Fraction × Whole

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Answer Key & Explanations

Fraction × Whole · Grade 5 · Worksheet 1

1. 3/4 × 16 = ? Answer: 12 Solution: We need to multiply the fraction 3/4 by the whole number 16. Interpret the multiplication. Multiplying a fraction by a whole number means we take a fraction of that whole number.
   Full step-by-step solution

   Step 1: Understand the problem. We need to multiply the fraction 3/4 by the whole number 16. So the problem is: 3/4 × 16. Step 2: Interpret the multiplication. Multiplying a fraction by a whole number means we take a fraction of that whole number. Here, 3/4 of 16 means we divide 16 into 4 equal parts and then take 3 of those parts. Step 3: Perform the calculation. One method is to multiply the numerator (top number of the fraction) by the whole number, then divide by the denominator (bottom number of the fraction). So: 3/4 × 16 = (3 × 16) / 4 Step 4: Multiply 3 by 16. 3 × 16 = 48 Step 5: Divide 48 by 4. 48 ÷ 4 = 12 Step 6: Conclusion. Therefore, 3/4 × 16 = 12. Final answer: 12

2. A construction crew is building a new playground. They need to pour concrete for 3/4 of the playground's surface area. If the total playground area is 800 square meters, how many square meters need concrete? Answer: 600 Solution: Identify the fraction of the playground that needs concrete: 3/4 Identify the total area: 800 square meters Multiply the fraction by the total area: 3/4 × 800 Calculate 3/4 × 800 = (3 × 800) ÷ 4 = 2400 ÷ 4 = 600 The area that needs concrete is 600 square meters.
   Full step-by-step solution

   Step 1: Identify the fraction of the playground that needs concrete: 3/4 Step 2: Identify the total area: 800 square meters Step 3: Multiply the fraction by the total area: 3/4 × 800 Step 4: Calculate 3/4 × 800 = (3 × 800) ÷ 4 = 2400 ÷ 4 = 600 Step 5: The area that needs concrete is 600 square meters.

3. A construction crew is building a new playground. They need to pour concrete for 3/4 of the rectangular play area. If the entire play area requires 600 square feet of concrete, how many square feet of concrete do they need to pour for the portion they're building? Answer: 450 Solution: Identify the total area: 600 square feet Identify the fraction needed: 3/4 Multiply the total area by the fraction: 600 × 3/4 Calculate 600 × 3 = 1800 Divide 1800 by 4 = 450 The crew needs to pour 450 square feet of concrete
   Full step-by-step solution

   Step 1: Identify the total area: 600 square feet Step 2: Identify the fraction needed: 3/4 Step 3: Multiply the total area by the fraction: 600 × 3/4 Step 4: Calculate 600 × 3 = 1800 Step 5: Divide 1800 by 4 = 450 Step 6: The crew needs to pour 450 square feet of concrete

4. Tom is baking cookies. Each batch needs 2/4 cup of sugar. If Tom makes 4 batches of cookies, how many cups of sugar does Tom need in total? Answer: 2 Solution: Each batch needs 2/4 cup of sugar. Multiply the fraction by the number of batches: 2/4 × 4 = (2 × 4)/4 = 2.
   Full step-by-step solution

   Step 1: Each batch needs 2/4 cup of sugar. Step 2: Multiply the fraction by the number of batches: 2/4 × 4 = (2 × 4)/4 = 2. The answer is 2 cups of sugar.

5. 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.

6. A rectangular garden is divided into 8 equal sections. If 5 of these sections are planted with vegetables, what fraction of the garden is planted with vegetables? Express your answer as a fraction in simplest form. Answer: 5/8 Solution: The garden is divided into 8 equal sections. This means the whole garden is represented by 8 sections, so the total is 8/8. Identify how many sections are planted with vegetables.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is divided into 8 equal sections. This means the whole garden is represented by 8 sections, so the total is 8/8. Step 2: Identify how many sections are planted with vegetables. The problem says 5 sections are planted with vegetables. Step 3: Write the fraction of the garden that is planted with vegetables. Since 5 out of 8 sections are planted with vegetables, the fraction is 5/8. Step 4: Check if the fraction can be simplified. The numbers 5 and 8 have no common factors other than 1, so 5/8 is already in simplest form. Step 5: State the final answer. The fraction of the garden planted with vegetables is 5/8.

7. In gym class, Charlotte runs laps around the track. Each lap is 4/5 of a mile. If Charlotte runs 10 laps, how many miles does Charlotte run in total? Answer: 8 Solution: Each lap is 4/5 of a mile. Multiply the fraction by the number of laps: 4/5 × 10 = (4 × 10)/5 = 8.
   Full step-by-step solution

   Step 1: Each lap is 4/5 of a mile. Step 2: Multiply the fraction by the number of laps: 4/5 × 10 = (4 × 10)/5 = 8. The answer is 8 miles.

8. A rectangular garden measures 3/4 mile long and 2/5 mile wide. What is the area of the garden in square miles? Answer: 3/10 Solution: To find the area of a rectangle, we multiply the length by the width. Write down the given dimensions. Length = 3/4 mile Width = 2/5 mile Write the formula for the area of a rectangle.
   Full step-by-step solution

   To find the area of a rectangle, we multiply the length by the width. Step 1: Write down the given dimensions. Length = 3/4 mile Width = 2/5 mile Step 2: Write the formula for the area of a rectangle. Area = Length × Width Step 3: Substitute the given values into the formula. Area = (3/4) × (2/5) Step 4: Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 2 = 6 Denominator: 4 × 5 = 20 So, Area = 6/20 Step 5: Simplify the fraction. Find the greatest common factor (GCF) of 6 and 20. The GCF is 2. Divide both the numerator and the denominator by 2. 6 ÷ 2 = 3 20 ÷ 2 = 10 So, 6/20 simplifies to 3/10. Step 6: State the final answer. The area of the garden is 3/10 square miles.

9. Emma shades 7/9 of a rectangular grid that has 18 squares in total. How many squares does she shade? Answer: 14 Solution: The grid has 18 squares. The denominator is 9, so divide the 18 squares into 9 equal groups: 18 divided by 9 = 2 squares per group.
   Full step-by-step solution

   Step 1: The grid has 18 squares. The denominator is 9, so divide the 18 squares into 9 equal groups: 18 divided by 9 = 2 squares per group. Step 2: The numerator is 7, so Emma shades 7 of these groups: 7 groups times 2 squares per group = 14 squares. Step 3: Alternatively, multiply the whole number by the fraction: 18 times 7/9 = (18 times 7) divided by 9 = 126 divided by 9 = 14. Emma shades 14 squares.