Whole ÷ Fraction

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Whole ÷ Fraction · Grade 5 · Worksheet 1

1. A school is organizing a field trip and needs to prepare snack bags. They have 8 kilograms of trail mix to distribute equally into bags that each hold 2/5 of a kilogram. How many complete snack bags can they make? Answer: 20 Solution: We need to find how many times 2/5 fits into 8. This is a division problem: 8 ÷ (2/5) Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2.
   Full step-by-step solution

   Step 1: We need to find how many times 2/5 fits into 8. This is a division problem: 8 ÷ (2/5) Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2. Step 3: Multiply 8 × (5/2) = (8 × 5)/2 = 40/2 = 20 Step 4: Since we're asked for complete snack bags, and 20 is a whole number, we have exactly 20 complete bags. The school can make 20 complete snack bags.

2. A school is organizing a field trip and needs to fill water bottles for all the students. They have a large 8-gallon water cooler. If each student's water bottle holds 2/5 of a gallon, how many complete water bottles can be filled from the full cooler? Answer: 20 Solution: We need to find how many 2/5 gallon portions fit into 8 gallons.
   Full step-by-step solution

   Step 1: We need to find how many 2/5 gallon portions fit into 8 gallons. Step 2: This is a division problem: 8 ÷ (2/5) Step 3: To divide by a fraction, we multiply by its reciprocal: 8 × (5/2) Step 4: Multiply 8 by 5: 8 × 5 = 40 Step 5: Divide 40 by 2: 40 ÷ 2 = 20 Step 6: Since the question asks for complete bottles, and 20 is a whole number, we have exactly 20 complete bottles. The answer is 20.

3. 12 ÷ 2/3 = ? Answer: 18 Solution: We are given: 12 ÷ 2/3 Understand the division by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2.
   Full step-by-step solution

   We are given: 12 ÷ 2/3 Step 1: Understand the division by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2. Step 2: Rewrite the expression: 12 ÷ 2/3 = 12 × 3/2 Step 3: Multiply 12 by 3/2: First, multiply 12 by 3: 12 × 3 = 36 Step 4: Now divide 36 by 2: 36 ÷ 2 = 18 Step 5: Final answer: 12 ÷ 2/3 = 18

4. Liam is making friendship bracelets for his class. He has 6 meters of colorful yarn. If each bracelet requires 3/4 of a meter of yarn, how many complete bracelets can Liam make? Answer: 8 Solution: We are told Liam has 6 meters of yarn and each bracelet uses 3/4 of a meter. We want to find how many complete bracelets he can make.
   Full step-by-step solution

   We are told Liam has 6 meters of yarn and each bracelet uses 3/4 of a meter. We want to find how many complete bracelets he can make. Step 1: Understand the problem We need to divide the total yarn length by the yarn length per bracelet: Total bracelets possible = (Total yarn) ÷ (Yarn per bracelet) Step 2: Write the division Total yarn = 6 meters Yarn per bracelet = 3/4 meter So: 6 ÷ (3/4) Step 3: Dividing by a fraction Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. So: 6 ÷ (3/4) = 6 × (4/3) Step 4: Multiply 6 × (4/3) = (6 × 4) / 3 = 24 / 3 Step 5: Simplify 24 / 3 = 8 Step 6: Interpret the result This means 8 complete bracelets can be made, with no yarn leftover for a 9th bracelet. Final answer: 8

5. Liam is making friendship bracelets for his class. He has a 6-meter long piece of colorful yarn. If each bracelet requires 3/4 of a meter of yarn, how many complete bracelets can Liam make? Answer: 8 Solution: Liam has 6 meters of yarn. Each bracelet uses 3/4 meter of yarn. We need to find how many complete bracelets he can make.
   Full step-by-step solution

