Whole ÷ Fraction

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Answer Key & Explanations

Whole ÷ Fraction · Grade 5 · Worksheet 3

1. A school is organizing a field trip and needs to pack snacks. They have 8 large bags of trail mix to distribute equally among students. If each student receives 2/5 of a bag, how many students can get a portion of trail mix? Answer: 20 Solution: We need to divide 8 bags by 2/5 of a bag per student Dividing by a fraction is the same as multiplying by its reciprocal 8 ÷ (2/5) = 8 × (5/2) 8 × 5 = 40 40 ÷ 2 = 20 Therefore, 20 students can get a portion of trail mix
   Full step-by-step solution

   Step 1: We need to divide 8 bags by 2/5 of a bag per student Step 2: Dividing by a fraction is the same as multiplying by its reciprocal Step 3: 8 ÷ (2/5) = 8 × (5/2) Step 4: 8 × 5 = 40 Step 5: 40 ÷ 2 = 20 Step 6: Therefore, 20 students can get a portion of trail mix

2. A construction crew needs to build a fence that is 720 feet long. Each section of fencing is 3/4 of a foot long. How many sections of fencing will they need to complete the entire fence? Answer: 960 Solution: We are told the total fence length is 720 feet, and each section is 3/4 of a foot long. We need to find the number of sections.
   Full step-by-step solution

   We are told the total fence length is 720 feet, and each section is 3/4 of a foot long. Step 1: Understand the problem We need to find the number of sections. If each section is 3/4 foot, then the number of sections times the length per section equals the total length. Let \( N \) = number of sections. We have: \( N \times (3/4) = 720 \) Step 2: Solve for \( N \) To find \( N \), divide both sides by \( 3/4 \): \( N = 720 \div (3/4) \) Step 3: Dividing by a fraction Dividing by \( 3/4 \) is the same as multiplying by its reciprocal \( 4/3 \): \( N = 720 \times (4/3) \) Step 4: Simplify the multiplication First, \( 720 \div 3 = 240 \). Then \( 240 \times 4 = 960 \). Step 5: Conclusion They need 960 sections to build the entire fence. Answer: 960

3. A factory needs to package 840 kilograms of flour into bags that each hold 3/5 of a kilogram. How many bags will they be able to fill completely? Answer: 1400 Solution: We need to find how many bags of 3/5 kg can be filled with 840 kg of flour. This means we need to calculate 840 ÷ (3/5). Dividing by a fraction is the same as multiplying by its reciprocal.
   Full step-by-step solution

   Step 1: We need to find how many bags of 3/5 kg can be filled with 840 kg of flour. This means we need to calculate 840 ÷ (3/5). Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/5 is 5/3. Step 3: So we calculate 840 × (5/3). Step 4: First, 840 ÷ 3 = 280 Step 5: Then, 280 × 5 = 1400 Step 6: The factory will be able to fill 1400 bags completely. The answer is 1400.

4. A rectangular garden is divided into sections for different vegetables. The garden is 12 meters long and 3/4 meter wide. If each vegetable section must be exactly 1/3 meter wide, how many complete vegetable sections can fit across the width of the garden? Answer: 2 Solution: The garden width is 3/4 meter and each section width is 1/3 meter To find how many sections fit, divide the total width by the section width: 3/4 ÷ 1/3 Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 × 3/1 Multiply the fractions: (3 × 3)/(4 × 1) = 9/4 Convert to a mixed…
   Full step-by-step solution

   Step 1: The garden width is 3/4 meter and each section width is 1/3 meter Step 2: To find how many sections fit, divide the total width by the section width: 3/4 ÷ 1/3 Step 3: Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 × 3/1 Step 4: Multiply the fractions: (3 × 3)/(4 × 1) = 9/4 Step 5: Convert to a mixed number: 9/4 = 2 1/4 Step 6: Since we need complete sections, we take the whole number part: 2 The answer is 2 complete vegetable sections.

