Fraction Division Words

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Fraction Division Words · Grade 6 · Worksheet 3

1. A factory produces 3/4 ton of recycled paper per hour. If they need to fill an order for 2 1/4 tons of paper, how many hours will it take to produce this amount? Express your answer as a fraction in simplest form. Answer: 3 Solution: The factory produces 3/4 ton per hour. They need to produce 2 1/4 tons total. We need to find how many hours it will take.
   Full step-by-step solution

   Step 1: Understand the problem. The factory produces 3/4 ton per hour. They need to produce 2 1/4 tons total. We need to find how many hours it will take. Step 2: Write the total needed as an improper fraction. 2 1/4 = 2 + 1/4 = 8/4 + 1/4 = 9/4 tons. Step 3: Let h be the number of hours. In h hours, the factory produces (3/4) * h tons. We set this equal to 9/4 tons: (3/4) * h = 9/4. Step 4: Solve for h. Multiply both sides by 4 to eliminate denominators: 3 * h = 9. Step 5: Divide both sides by 3: h = 9 / 3 = 3. Step 6: Conclusion. It will take 3 hours to produce 2 1/4 tons at a rate of 3/4 ton per hour.

2. Liam is making a special fruit punch for a school event. The recipe requires 3/4 cup of orange juice for every 2 cups of apple juice. If Liam wants to use 5 cups of apple juice, how many cups of orange juice will he need? Answer: 1 7/8 Solution: The recipe says: 3/4 cup orange juice for every 2 cups apple juice. This means the ratio of orange juice to apple juice is: (3/4) : 2 How much orange juice per 1 cup of apple juice?
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the ratio** The recipe says: 3/4 cup orange juice for every 2 cups apple juice. This means the ratio of orange juice to apple juice is: (3/4) : 2 --- **Step 2: Find the unit rate** How much orange juice per 1 cup of apple juice? Divide both parts of the ratio by 2: Orange juice = (3/4) ÷ 2 = (3/4) × (1/2) = 3/8 cup So for 1 cup apple juice, you need 3/8 cup orange juice. --- **Step 3: Apply to 5 cups of apple juice** Multiply the unit rate by 5: Orange juice needed = 5 × (3/8) = 15/8 cups. --- **Step 4: Convert to mixed number** 15/8 = 8/8 + 7/8 = 1 + 7/8 = 1 7/8 cups. --- **Step 5: Check** From the original ratio: 2 cups apple → 3/4 cup orange Multiply apple by 2.5 to get 5 cups: 3/4 × 2.5 = 3/4 × 5/2 = 15/8 = 1 7/8 cups. ✓ --- **Final answer:** 1 7/8

3. 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 large charter bus can hold. If a large charter bus can transport 45 students, how many school buses are needed to transport all the students? Answer: 6 Solution: Find the capacity of one school bus. A school bus carries 2/3 of what a charter bus carries. Charter bus capacity = 45 students.
   Full step-by-step solution

   Step 1: Find the capacity of one school bus. A school bus carries 2/3 of what a charter bus carries. Charter bus capacity = 45 students. School bus capacity = (2/3) × 45 = 90/3 = 30 students. Step 2: Determine how many school buses are needed for 180 students. Number of buses = Total students ÷ Capacity per bus = 180 ÷ 30 = 6. Step 3: Verify: 6 buses × 30 students/bus = 180 students, which matches the total. The answer is 6.

4. Noah has 7 1/6 cups of flour. He wants to make batches of cookies that each require 2/3 cup of flour. How many full batches can he make? Answer: 10 Solution: Convert the mixed number 7 1/6 to an improper fraction. 7 1/6 = (7 × 6 + 1)/6 = (42 + 1)/6 = 43/6. Write the division problem: 43/6 ÷ 2/3.
   Full step-by-step solution

   Step 1: Convert the mixed number 7 1/6 to an improper fraction. 7 1/6 = (7 × 6 + 1)/6 = (42 + 1)/6 = 43/6. Step 2: Write the division problem: 43/6 ÷ 2/3. Step 3: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. So, 43/6 × 3/2. Step 4: Multiply the numerators: 43 × 3 = 129. Step 5: Multiply the denominators: 6 × 2 = 12. Step 6: This gives 129/12. Step 7: Simplify the fraction. Divide numerator and denominator by 3: 129 ÷ 3 = 43, 12 ÷ 3 = 4. So 129/12 = 43/4. Step 8: Convert 43/4 to a mixed number: 43 ÷ 4 = 10 remainder 3, so 10 3/4. Step 9: Since we need full batches, we take only the whole number part: 10. Final answer: 10.

