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Fraction Division

Grade 5 · Fractions · Worksheet 1

  1. Liam is making a large batch of lemonade for a school event. He has 3/4 of a cup of lemon juice concentrate and needs to divide it equally among 6 pitchers. What fraction of a cup of lemon juice concentrate should he put in each pitcher? Answer: ______________
  2. 8/9 ÷ 2/3 = ? Answer: ______________
  3. 3/4 ÷ 1/8 = ? Answer: ______________
  4. Emma is making a large batch of cookies for a bake sale. The recipe requires 3/4 cup of chocolate chips for each batch. If she has 5 1/4 cups of chocolate chips in total, how many full batches of cookies can Emma make? Answer: ______________
  5. Liam is making a special trail mix for his hiking club. He has 3/4 pound of almonds and wants to divide them equally into small bags that each hold 1/8 pound. How many bags can Liam fill with almonds? Answer: ______________
  6. Emma is making a large batch of soup for a community dinner. She has 2 1/2 liters of vegetable broth and needs to divide it equally among several pots. If each pot requires 3/4 of a liter of broth, how many full pots of soup can Emma make? Answer: ______________
  7. A rectangular prism-shaped fish tank has a length of 2.5 meters, a width of 1.2 meters, and a height of 0.8 meters. What is the volume of the fish tank in cubic meters?
    Answer: ______________
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Answer Key & Explanations

Fraction Division · Grade 5 · Worksheet 1

  1. Liam is making a large batch of lemonade for a school event. He has 3/4 of a cup of lemon juice concentrate and needs to divide it equally among 6 pitchers. What fraction of a cup of lemon juice concentrate should he put in each pitcher? Answer: 1/8 Solution: Liam has 3/4 of a cup of lemon juice concentrate. He needs to divide it equally among 6 pitchers.
    Full step-by-step solution

    Liam has 3/4 of a cup of lemon juice concentrate. He needs to divide it equally among 6 pitchers. Step 1: Understand the operation. Dividing 3/4 cup among 6 pitchers means we need to calculate: (3/4) ÷ 6 Step 2: Dividing by a whole number is the same as multiplying by its reciprocal. So, (3/4) ÷ 6 = (3/4) × (1/6) Step 3: Multiply the numerators and denominators. Numerator: 3 × 1 = 3 Denominator: 4 × 6 = 24 So we get 3/24 Step 4: Simplify the fraction. Both 3 and 24 can be divided by 3: 3 ÷ 3 = 1 24 ÷ 3 = 8 So, 3/24 = 1/8 Therefore, Liam should put 1/8 of a cup of lemon juice concentrate in each pitcher.

  2. 8/9 ÷ 2/3 = ? Answer: 4/3 Solution: Write the division problem: 8/9 ÷ 2/3 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2.
    Full step-by-step solution

    Step 1: Write the division problem: 8/9 ÷ 2/3 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. Step 3: Rewrite the problem as multiplication: 8/9 × 3/2 Step 4: Multiply the numerators: 8 × 3 = 24 Step 5: Multiply the denominators: 9 × 2 = 18 Step 6: Simplify the fraction: 24/18 = 4/3 The answer is 4/3.

  3. 3/4 ÷ 1/8 = ? Answer: 6 Solution: Write the division problem: 3/4 ÷ 1/8 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/8 is 8/1.
    Full step-by-step solution

    Step 1: Write the division problem: 3/4 ÷ 1/8 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/8 is 8/1. Step 3: Rewrite the problem as multiplication: 3/4 × 8/1 Step 4: Multiply the numerators: 3 × 8 = 24 Step 5: Multiply the denominators: 4 × 1 = 4 Step 6: Simplify the fraction: 24/4 = 6 The answer is 6.

