Multiply Fractions by Whole

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Multiply Fractions by Whole · Grade 4 · Worksheet 2

1. A farmer has 150 meters of fencing to enclose a rectangular garden. The length of the garden is 2/3 of the total fencing available. How many meters of fencing does the farmer use for the length of the garden? Answer: 100 Solution: 1. The length of the garden uses 2/3 of the total fencing available. 2.
   Full step-by-step solution

   Let's go step-by-step. 1. Understand the problem: The farmer has 150 meters of fencing in total. The length of the garden uses 2/3 of the total fencing available. 2. Identify what is being asked: They want the meters of fencing used for the length of the garden. 3. Interpret "length of the garden" in this context: Usually, "length" means one of the longer sides of the rectangle, but here it says "the length of the garden is 2/3 of the total fencing available." This means: Length = (2/3) × Total fencing. 4. Calculate: Total fencing = 150 meters. Length = (2/3) × 150. 5. Perform the multiplication: First, 150 ÷ 3 = 50. Then, 50 × 2 = 100. 6. Conclusion: The farmer uses 100 meters of fencing for the length of the garden. Final answer: 100

2. Kaia is organizing a community garden. Each garden bed requires 5/8 of a bag of soil. If Kaia needs to fill 24 garden beds, how many bags of soil does she need in total? Answer: 15 Solution: Each garden bed needs 5/8 of a bag of soil. Kaia needs to fill 24 garden beds. Multiply the amount per bed by the number of beds: 24 × 5/8.
   Full step-by-step solution

   Step 1: Each garden bed needs 5/8 of a bag of soil. Step 2: Kaia needs to fill 24 garden beds. Step 3: Multiply the amount per bed by the number of beds: 24 × 5/8. Step 4: Write 24 as a fraction: 24/1. Step 5: Multiply the numerators: 24 × 5 = 120. Step 6: Multiply the denominators: 1 × 8 = 8. Step 7: So, 24 × 5/8 = 120/8. Step 8: Simplify the fraction: 120 ÷ 8 = 15. The answer is 15 bags of soil.

3. Liam is baking cookies for his class party. He needs to make 3/4 of a batch of cookies. If one batch requires 2 cups of flour, how many cups of flour does Liam need for 3/4 of a batch? Answer: 1.5 Solution: One full batch of cookies requires 2 cups of flour. Liam is making 3/4 of a batch, so we need to find 3/4 of 2 cups. Set up the calculation.
   Full step-by-step solution

   Step 1: Understand the problem. One full batch of cookies requires 2 cups of flour. Liam is making 3/4 of a batch, so we need to find 3/4 of 2 cups. Step 2: Set up the calculation. To find a fraction of a number, multiply the fraction by the number. So, we calculate: 3/4 × 2 Step 3: Multiply the fraction by the whole number. 3/4 × 2 = (3 × 2) / 4 Step 4: Perform the multiplication. 3 × 2 = 6 So, we have 6 / 4 Step 5: Simplify the fraction. 6/4 can be simplified by dividing numerator and denominator by 2: 6 ÷ 2 = 3 4 ÷ 2 = 2 So, 6/4 = 3/2 Step 6: Convert to decimal (if needed). 3/2 = 1.5 Step 7: State the answer. Liam needs 1.5 cups of flour for 3/4 of a batch.

4. Emma is making friendship bracelets for her classmates. She needs 3/4 of a yard of string for each bracelet. If she wants to make 12 bracelets, how many yards of string does Emma need in total? Answer: 9 Solution: Emma needs 3/4 yard of string for each bracelet She wants to make 12 bracelets Multiply the amount per bracelet by the number of bracelets: 3/4 × 12 Convert 12 to a fraction: 12 = 12/1 Multiply the fractions: (3/4) × (12/1) = (3 × 12)/(4 × 1) = 36/4 Simplify the fraction: 36 ÷ 4 = 9 Emma needs 9…
   Full step-by-step solution

   Step 1: Emma needs 3/4 yard of string for each bracelet Step 2: She wants to make 12 bracelets Step 3: Multiply the amount per bracelet by the number of bracelets: 3/4 × 12 Step 4: Convert 12 to a fraction: 12 = 12/1 Step 5: Multiply the fractions: (3/4) × (12/1) = (3 × 12)/(4 × 1) = 36/4 Step 6: Simplify the fraction: 36 ÷ 4 = 9 Step 7: Emma needs 9 yards of string total The answer is 9.

