Fraction Division

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Answer Key & Explanations

Fraction Division · Grade 5 · Worksheet 3

1. A rectangular prism has a length of 15.2 cm, a width of 6.8 cm, and a height of 4.5 cm. What is the volume of this prism in cubic centimeters? Answer: 465.12 Solution: The formula for the volume of a rectangular prism is length × width × height. Write down the given dimensions: length = 15.2 cm, width = 6.8 cm, height = 4.5 cm. Multiply the length and width first: 15.2 × 6.8.
   Full step-by-step solution

   Step 1: The formula for the volume of a rectangular prism is length × width × height. Step 2: Write down the given dimensions: length = 15.2 cm, width = 6.8 cm, height = 4.5 cm. Step 3: Multiply the length and width first: 15.2 × 6.8. 15.2 × 6.8 = 103.36 Step 4: Now multiply this result by the height: 103.36 × 4.5. 103.36 × 4.5 = 465.12 Step 5: The volume is 465.12 cubic centimeters.

2. Olivia is making a model of a garden path. She has a board that is 3/5 of a metre long. She needs to cut the board into equal sections, each 1/15 of a metre long, to represent stepping stones. How many stepping stone sections can Olivia cut from the board? Answer: 9 Solution: We are dividing 3/5 of a metre into pieces that are each 1/15 of a metre. This is the division problem: 3/5 divided by 1/15. To divide fractions, multiply by the reciprocal of the second fraction.
   Full step-by-step solution

   Step 1: Understand the problem. We are dividing 3/5 of a metre into pieces that are each 1/15 of a metre. This is the division problem: 3/5 divided by 1/15. Step 2: To divide fractions, multiply by the reciprocal of the second fraction. The reciprocal of 1/15 is 15/1. So, 3/5 divided by 1/15 equals 3/5 times 15/1. Step 3: Multiply the numerators: 3 times 15 = 45. Step 4: Multiply the denominators: 5 times 1 = 5. Step 5: Simplify the fraction: 45/5 = 9. The answer is 9 stepping stone sections.

3. A rectangular prism has a length of 12 cm, a width of 8 cm, and a height of 5 cm. What is the volume of this prism in cubic centimeters? Answer: 480 Solution: To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Write down the given measurements.
   Full step-by-step solution

   To find the volume of a rectangular prism, we use the formula: Volume = length × width × height Step 1: Write down the given measurements. Length = 12 cm Width = 8 cm Height = 5 cm Step 2: Substitute the given numbers into the volume formula. Volume = 12 × 8 × 5 Step 3: Perform the multiplication step by step. First, multiply the length and the width. 12 × 8 = 96 Step 4: Now multiply this result by the height. 96 × 5 = 480 Step 5: State the final answer with the correct units. The volume of the rectangular prism is 480 cubic centimeters.

4. Liam is making a large batch of lemonade for a school event. He has 3.5 liters of lemon juice concentrate. If each pitcher of lemonade requires 0.25 liters of concentrate, how many full pitchers can Liam make? Answer: 14 Solution: We are told that Liam has 3.5 liters of lemon juice concentrate. Each pitcher requires 0.25 liters of concentrate. We want to know how many full pitchers he can make.
   Full step-by-step solution

   We are told that Liam has 3.5 liters of lemon juice concentrate. Each pitcher requires 0.25 liters of concentrate. We want to know how many full pitchers he can make. Step 1: Write the problem as a division. Total concentrate = 3.5 liters Concentrate per pitcher = 0.25 liters Number of pitchers = Total concentrate ÷ Concentrate per pitcher Number of pitchers = 3.5 ÷ 0.25 Step 2: Make the division easier to handle. Dividing by 0.25 is the same as multiplying by 4, because 1 ÷ 0.25 = 4. So 3.5 ÷ 0.25 = 3.5 × 4 Step 3: Multiply. 3.5 × 4 = 14 Step 4: Interpret the result. Since 14 is a whole number, Liam can make exactly 14 full pitchers with no leftover concentrate. Answer: 14

5. A factory produces 840 meters of fabric each day. The fabric is cut into equal pieces that are each 3/5 of a meter long. How many pieces of fabric does the factory produce each day? Answer: 1400 Solution: The factory produces 840 meters of fabric total Each piece is 3/5 of a meter long To find how many pieces, divide the total fabric by the length of each piece: 840 ÷ (3/5) Dividing by a fraction is the same as multiplying by its reciprocal: 840 × (5/3) Calculate 840 × 5 = 4200 Divide 4200 ÷ 3 =…
   Full step-by-step solution

   Step 1: The factory produces 840 meters of fabric total Step 2: Each piece is 3/5 of a meter long Step 3: To find how many pieces, divide the total fabric by the length of each piece: 840 ÷ (3/5) Step 4: Dividing by a fraction is the same as multiplying by its reciprocal: 840 × (5/3) Step 5: Calculate 840 × 5 = 4200 Step 6: Divide 4200 ÷ 3 = 1400 Step 7: The factory produces 1400 pieces of fabric each day The answer is 1400.

6. 7/9 ÷ 1/3 = ? Answer: 7/3 Solution: Write the division problem: 7/9 ÷ 1/3 Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/3 is 3/1.
   Full step-by-step solution

   Step 1: Write the division problem: 7/9 ÷ 1/3 Step 2: Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/3 is 3/1. Step 3: Rewrite the problem as multiplication: 7/9 × 3/1 Step 4: Multiply the numerators: 7 × 3 = 21 Step 5: Multiply the denominators: 9 × 1 = 9 Step 6: Simplify the fraction: 21/9 = 7/3 The answer is 7/3.