2/3 = (10 × 3 + 2)/3 = (30 + 2)/3 = 32/3 meters. Write the division problem: 32/3 ÷ 2/3.
   Full step-by-step solution

   Step 1: Write the total length as an improper fraction. 10 2/3 = (10 × 3 + 2)/3 = (30 + 2)/3 = 32/3 meters. Step 2: Write the division problem: 32/3 ÷ 2/3. Step 3: To divide by a fraction, multiply by its reciprocal. The reciprocal of 2/3 is 3/2. Step 4: Rewrite as multiplication: 32/3 × 3/2. Step 5: Multiply the numerators: 32 × 3 = 96. Step 6: Multiply the denominators: 3 × 2 = 6. Step 7: This gives 96/6. Step 8: Simplify: 96 ÷ 6 = 16. Final Answer: 16 pieces.