5. Noah is building bookshelves for his classroom library. Each bookshelf requires 3/4 of a gallon of paint. If Noah needs to build 16 bookshelves, how many gallons of paint does he need in total? Answer: 12 Solution: Each bookshelf requires 3/4 gallon of paint Noah needs to build 16 bookshelves Multiply the amount per bookshelf by the number of bookshelves: 3/4 × 16 Write 16 as a fraction: 16 = 16/1 Multiply the fractions: (3 × 16)/(4 × 1) = 48/4 Simplify the fraction: 48 ÷ 4 = 12 The answer is 12 gallons of…
   Full step-by-step solution

   Step 1: Each bookshelf requires 3/4 gallon of paint Step 2: Noah needs to build 16 bookshelves Step 3: Multiply the amount per bookshelf by the number of bookshelves: 3/4 × 16 Step 4: Write 16 as a fraction: 16 = 16/1 Step 5: Multiply the fractions: (3 × 16)/(4 × 1) = 48/4 Step 6: Simplify the fraction: 48 ÷ 4 = 12 The answer is 12 gallons of paint.

6. A construction crew is building a new playground. They need to install 3/4 of the planned swings. If the full plan calls for 24 swings, how many swings will they install? Answer: 18 Solution: The problem asks for 3/4 of 24 swings.
   Full step-by-step solution

   Step 1: The problem asks for 3/4 of 24 swings. Step 2: To find a fraction of a whole number, multiply the fraction by the whole number: 3/4 × 24 Step 3: Write 24 as a fraction: 24/1 Step 4: Multiply the numerators: 3 × 24 = 72 Step 5: Multiply the denominators: 4 × 1 = 4 Step 6: Simplify the fraction: 72/4 = 18 Step 7: The construction crew will install 18 swings.

7. A rectangular classroom floor is tiled with square tiles. The floor has 15 rows of tiles and 12 columns of tiles. If you look at the entire floor, how many tiles are there in total? Answer: 180 Solution: The classroom floor has 15 rows of tiles Each row has 12 tiles To find the total number of tiles, multiply the number of rows by the number of tiles in each row 15 × 12 = 180 There are 180 tiles total on the classroom floor
   Full step-by-step solution

   Step 1: The classroom floor has 15 rows of tiles Step 2: Each row has 12 tiles Step 3: To find the total number of tiles, multiply the number of rows by the number of tiles in each row Step 4: 15 × 12 = 180 Step 5: There are 180 tiles total on the classroom floor

8. 8 × 2/7 = ? Answer: 16/7 Solution: Write the whole number as a fraction: 8 = 8/1 Multiply the numerators: 8 × 2 = 16 Multiply the denominators: 1 × 7 = 7 Combine the results: 16/7 The answer is 16/7.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 8 = 8/1 Step 2: Multiply the numerators: 8 × 2 = 16 Step 3: Multiply the denominators: 1 × 7 = 7 Step 4: Combine the results: 16/7 The answer is 16/7.

9. A rectangular classroom floor is covered with square tiles. The floor has 12 tiles along its length and 8 tiles along its width. If each tile measures 1 foot on each side, what is the area of the classroom floor in square feet? Answer: 96 Solution: The classroom floor has 12 tiles along the length and 8 tiles along the width.
   Full step-by-step solution

   Step 1: The classroom floor has 12 tiles along the length and 8 tiles along the width. Step 2: To find the total number of tiles, multiply the number of tiles along the length by the number of tiles along the width: 12 × 8 Step 3: Calculate 12 × 8 = 96 Step 4: Since each tile measures 1 foot on each side, each tile has an area of 1 square foot. Step 5: Therefore, the total area of the classroom floor is 96 square feet. The answer is 96.