   Step 1: Understand the problem. Liam has 6 meters of yarn. Each bracelet uses 3/4 meter of yarn. We need to find how many complete bracelets he can make. Step 2: Set up the division. To find the number of bracelets, divide the total yarn length by the yarn needed per bracelet: Number of bracelets = Total yarn ÷ Yarn per bracelet Number of bracelets = 6 ÷ (3/4) Step 3: Recall division with fractions. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. So: 6 ÷ (3/4) = 6 × (4/3) Step 4: Multiply. 6 × (4/3) = (6 × 4) / 3 = 24 / 3 Step 5: Simplify. 24 / 3 = 8 Step 6: Interpret the result. The result is exactly 8, meaning Liam can make 8 complete bracelets with no yarn left over. Final answer: 8

6. A construction crew needs to build a fence that is 750 feet long. Each section of fencing is 3/4 of a foot long. How many sections of fencing does the crew need to complete the entire fence? Answer: 1000 Solution: We need to find how many 3/4-foot sections are needed to make a 750-foot fence. We have a total length of 750 feet. Each section is 3/4 of a foot long.
   Full step-by-step solution

   We need to find how many 3/4-foot sections are needed to make a 750-foot fence. Step 1: Understand the problem. We have a total length of 750 feet. Each section is 3/4 of a foot long. We want the number of sections, which is: Total length ÷ Length per section. Step 2: Write the division. Number of sections = 750 ÷ (3/4) Step 3: Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, 750 ÷ (3/4) = 750 × (4/3) Step 4: Multiply 750 by 4. 750 × 4 = 3000 Step 5: Divide 3000 by 3. 3000 ÷ 3 = 1000 Step 6: Interpret the result. The crew needs 1000 sections to complete the fence. Final answer: 1000

7. A school is organizing a field trip and needs to fill water bottles for the students. They have a 10-gallon water cooler. If each student's water bottle holds 2/5 of a gallon, how many complete water bottles can they fill from the full cooler? Answer: 25 Solution: Identify the total amount of water: 10 gallons. Identify the amount per bottle: 2/5 of a gallon. To find how many bottles can be filled, divide the total water by the water per bottle: 10 ÷ (2/5).
   Full step-by-step solution

   Step 1: Identify the total amount of water: 10 gallons. Step 2: Identify the amount per bottle: 2/5 of a gallon. Step 3: To find how many bottles can be filled, divide the total water by the water per bottle: 10 ÷ (2/5). Step 4: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/5 is 5/2. Step 5: Calculate 10 × (5/2) = (10/1) × (5/2) = (10 × 5) / (1 × 2) = 50 / 2 = 25. Step 6: The problem asks for complete bottles, and 25 is a whole number, so they can fill 25 complete bottles. The answer is 25.

8. 24 ÷ 3/4 = ? Answer: 32 Solution: Write the division problem: 24 ÷ 3/4 Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3.
   Full step-by-step solution

   Step 1: Write the division problem: 24 ÷ 3/4 Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. Step 3: Rewrite the problem as multiplication: 24 × 4/3 Step 4: Multiply 24 by the numerator: 24 × 4 = 96 Step 5: Divide by the denominator: 96 ÷ 3 = 32 Step 6: The answer is 32.

9. A factory needs to package 600 kilograms of flour into bags that each hold 3/5 of a kilogram. How many bags will they need for all the flour? Answer: 1000 Solution: We need to find how many bags are needed for 600 kg of flour, with each bag holding 3/5 kg. This means we need to divide 600 by 3/5.
   Full step-by-step solution

   Step 1: We need to find how many bags are needed for 600 kg of flour, with each bag holding 3/5 kg. Step 2: This means we need to divide 600 by 3/5. Step 3: Dividing by a fraction is the same as multiplying by its reciprocal, so 600 ÷ 3/5 = 600 × 5/3. Step 4: Multiply 600 by 5 to get 3000. Step 5: Divide 3000 by 3 to get 1000. Step 6: The factory will need 1000 bags to package all the flour.