5. Liam has a ribbon that is 9 yards long. Liam cuts it into pieces that are each 3 yard long. How many pieces does Liam get? Answer: 3 Solution: Total ribbon length: 9 yards. Each piece length: 3 yard. Number of pieces = 9 ÷ 3 = 9 × (1/3) = 3.
   Full step-by-step solution

   Step 1: Total ribbon length: 9 yards. Step 2: Each piece length: 3 yard. Step 3: Number of pieces = 9 ÷ 3 = 9 × (1/3) = 3. The answer is 3 pieces.

6. Noah has 7 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: 11 Solution: Convert the mixed number to an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3. Divide the total flour by the amount per batch: 22/3 ÷ 2/3.
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction. 7 1/3 = (7 × 3 + 1)/3 = (21 + 1)/3 = 22/3. Step 2: Divide the total flour by the amount per batch: 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: Noah can make 11 batches of cookies.

7. Tane is making gift bags for a party. Each gift bag needs 3 cup of candy. If Tane has 6 cups of candy, how many full gift bags can Tane make? Answer: 2 Solution: Identify the total candy: 6 cups. Each bag needs 3 cup. Divide: 6 ÷ 3 = 6 ÷ (3) = 6 × (1/3) = 2.
   Full step-by-step solution

   Step 1: Identify the total candy: 6 cups. Step 2: Each bag needs 3 cup. Step 3: Divide: 6 ÷ 3 = 6 ÷ (3) = 6 × (1/3) = 2. The answer is 2 full gift bags.

8. Liam is mixing paint for an art project. He needs to create 3/4 of a liter of purple paint by mixing red and blue paint in a ratio of 2:3. How many milliliters of red paint does Liam need? (Remember: 1 liter = 1000 milliliters) Answer: 300 Solution: Liam needs 3/4 of a liter of purple paint. The mixing ratio of red to blue is 2:3. We are asked for the amount of red paint in milliliters.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the problem** Liam needs 3/4 of a liter of purple paint. The mixing ratio of red to blue is 2:3. We are asked for the amount of red paint in milliliters. --- **Step 2: Convert total paint volume to milliliters** 1 liter = 1000 milliliters. So 3/4 liter = (3/4) × 1000 ml = 0.75 × 1000 ml = 750 ml. Total purple paint = 750 ml. --- **Step 3: Understand the ratio** Red : Blue = 2 : 3 This means for every 2 parts red, there are 3 parts blue. Total parts = 2 + 3 = 5 parts. --- **Step 4: Find the amount of red paint in liters (fraction of total)** Fraction of total mixture that is red = 2/5. So red paint volume in liters = (2/5) × (3/4 liters) = (2/5) × (3/4) = 6/20 = 3/10 liters. --- **Step 5: Convert red paint volume to milliliters** 3/10 liters = (3/10) × 1000 ml = 0.3 × 1000 ml = 300 ml. --- **Step 6: Conclusion** Liam needs **300 milliliters** of red paint. --- **Final answer:** 300

9. A recipe for a large batch of cookies requires 3/4 cup of chocolate chips. Liam has 4 1/2 cups of chocolate chips. How many full batches of cookies can he make? Answer: 6 Solution: - One batch requires 3/4 cup of chocolate chips. - Liam has 4 1/2 cups of chocolate chips. Convert 4 1/2 into an improper fraction.
   Full step-by-step solution

   We are told: - One batch requires 3/4 cup of chocolate chips. - Liam has 4 1/2 cups of chocolate chips. Step 1: Convert 4 1/2 into an improper fraction. 4 1/2 = 4 + 1/2 = 8/2 + 1/2 = 9/2 cups. Step 2: We need to find how many batches he can make. Number of batches = (total chips) ÷ (chips per batch) = (9/2) ÷ (3/4) Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. (9/2) ÷ (3/4) = (9/2) × (4/3) Step 4: Multiply the fractions. Multiply numerators: 9 × 4 = 36 Multiply denominators: 2 × 3 = 6 So we have 36/6. Step 5: Simplify 36/6. 36 ÷ 6 = 6. Step 6: The problem asks for full batches. Since 6 is a whole number, he can make 6 full batches. Final answer: 6