Fraction × Whole

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Answer Key & Explanations

Fraction × Whole · Grade 5 · Worksheet 3

1. A rectangular garden is shown on a grid where each square represents 1 square meter. The garden is 8 meters long and 6 meters wide. Sophia plants flowers in 5/8 of the garden. How many square meters of the garden are planted with flowers? Answer: 30 Solution: Find the total area of the garden. The garden is 8 meters long and 6 meters wide. Area = length × width = 8 × 6 = 48 square meters.
   Full step-by-step solution

   Step 1: Find the total area of the garden. The garden is 8 meters long and 6 meters wide. Area = length × width = 8 × 6 = 48 square meters. Step 2: One-eighth of the garden is 1/8 of 48. Multiply: 1/8 × 48 = 48 ÷ 8 = 6 square meters. Step 3: Sophia plants flowers in 5/8 of the garden. So multiply the area of one-eighth by 5: 5 × 6 = 30 square meters. The answer is 30.

2. 7/8 × 960 = ? Answer: 840 Solution: Write the whole number as a fraction: 960 = 960/1 Multiply the fractions: (7/8) × (960/1) = (7 × 960)/(8 × 1) Calculate the numerator: 7 × 960 = 6720 Calculate the denominator: 8 × 1 = 8 Divide the numerator by the denominator: 6720 ÷ 8 = 840 The answer is 840.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 960 = 960/1 Step 2: Multiply the fractions: (7/8) × (960/1) = (7 × 960)/(8 × 1) Step 3: Calculate the numerator: 7 × 960 = 6720 Step 4: Calculate the denominator: 8 × 1 = 8 Step 5: Divide the numerator by the denominator: 6720 ÷ 8 = 840 The answer is 840.

3. 7/8 × 96 = ? Answer: 84 Solution: Write the whole number as a fraction: 96 = 96/1 Multiply the fractions: (7/8) × (96/1) = (7 × 96)/(8 × 1) Calculate the numerator: 7 × 96 = 672 Calculate the denominator: 8 × 1 = 8 Divide the numerator by the denominator: 672 ÷ 8 = 84 The answer is 84.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 96 = 96/1 Step 2: Multiply the fractions: (7/8) × (96/1) = (7 × 96)/(8 × 1) Step 3: Calculate the numerator: 7 × 96 = 672 Step 4: Calculate the denominator: 8 × 1 = 8 Step 5: Divide the numerator by the denominator: 672 ÷ 8 = 84 The answer is 84.

4. A rectangular swimming pool is drawn on a coordinate plane with corners at (1,2), (7,2), (7,6), and (1,6). Each unit on the grid represents 3 meters. What is the area of the swimming pool in square meters? Answer: 216 Solution: Find the length of the rectangle using the x-coordinates: 7 - 1 = 6 units Find the width of the rectangle using the y-coordinates: 6 - 2 = 4 units Calculate the area in grid units: 6 × 4 = 24 square units Convert to actual meters: Each unit represents 3 meters, so area = 24 × (3 × 3) = 24 × 9…
   Full step-by-step solution

   Step 1: Find the length of the rectangle using the x-coordinates: 7 - 1 = 6 units Step 2: Find the width of the rectangle using the y-coordinates: 6 - 2 = 4 units Step 3: Calculate the area in grid units: 6 × 4 = 24 square units Step 4: Convert to actual meters: Each unit represents 3 meters, so area = 24 × (3 × 3) = 24 × 9 Step 5: Calculate final area: 24 × 9 = 216 The answer is 216 square meters.

5. A factory produces 720 meters of fabric per hour. If they use 5/8 of this fabric to make shirts, how many meters of fabric are used for shirts each hour? Answer: 450 Solution: The factory produces 720 meters of fabric per hour. They use 5/8 of this fabric to make shirts. We need to find how many meters of fabric are used for shirts each hour.
   Full step-by-step solution

   Step 1: Understand the problem. The factory produces 720 meters of fabric per hour. They use 5/8 of this fabric to make shirts. We need to find how many meters of fabric are used for shirts each hour. Step 2: Identify the operation needed. Using a fraction of a quantity means multiplying the total quantity by the fraction. So, fabric used for shirts = 720 × (5/8). Step 3: Perform the multiplication. First, multiply 720 by 5: 720 × 5 = 3600. Step 4: Divide by the denominator. Now divide 3600 by 8: 3600 ÷ 8 = 450. Step 5: Conclusion. Thus, the amount of fabric used for shirts each hour is 450 meters. Final answer: 450

6. 4/7 × 875 = ? Answer: 500 Solution: Write the whole number as a fraction: 875 = 875/1 Multiply the fractions: (4/7) × (875/1) = (4 × 875)/(7 × 1) Calculate the numerator: 4 × 875 = 3500 Calculate the denominator: 7 × 1 = 7 Divide the numerator by the denominator: 3500 ÷ 7 = 500 The answer is 500.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 875 = 875/1 Step 2: Multiply the fractions: (4/7) × (875/1) = (4 × 875)/(7 × 1) Step 3: Calculate the numerator: 4 × 875 = 3500 Step 4: Calculate the denominator: 7 × 1 = 7 Step 5: Divide the numerator by the denominator: 3500 ÷ 7 = 500 The answer is 500.

7. Mere is painting a large rectangular mural on a wall. The mural is divided into 15 equal rectangular sections arranged in a 3-by-5 grid. She has finished painting 2/3 of the total sections. How many sections has Mere painted? Answer: 10 Solution: The mural has 15 sections in total. To find 2/3 of the sections, first find 1/3 of the sections by dividing 15 by 3: 15 ÷ 3 = 5 sections in each third.
   Full step-by-step solution

   Step 1: The mural has 15 sections in total. Step 2: To find 2/3 of the sections, first find 1/3 of the sections by dividing 15 by 3: 15 ÷ 3 = 5 sections in each third. Step 3: Multiply the number of sections in one third by 2 to get two thirds: 5 × 2 = 10 sections. Step 4: Alternatively, multiply the whole number by the fraction: 15 × 2/3 = (15 × 2) / 3 = 30 / 3 = 10. Mere has painted 10 sections of the mural.