Fraction Multiplication

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Answer Key & Explanations

Fraction Multiplication · Grade 5 · Worksheet 1

1. A rectangular prism is drawn with a length of 6 cm, width of 4 cm, and height of 5 cm. What is the volume of this prism in cubic centimeters? Answer: 120 Solution: The formula for volume of a rectangular prism is length × width × height Substitute the given measurements: 6 cm × 4 cm × 5 cm First multiply 6 × 4 = 24 Then multiply 24 × 5 = 120 The volume is 120 cubic centimeters The answer is 120.
   Full step-by-step solution

   Step 1: The formula for volume of a rectangular prism is length × width × height Step 2: Substitute the given measurements: 6 cm × 4 cm × 5 cm Step 3: First multiply 6 × 4 = 24 Step 4: Then multiply 24 × 5 = 120 Step 5: The volume is 120 cubic centimeters The answer is 120.

2. Liam is building a rectangular garden that measures 3/4 meters wide and 2 1/2 meters long. What is the total area of Liam's garden in square meters? Answer: 1 7/8 Solution: To find the area of a rectangle, multiply the length by the width. Write down the given measurements. Width = 3/4 meters Length = 2 1/2 meters Convert the mixed number for the length into an improper fraction to make multiplication easier.
   Full step-by-step solution

   To find the area of a rectangle, multiply the length by the width. Step 1: Write down the given measurements. Width = 3/4 meters Length = 2 1/2 meters Step 2: Convert the mixed number for the length into an improper fraction to make multiplication easier. 2 1/2 = (2 * 2 + 1) / 2 = (4 + 1) / 2 = 5/2 Step 3: Multiply the length and the width. Area = (Length) * (Width) Area = (5/2) * (3/4) Step 4: Multiply the fractions. Multiply the numerators together: 5 * 3 = 15 Multiply the denominators together: 2 * 4 = 8 So, Area = 15/8 Step 5: Convert the improper fraction to a mixed number. Divide 15 by 8. 8 goes into 15 one time (1 * 8 = 8). The remainder is 15 - 8 = 7. So, 15/8 = 1 7/8 Step 6: State the final answer with units. The total area of Liam's garden is 1 7/8 square meters.

3. 2/3 × 750 = ? Answer: 500 Solution: Understand that 2/3 × 750 means finding two-thirds of 750 First find one-third of 750 by dividing: 750 ÷ 3 = 250 Since we need two-thirds, multiply the result by 2: 250 × 2 = 500 Therefore, 2/3 × 750 = 500 The answer is 500.
   Full step-by-step solution

   Step 1: Understand that 2/3 × 750 means finding two-thirds of 750 Step 2: First find one-third of 750 by dividing: 750 ÷ 3 = 250 Step 3: Since we need two-thirds, multiply the result by 2: 250 × 2 = 500 Step 4: Therefore, 2/3 × 750 = 500 The answer is 500.

4. Sophia is making a large batch of lemonade for a school fundraiser. The recipe calls for 8 cups of water. She decides to make only 3/4 of the recipe to test it first. What does 3/4 × 8 mean in this situation, and how many cups of water should Sophia use? Answer: 6 Solution: It means finding 3/4 of 8 cups of water. First, find what 1/4 of 8 is. 1/4 of 8 means dividing 8 into 4 equal parts: 8 ÷ 4 = 2.
   Full step-by-step solution

   Step 1: Understand the meaning of 3/4 × 8. It means finding 3/4 of 8 cups of water. Step 2: First, find what 1/4 of 8 is. 1/4 of 8 means dividing 8 into 4 equal parts: 8 ÷ 4 = 2. So, 1/4 of 8 is 2 cups. Step 3: Since we want 3/4, we take 3 of those parts: 3 × 2 = 6 cups. Step 4: Alternatively, multiply directly: 3/4 × 8 = (3 × 8) / 4 = 24 / 4 = 6. The answer is 6 cups.

5. 5/7 × 693 = ? Answer: 495 Solution: Understand that 5/7 × 693 means finding five-sevenths of 693 First find one-seventh of 693 by dividing: 693 ÷ 7 = 99 Since we need five-sevenths, multiply the result by 5: 99 × 5 = 495 Therefore, 5/7 × 693 = 495 The answer is 495.
   Full step-by-step solution

   Step 1: Understand that 5/7 × 693 means finding five-sevenths of 693 Step 2: First find one-seventh of 693 by dividing: 693 ÷ 7 = 99 Step 3: Since we need five-sevenths, multiply the result by 5: 99 × 5 = 495 Step 4: Therefore, 5/7 × 693 = 495 The answer is 495.

6. Liam is building a rectangular garden that measures 3/4 meters by 2/5 meters. He wants to cover the entire garden with soil. What is the total area of Liam's garden in square meters? Answer: 3/10 Solution: To find the area of a rectangle, multiply the length by the width. Write down the length and width. Length = 3/4 meters Width = 2/5 meters Multiply the two fractions.
   Full step-by-step solution

   To find the area of a rectangle, multiply the length by the width. Step 1: Write down the length and width. Length = 3/4 meters Width = 2/5 meters Step 2: Multiply the two fractions. Area = (3/4) * (2/5) Step 3: Multiply the numerators (top numbers) together. 3 * 2 = 6 Step 4: Multiply the denominators (bottom numbers) together. 4 * 5 = 20 Step 5: Write the new fraction. Area = 6/20 Step 6: Simplify the fraction by finding the greatest common factor of 6 and 20, which is 2. Divide both the numerator and denominator by 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 Step 7: Write the simplified fraction. Area = 3/10 Therefore, the total area of Liam's garden is 3/10 square meters.

7. Emma is making a fruit salad for a class party. She uses 3/4 of a cup of strawberries and 2/3 of a cup of blueberries. What is the total amount of fruit, in cups, that Emma uses for the salad? Answer: 17/12 Solution: Identify the fractions to be added: 3/4 and 2/3. Find a common denominator for 4 and 3. The least common multiple is 12.
   Full step-by-step solution

   Step 1: Identify the fractions to be added: 3/4 and 2/3. Step 2: Find a common denominator for 4 and 3. The least common multiple is 12. Step 3: Convert 3/4 to an equivalent fraction with denominator 12: (3/4) = (3 × 3)/(4 × 3) = 9/12. Step 4: Convert 2/3 to an equivalent fraction with denominator 12: (2/3) = (2 × 4)/(3 × 4) = 8/12. Step 5: Add the fractions: 9/12 + 8/12 = 17/12. Step 6: The fraction 17/12 is the total amount of fruit in cups. The answer is 17/12.