Fraction × Whole

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Fraction × Whole · Grade 5 · Worksheet 3

1. Nikau is making fruit punch for a party. Each glass holds 3/8 of a pitcher. If Nikau pours 16 glasses, how many pitchers of punch does Nikau serve? Answer: 6 Solution: Each glass holds 3/8 of a pitcher. Multiply the fraction by the number of glasses: 3/8 × 16 = (3 × 16)/8 = 6.
   Full step-by-step solution

   Step 1: Each glass holds 3/8 of a pitcher. Step 2: Multiply the fraction by the number of glasses: 3/8 × 16 = (3 × 16)/8 = 6. The answer is 6 pitchers.

2. 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.

3. Emma is arranging a pattern of tiles on a rectangular board. The board is divided into 9 equal columns. She colors 2/3 of the columns blue. Each blue column contains 7 tiles. How many total tiles are in the blue columns? Answer: 42 Solution: Find the number of blue columns. 2/3 of 9 = (2/3) x 9 = 18/3 = 6 blue columns. Each blue column has 7 tiles.
   Full step-by-step solution

   Step 1: Find the number of blue columns. 2/3 of 9 = (2/3) x 9 = 18/3 = 6 blue columns. Step 2: Each blue column has 7 tiles. Multiply the number of blue columns by the tiles per column: 6 x 7 = 42. The answer is 42.

4. 4/7 × 84 = ? Answer: 48 Solution: Write the whole number as a fraction: 84 = 84/1 Multiply the fractions: (4/7) × (84/1) = (4 × 84)/(7 × 1) Calculate the numerator: 4 × 84 = 336 Calculate the denominator: 7 × 1 = 7 Divide the numerator by the denominator: 336 ÷ 7 = 48 The answer is 48.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 84 = 84/1 Step 2: Multiply the fractions: (4/7) × (84/1) = (4 × 84)/(7 × 1) Step 3: Calculate the numerator: 4 × 84 = 336 Step 4: Calculate the denominator: 7 × 1 = 7 Step 5: Divide the numerator by the denominator: 336 ÷ 7 = 48 The answer is 48.

5. A construction crew is building a new playground. They need to mix concrete for the foundation, and each batch requires 3/4 of a bag of cement. If they need to make 8 batches of concrete, how many total bags of cement will they use? Answer: 6 Solution: Identify the operation needed - multiplying a fraction by a whole number Write the multiplication problem: 3/4 × 8 Convert the whole number to a fraction: 8 = 8/1 Multiply the fractions: (3 × 8)/(4 × 1) = 24/4 Simplify the fraction: 24 ÷ 4 = 6 The construction crew will use 6 bags of cement in…
   Full step-by-step solution

   Step 1: Identify the operation needed - multiplying a fraction by a whole number Step 2: Write the multiplication problem: 3/4 × 8 Step 3: Convert the whole number to a fraction: 8 = 8/1 Step 4: Multiply the fractions: (3 × 8)/(4 × 1) = 24/4 Step 5: Simplify the fraction: 24 ÷ 4 = 6 Step 6: The construction crew will use 6 bags of cement in total.

6. Olivia is designing a rectangular flag that is 7/9 of a meter wide and 585 meters long. She draws the flag on a grid where each unit represents 1 meter. What is the area of the flag in square meters? Answer: 455 Solution: The area of a rectangle is length times width. Here, length = 585 meters and width = 7/9 meter. Multiply: 585 × (7/9) = (585 × 7) / 9.
   Full step-by-step solution

   Step 1: The area of a rectangle is length times width. Here, length = 585 meters and width = 7/9 meter. Step 2: Multiply: 585 × (7/9) = (585 × 7) / 9. Step 3: First, multiply 585 by 7: 585 × 7 = 4095. Step 4: Then, divide 4095 by 9: 4095 ÷ 9 = 455. Step 5: The area is 455 square meters. The answer is 455.

7. 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

8. Tane draws a rectangle on a coordinate grid. The four corners are at (10, 10), (10, 19), (25, 19), and (25, 10). Each unit on the grid represents 1 meter. He then shades 4/5 of the rectangle. What is the area of the shaded part in square meters? Answer: 108 Solution: Find the length of the rectangle. The x-coordinates go from 10 to 25, so length = 25 - 10 = 15 meters. Step 2: Find the width of the rectangle.
   Full step-by-step solution

   Step 1: Find the length of the rectangle. The x-coordinates go from 10 to 25, so length = 25 - 10 = 15 meters. Step 2: Find the width of the rectangle. The y-coordinates go from 10 to 19, so width = 19 - 10 = 9 meters. Step 3: Find the total area of the rectangle. Area = length × width = 15 × 9 = 135 square meters. Step 4: Tane shades 4/5 of the rectangle. To find 4/5 of 135, multiply: 4/5 × 135. Step 5: Write 135 as a fraction: 135/1. Multiply numerators: 4 × 135 = 540. Multiply denominators: 5 × 1 = 5. So 4/5 × 135 = 540/5. Step 6: Simplify 540/5 by dividing numerator and denominator by 5: 540 ÷ 5 = 108, 5 ÷ 5 = 1, so 540/5 = 108. The shaded area is 108 square meters.

9. Hana is designing a rectangular garden on a grid. The garden has corners at (0, 0), (504, 0), (504, 2/3), and (0, 2/3). Each unit on the grid represents 1 meter. What is the area of Hana's garden in square meters? Answer: 336 Solution: Find the length of the rectangle by subtracting the x-coordinates: 504 - 0 = 504 meters. Find the width of the rectangle by subtracting the y-coordinates: 2/3 - 0 = 2/3 meters.
   Full step-by-step solution

   Step 1: Find the length of the rectangle by subtracting the x-coordinates: 504 - 0 = 504 meters. Step 2: Find the width of the rectangle by subtracting the y-coordinates: 2/3 - 0 = 2/3 meters. Step 3: Use the area formula for a rectangle: area = length × width. Step 4: Multiply: 504 × 2/3 = (504 × 2) / 3 = 1008 / 3 = 336. The area of Hana's garden is 336 square meters.