Whole ÷ Fraction

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Answer Key & Explanations

Whole ÷ Fraction · Grade 5 · Worksheet 2

1. The school cafeteria is preparing for a pizza party and has 8 large pizzas to serve. If each student will receive 2/5 of a pizza, how many students can be served with the 8 pizzas? Answer: 20 Solution: We need to find how many times 2/5 fits into 8 whole pizzas.
   Full step-by-step solution

   Step 1: We need to find how many times 2/5 fits into 8 whole pizzas. Step 2: This is a division problem: 8 ÷ (2/5) Step 3: To divide by a fraction, we multiply by its reciprocal: 8 × (5/2) Step 4: Multiply 8 by 5: 8 × 5 = 40 Step 5: Divide 40 by 2: 40 ÷ 2 = 20 Step 6: Therefore, 20 students can be served with the 8 pizzas. The answer is 20.

2. The school art club is preparing for a mural project and has 8 meters of special border tape. Each section of the mural requires 2/5 of a meter of tape to outline the design. How many complete mural sections can the art club outline with their tape? Answer: 20 Solution: Identify what we're solving: We need to find how many complete sections we can make from 8 meters of tape, with each section using 2/5 meter.
   Full step-by-step solution

   Step 1: Identify what we're solving: We need to find how many complete sections we can make from 8 meters of tape, with each section using 2/5 meter. Step 2: Set up the division: 8 ÷ (2/5) Step 3: When dividing by a fraction, multiply by its reciprocal: 8 × (5/2) Step 4: Multiply: (8 × 5)/2 = 40/2 Step 5: Simplify: 40 ÷ 2 = 20 Step 6: Since we're asked for complete sections and 20 is a whole number, we have exactly 20 complete sections. The art club can outline 20 complete mural sections.

3. A rectangular garden is divided into 8 equal sections. Each section is planted with a different type of flower. If the total area of the garden is 600 square feet, what is the area of each flower section? Answer: 75 Solution: We are told the rectangular garden is divided into 8 equal sections. The total area of the garden is 600 square feet.
   Full step-by-step solution

   We are told the rectangular garden is divided into 8 equal sections. The total area of the garden is 600 square feet. Since the sections are equal, the area of each section is the total area divided by the number of sections. So, Area of each section = Total area / Number of sections Area of each section = 600 / 8 Now, perform the division: 600 ÷ 8 = 75 Therefore, each flower section has an area of 75 square feet. Final answer: 75

4. The school art club is creating a large mural and needs to divide a 10-foot long roll of special border paper into sections that are each 2/5 of a foot long for decorative frames. How many complete decorative frame sections can they cut from the entire roll? Answer: 25 Solution: We need to divide 10 feet by 2/5 foot per section Dividing by a fraction is the same as multiplying by its reciprocal 10 ÷ (2/5) = 10 × (5/2) 10 × 5 = 50 50 ÷ 2 = 25 Since we're asked for complete sections, and 25 is a whole number, we have exactly 25 complete sections The answer is 25.
   Full step-by-step solution

   Step 1: We need to divide 10 feet by 2/5 foot per section Step 2: Dividing by a fraction is the same as multiplying by its reciprocal Step 3: 10 ÷ (2/5) = 10 × (5/2) Step 4: 10 × 5 = 50 Step 5: 50 ÷ 2 = 25 Step 6: Since we're asked for complete sections, and 25 is a whole number, we have exactly 25 complete sections The answer is 25.

5. The school art club is making mosaic tiles for a community project. They have a large sheet of colored glass that is 8 feet long. Each mosaic tile requires 2/3 of a foot of glass. How many complete mosaic tiles can they cut from the glass sheet? Answer: 12 Solution: Identify the total length of glass available: 8 feet. Identify the length needed for one tile: 2/3 of a foot. To find the number of tiles, divide the total length by the length per tile: 8 ÷ (2/3).
   Full step-by-step solution

   Step 1: Identify the total length of glass available: 8 feet. Step 2: Identify the length needed for one tile: 2/3 of a foot. Step 3: To find the number of tiles, divide the total length by the length per tile: 8 ÷ (2/3). Step 4: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2. Step 5: Multiply: 8 × (3/2) = (8 × 3) / 2 = 24 / 2 = 12. Step 6: The problem asks for complete tiles, and 12 is a whole number, so the answer is 12 complete tiles.

6. The school cafeteria is preparing for a pizza party and has 8 large pizzas to share equally among the fifth-grade classes. If each class gets 2/3 of a pizza, how many fifth-grade classes can be served with the available pizzas? Answer: 12 Solution: We need to find how many groups of 2/3 are in 8 whole pizzas. Write the division problem: 8 ÷ (2/3) When dividing by a fraction, we multiply by its reciprocal. The reciprocal of 2/3 is 3/2.
   Full step-by-step solution

   Step 1: We need to find how many groups of 2/3 are in 8 whole pizzas. Step 2: Write the division problem: 8 ÷ (2/3) Step 3: When dividing by a fraction, we multiply by its reciprocal. The reciprocal of 2/3 is 3/2. Step 4: Multiply: 8 × (3/2) = (8 × 3)/2 = 24/2 Step 5: Simplify: 24/2 = 12 Step 6: This means 12 classes can each get 2/3 of a pizza. The answer is 12.

7. Liam is making friendship bracelets for his class. He has a 6-meter long spool of colorful yarn. If each bracelet requires 1/4 meter of yarn, how many complete bracelets can Liam make? Answer: 24 Solution: - Total yarn length = 6 meters - Yarn needed per bracelet = 1/4 meter We want the number of complete bracelets Liam can make. This means we divide the total yarn length by the yarn per bracelet.
   Full step-by-step solution

   We are given: - Total yarn length = 6 meters - Yarn needed per bracelet = 1/4 meter Step 1: Understand the problem We want the number of complete bracelets Liam can make. This means we divide the total yarn length by the yarn per bracelet. Step 2: Write the division Number of bracelets = Total yarn ÷ Yarn per bracelet = 6 ÷ (1/4) Step 3: Recall dividing by a fraction Dividing by 1/4 is the same as multiplying by 4. So: 6 ÷ (1/4) = 6 × 4 Step 4: Perform the multiplication 6 × 4 = 24 Step 5: Interpret the result Since 24 is a whole number, Liam can make exactly 24 bracelets with no yarn left over. Answer: 24

8. 18 ÷ 3/4 = ? Answer: 24 Solution: Start with 18 ÷ 3/4 Dividing by a fraction is the same as multiplying by its reciprocal The reciprocal of 3/4 is 4/3 Rewrite as 18 × 4/3 Multiply 18 × 4 = 72 Divide 72 ÷ 3 = 24 The answer is 24.
   Full step-by-step solution

   Step 1: Start with 18 ÷ 3/4 Step 2: Dividing by a fraction is the same as multiplying by its reciprocal Step 3: The reciprocal of 3/4 is 4/3 Step 4: Rewrite as 18 × 4/3 Step 5: Multiply 18 × 4 = 72 Step 6: Divide 72 ÷ 3 = 24 The answer is 24.