Fraction × Whole

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Answer Key & Explanations

Fraction × Whole · Grade 5 · Worksheet 1

1. 3/5 × 45 = ? Answer: 27 Solution: Write the whole number as a fraction: 45 = 45/1 Multiply the fractions: (3/5) × (45/1) = (3 × 45)/(5 × 1) Calculate the numerator: 3 × 45 = 135 Calculate the denominator: 5 × 1 = 5 Simplify the fraction: 135/5 = 27 The answer is 27.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 45 = 45/1 Step 2: Multiply the fractions: (3/5) × (45/1) = (3 × 45)/(5 × 1) Step 3: Calculate the numerator: 3 × 45 = 135 Step 4: Calculate the denominator: 5 × 1 = 5 Step 5: Simplify the fraction: 135/5 = 27 The answer is 27.

2. 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

3. 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.

4. 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.

5. A rectangular swimming pool is drawn on a coordinate plane with corners at (0,0), (12,0), (12,8), and (0,8). Each unit on the grid represents 1 meter. What is the area of the pool in square meters? Answer: 96 Solution: Identify the length of the rectangle from the x-coordinates. The left side is at x=0 and the right side is at x=12, so the length is 12 - 0 = 12 meters. Identify the width of the rectangle from the y-coordinates.
   Full step-by-step solution

   Step 1: Identify the length of the rectangle from the x-coordinates. The left side is at x=0 and the right side is at x=12, so the length is 12 - 0 = 12 meters. Step 2: Identify the width of the rectangle from the y-coordinates. The bottom is at y=0 and the top is at y=8, so the width is 8 - 0 = 8 meters. Step 3: Calculate the area using the formula: area = length × width. Step 4: Multiply: 12 × 8 = 96. The area of the pool is 96 square meters.

6. In gym class, Nikau runs laps around the track. Each lap is 3/5 of a mile. If Nikau runs 10 laps, how many miles does Nikau run in total? Answer: 6 Solution: Each lap is 3/5 of a mile. Multiply the fraction by the number of laps: 3/5 × 10 = (3 × 10)/5 = 6.
   Full step-by-step solution

   Step 1: Each lap is 3/5 of a mile. Step 2: Multiply the fraction by the number of laps: 3/5 × 10 = (3 × 10)/5 = 6. The answer is 6 miles.

7. Zoe is baking cookies. Each batch needs 1/4 cup of sugar. If Zoe makes 8 batches of cookies, how many cups of sugar does Zoe need in total? Answer: 2 Solution: Each batch needs 1/4 cup of sugar. Multiply the fraction by the number of batches: 1/4 × 8 = (1 × 8)/4 = 2.
   Full step-by-step solution

   Step 1: Each batch needs 1/4 cup of sugar. Step 2: Multiply the fraction by the number of batches: 1/4 × 8 = (1 × 8)/4 = 2. The answer is 2 cups of sugar.

8. Liam is baking cookies for his school bake sale. He needs to make 3/4 of a batch for each classroom, and there are 5 classrooms participating. How many total batches of cookies does Liam need to bake? Answer: 3 3/4 Solution: Liam needs to make 3/4 of a batch for each classroom. There are 5 classrooms. 5 × (3/4) Multiply the whole number by the fraction.
   Full step-by-step solution

   Liam needs to make 3/4 of a batch for each classroom. There are 5 classrooms. So the total number of batches needed is: 5 × (3/4) Step 1: Multiply the whole number by the fraction. 5 × 3/4 = (5 × 3) / 4 Step 2: Multiply numerator. 5 × 3 = 15 Step 3: Write as a fraction. 15/4 Step 4: Convert the improper fraction to a mixed number. 15 ÷ 4 = 3 remainder 3, so: 15/4 = 3 3/4 So Liam needs to bake 3 3/4 batches of cookies.

9. 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.