  4. Emma is making a large batch of cookies for a bake sale. The recipe requires 3/4 cup of chocolate chips for each batch. If she has 5 1/4 cups of chocolate chips in total, how many full batches of cookies can Emma make? Answer: 7 Solution: Convert the mixed number to an improper fraction. Emma has 5 1/4 cups of chocolate chips. 5 1/4 = (5 × 4 + 1)/4 = 21/4 cups.
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction. Emma has 5 1/4 cups of chocolate chips. 5 1/4 = (5 × 4 + 1)/4 = 21/4 cups. Step 2: Each batch requires 3/4 cup of chocolate chips. To find how many batches she can make, divide the total amount by the amount per batch: (21/4) ÷ (3/4). Step 3: Dividing by a fraction is the same as multiplying by its reciprocal. So, (21/4) ÷ (3/4) = (21/4) × (4/3). Step 4: Multiply the fractions: (21/4) × (4/3) = (21 × 4)/(4 × 3) = 84/12. Step 5: Simplify the fraction: 84 ÷ 12 = 7. Step 6: Since the problem asks for full batches, the answer is 7. The answer is 7.

  5. Liam is making a special trail mix for his hiking club. He has 3/4 pound of almonds and wants to divide them equally into small bags that each hold 1/8 pound. How many bags can Liam fill with almonds? Answer: 6 Solution: We are told that Liam has 3/4 pound of almonds and each bag holds 1/8 pound. We want to find how many bags he can fill.
    Full step-by-step solution

    We are told that Liam has 3/4 pound of almonds and each bag holds 1/8 pound. We want to find how many bags he can fill. Step 1: Understand the problem. We need to divide the total amount of almonds by the amount per bag: Total almonds = 3/4 pound Amount per bag = 1/8 pound Number of bags = (Total almonds) ÷ (Amount per bag) Step 2: Write the division expression. Number of bags = (3/4) ÷ (1/8) Step 3: Recall that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/8 is 8/1, which is 8. So, (3/4) ÷ (1/8) = (3/4) × (8/1) Step 4: Multiply the fractions. Multiply numerators: 3 × 8 = 24 Multiply denominators: 4 × 1 = 4 So we have 24/4 Step 5: Simplify 24/4. 24 ÷ 4 = 6 Step 6: Conclusion. Liam can fill 6 bags with almonds.

  6. Emma is making a large batch of soup for a community dinner. She has 2 1/2 liters of vegetable broth and needs to divide it equally among several pots. If each pot requires 3/4 of a liter of broth, how many full pots of soup can Emma make? Answer: 3 Solution: Convert the mixed number to an improper fraction. 2 1/2 = 5/2 We need to divide the total broth by the amount per pot: 5/2 ÷ 3/4 When dividing fractions, multiply by the reciprocal: 5/2 × 4/3 Multiply the numerators: 5 × 4 = 20 Multiply the denominators: 2 × 3 = 6 Simplify the fraction: 20/6 =…
    Full step-by-step solution

    Step 1: Convert the mixed number to an improper fraction. 2 1/2 = 5/2 Step 2: We need to divide the total broth by the amount per pot: 5/2 ÷ 3/4 Step 3: When dividing fractions, multiply by the reciprocal: 5/2 × 4/3 Step 4: Multiply the numerators: 5 × 4 = 20 Step 5: Multiply the denominators: 2 × 3 = 6 Step 6: Simplify the fraction: 20/6 = 10/3 = 3 1/3 Step 7: Since we can only make full pots, we take the whole number part: 3 The answer is 3 full pots.

  7. A rectangular prism-shaped fish tank has a length of 2.5 meters, a width of 1.2 meters, and a height of 0.8 meters. What is the volume of the fish tank in cubic meters? Answer: 2.4 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given values: Volume = 2.5 × 1.2 × 0.8 Multiply the first two numbers: 2.5 × 1.2 = 3.0 Multiply the result by the height: 3.0 × 0.8 = 2.4 The volume is 2.4 cubic meters.
    Full step-by-step solution

    Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given values: Volume = 2.5 × 1.2 × 0.8 Step 3: Multiply the first two numbers: 2.5 × 1.2 = 3.0 Step 4: Multiply the result by the height: 3.0 × 0.8 = 2.4 Step 5: The volume is 2.4 cubic meters.