Fraction × Whole

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Answer Key & Explanations

Fraction × Whole · Grade 5 · Worksheet 2

1. A construction crew is building a new playground. They need to install 3/4 of a ton of sand in each of the 8 sandboxes. How many tons of sand do they need in total? Answer: 6 Solution: When you multiply a fraction by a whole number, you're finding that fractional part of the whole number.
   Full step-by-step solution

   When you multiply a fraction by a whole number, you're finding that fractional part of the whole number. For example, if you needed 2/3 of a cup of flour for each of 6 recipes, you would multiply 2/3 by 6 to find the total flour needed.

2. 3/4 × 720 = ? Answer: 540 Solution: Write the whole number as a fraction: 720 = 720/1 Multiply the fractions: (3/4) × (720/1) = (3 × 720)/(4 × 1) Calculate the numerator: 3 × 720 = 2160 Calculate the denominator: 4 × 1 = 4 Divide the numerator by the denominator: 2160 ÷ 4 = 540 The answer is 540.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 720 = 720/1 Step 2: Multiply the fractions: (3/4) × (720/1) = (3 × 720)/(4 × 1) Step 3: Calculate the numerator: 3 × 720 = 2160 Step 4: Calculate the denominator: 4 × 1 = 4 Step 5: Divide the numerator by the denominator: 2160 ÷ 4 = 540 The answer is 540.

3. A construction crew is building a new playground. They need to pour concrete for 8 rectangular sections that will become activity areas. Each section requires 3/4 of a cubic meter of concrete. How many cubic meters of concrete do they need in total? Answer: 6 Solution: Identify the numbers to multiply: 8 sections × 3/4 cubic meter per section Write the multiplication: 8 × 3/4 Multiply the whole number by the numerator: 8 × 3 = 24 Keep the same denominator: 24/4 Simplify the fraction: 24 ÷ 4 = 6 The total concrete needed is 6 cubic meters
   Full step-by-step solution

   Step 1: Identify the numbers to multiply: 8 sections × 3/4 cubic meter per section Step 2: Write the multiplication: 8 × 3/4 Step 3: Multiply the whole number by the numerator: 8 × 3 = 24 Step 4: Keep the same denominator: 24/4 Step 5: Simplify the fraction: 24 ÷ 4 = 6 Step 6: The total concrete needed is 6 cubic meters

4. 3/5 × 20 = ? Answer: 12 Solution: Write the multiplication: 3/5 × 20 Multiply the numerator by the whole number: 3 × 20 = 60 Keep the same denominator: 60/5 Divide 60 by 5: 60 ÷ 5 = 12 The answer is 12.
   Full step-by-step solution

   Step 1: Write the multiplication: 3/5 × 20 Step 2: Multiply the numerator by the whole number: 3 × 20 = 60 Step 3: Keep the same denominator: 60/5 Step 4: Divide 60 by 5: 60 ÷ 5 = 12 The answer is 12.

5. Amelia is painting a fence. Each section of the fence takes 3/6 of a gallon of paint. If Amelia paints 8 sections, how many gallons of paint does Amelia use? Answer: 4 Solution: Each section uses 3/6 gallon of paint. Multiply the fraction by the number of sections: 3/6 × 8 = (3 × 8)/6 = 4.
   Full step-by-step solution

   Step 1: Each section uses 3/6 gallon of paint. Step 2: Multiply the fraction by the number of sections: 3/6 × 8 = (3 × 8)/6 = 4. The answer is 4 gallons.

6. 5/9 × 720 = ? Answer: 400 Solution: Write the whole number as a fraction: 720 = 720/1 Multiply the fractions: (5/9) × (720/1) = (5 × 720)/(9 × 1) Calculate the numerator: 5 × 720 = 3600 Calculate the denominator: 9 × 1 = 9 Divide the numerator by the denominator: 3600 ÷ 9 = 400 The answer is 400.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 720 = 720/1 Step 2: Multiply the fractions: (5/9) × (720/1) = (5 × 720)/(9 × 1) Step 3: Calculate the numerator: 5 × 720 = 3600 Step 4: Calculate the denominator: 9 × 1 = 9 Step 5: Divide the numerator by the denominator: 3600 ÷ 9 = 400 The answer is 400.

7. Tane is baking cookies. Each batch needs 2/4 cup of sugar. If Tane makes 8 batches of cookies, how many cups of sugar does Tane need in total? Answer: 4 Solution: Each batch needs 2/4 cup of sugar. Multiply the fraction by the number of batches: 2/4 × 8 = (2 × 8)/4 = 4.
   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 × 8 = (2 × 8)/4 = 4. The answer is 4 cups of sugar.

8. 3/5 × 25 = ? Answer: 15 Solution: Write the multiplication: 3/5 × 25 Multiply the numerator by the whole number: 3 × 25 = 75 Keep the same denominator: 75/5 Simplify the fraction: 75 ÷ 5 = 15 The answer is 15.
   Full step-by-step solution

   Step 1: Write the multiplication: 3/5 × 25 Step 2: Multiply the numerator by the whole number: 3 × 25 = 75 Step 3: Keep the same denominator: 75/5 Step 4: Simplify the fraction: 75 ÷ 5 = 15 The answer is 15.

9. Mere is painting a fence. Each section of the fence takes 3/6 of a gallon of paint. If Mere paints 10 sections, how many gallons of paint does Mere use? Answer: 5 Solution: Each section uses 3/6 gallon of paint. Multiply the fraction by the number of sections: 3/6 × 10 = (3 × 10)/6 = 5.
   Full step-by-step solution

   Step 1: Each section uses 3/6 gallon of paint. Step 2: Multiply the fraction by the number of sections: 3/6 × 10 = (3 × 10)/6 = 5. The answer is 5 gallons.