5. A school is organizing a field trip and needs to prepare snack bags. They have 8 kilograms of trail mix to distribute equally among the students. If each snack bag should contain 2/5 of a kilogram of trail mix, how many complete snack bags can they make? Answer: 20 Solution: We need to divide the total trail mix by the amount per bag: 8 ÷ (2/5) Dividing by a fraction is the same as multiplying by its reciprocal: 8 × (5/2) Multiply the whole number by the numerator: 8 × 5 = 40 Divide by the denominator: 40 ÷ 2 = 20 Since we're asked for complete snack bags, and 20 is…
   Full step-by-step solution

   Step 1: We need to divide the total trail mix by the amount per bag: 8 ÷ (2/5) Step 2: Dividing by a fraction is the same as multiplying by its reciprocal: 8 × (5/2) Step 3: Multiply the whole number by the numerator: 8 × 5 = 40 Step 4: Divide by the denominator: 40 ÷ 2 = 20 Step 5: Since we're asked for complete snack bags, and 20 is a whole number, we have exactly 20 complete snack bags. The answer is 20 complete snack bags.

6. A rectangular garden is divided into 8 equal sections. If each section represents 1/4 of a flower bed, how many whole flower beds are represented by the entire garden? Answer: 2 Solution: The garden is divided into 8 equal sections. Each section represents 1/4 of a flower bed. We want to find how many whole flower beds are represented by the entire garden.
   Full step-by-step solution

   Let's go step-by-step. Step 1: Understand the problem. The garden is divided into 8 equal sections. Each section represents 1/4 of a flower bed. We want to find how many whole flower beds are represented by the entire garden. Step 2: Find the total fraction of flower beds represented by the garden. If 1 section = 1/4 flower bed, then 8 sections = 8 × (1/4) flower beds. Step 3: Multiply. 8 × (1/4) = 8/4. Step 4: Simplify the fraction. 8/4 = 2. Step 5: Interpret the result. 2 means 2 whole flower beds. So the entire garden represents 2 whole flower beds.

7. 8 ÷ 1/4 = ? Answer: 32 Solution: We are solving: 8 ÷ 1/4 Understand the division by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/4 is 4/1, which is just 4.
   Full step-by-step solution

   Step-by-step solution: We are solving: 8 ÷ 1/4 Step 1: Understand the division by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/4 is 4/1, which is just 4. Step 2: Rewrite the division as multiplication. So, 8 ÷ 1/4 becomes 8 × 4. Step 3: Perform the multiplication. 8 × 4 = 32 Step 4: Final answer. Therefore, 8 ÷ 1/4 = 32.

8. 8 ÷ 2/3 = ? Answer: 12 Solution: We are dividing 8 by the fraction 2/3. The expression is: 8 ÷ 2/3 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

   Step 1: Understand the problem We are dividing 8 by the fraction 2/3. The expression is: 8 ÷ 2/3 Step 2: Recall the rule for dividing by a fraction Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2. Step 3: Rewrite the division as multiplication So, 8 ÷ 2/3 becomes 8 × 3/2. Step 4: Multiply First, multiply 8 by the numerator 3: 8 × 3 = 24 Step 5: Divide by the denominator Now divide 24 by the denominator 2: 24 ÷ 2 = 12 Step 6: Conclusion Therefore, 8 ÷ 2/3 = 12.

9. A rectangular swimming pool is 12 meters long and is divided into equal sections for swimming lanes. Each swimming lane is exactly 3/4 meter wide. How many complete swimming lanes can fit across the width of the pool? Answer: 16 Solution: The pool is 12 meters wide and each lane is 3/4 meter wide.
   Full step-by-step solution

   Step 1: The pool is 12 meters wide and each lane is 3/4 meter wide. Step 2: To find how many lanes fit, divide the total width by the width of one lane: 12 ÷ 3/4 Step 3: Dividing by a fraction is the same as multiplying by its reciprocal: 12 × 4/3 Step 4: Multiply 12 by 4: 12 × 4 = 48 Step 5: Divide 48 by 3: 48 ÷ 3 = 16 Step 6: Since we're asked for complete lanes, and 16 is a whole number, we have exactly 16 complete lanes. The answer is 16.