Multiply Fractions by Whole

lessonbunny.com

Answer Key & Explanations

Multiply Fractions by Whole · Grade 4 · Worksheet 2

1. 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.

2. 12 × 2/7 = ? Answer: 24/7 Solution: Write the whole number as a fraction: 12 = 12/1 Multiply the numerators: 12 × 2 = 24 Multiply the denominators: 1 × 7 = 7 Combine the results: 24/7 The answer is 24/7.
   Full step-by-step solution

   Step 1: Write the whole number as a fraction: 12 = 12/1 Step 2: Multiply the numerators: 12 × 2 = 24 Step 3: Multiply the denominators: 1 × 7 = 7 Step 4: Combine the results: 24/7 The answer is 24/7.

3. A construction crew is building a fence around a rectangular playground that measures 120 feet long and 80 feet wide. They need to install fence posts every 3/4 of a foot along the entire perimeter. How many fence posts will they need in total? Answer: 534 Solution: Perimeter = 2 × (length + width) = 2 × (120 + 80) = 2 × 200 = 400 feet Since posts are placed every 3/4 foot, we divide the perimeter by 3/4 400 ÷ (3/4) = 400 × (4/3) = 1600/3 = 533.333...
   Full step-by-step solution

   Step 1: Find the perimeter of the rectangular playground Perimeter = 2 × (length + width) = 2 × (120 + 80) = 2 × 200 = 400 feet Step 2: Calculate how many fence posts are needed Since posts are placed every 3/4 foot, we divide the perimeter by 3/4 400 ÷ (3/4) = 400 × (4/3) = 1600/3 = 533.333... Step 3: Interpret the result Since we can't have a fraction of a fence post, and we need posts at both the start and end of the fence, we round up to the next whole number 533.333... means we need 534 posts total Step 4: Verify the reasoning If we place posts every 3/4 foot along 400 feet: - First post at 0 feet - Last post at 400 feet - Number of intervals = 400 ÷ (3/4) = 533.33 intervals - Number of posts = number of intervals + 1 = 533.33 + 1 = 534.33 - Since we can't have partial posts, we need 534 total posts The answer is 534.

4. Matiu is helping his family pack care packages for a community fundraiser. Each care package needs 5/8 of a kilogram of rice. If Matiu's family prepares 112 care packages, how many kilograms of rice will they need in total? Answer: 70 Solution: Each care package needs 5/8 of a kilogram of rice. There are 112 care packages. Multiply the amount per package by the number of packages: 112 × 5/8.
   Full step-by-step solution

   Step 1: Each care package needs 5/8 of a kilogram of rice. Step 2: There are 112 care packages. Step 3: Multiply the amount per package by the number of packages: 112 × 5/8. Step 4: Write 112 as a fraction: 112 = 112/1. Step 5: Multiply the numerators: 112 × 5 = 560. Step 6: Multiply the denominators: 1 × 8 = 8. Step 7: Simplify the fraction: 560 ÷ 8 = 70. The answer is 70 kilograms of rice.

5. Liam is baking cookies for his class party. He needs to make 3/4 of a batch for each of the 24 students in his class. How many total batches of cookies does Liam need to bake? Answer: 18 Solution: Liam needs to make 3/4 of a batch for each student. There are 24 students in his class. Multiply the fraction of a batch per student by the number of students.
   Full step-by-step solution

   Liam needs to make 3/4 of a batch for each student. There are 24 students in his class. Step 1: Multiply the fraction of a batch per student by the number of students. 3/4 × 24 Step 2: Write 24 as a fraction: 24 = 24/1. So the multiplication becomes: 3/4 × 24/1 Step 3: Multiply the numerators: 3 × 24 = 72 Multiply the denominators: 4 × 1 = 4 So we have 72/4 Step 4: Simplify 72/4. 72 ÷ 4 = 18 Therefore, Liam needs to bake 18 total batches of cookies.

6. 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.

7. A construction crew is building a new playground. They need to install 3/4 of the planned swings. If the original plan called for 24 swings, how many swings will they actually 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.