Whole ÷ Fraction

lessonbunny.com

Answer Key & Explanations

Whole ÷ Fraction · Grade 5 · Worksheet 3

1. A rectangular swimming pool is 15 meters long and divided into lanes that are each 3/4 meter wide. How many complete swimming lanes can fit across the width of the pool? Answer: 20 Solution: The pool is 15 meters wide and each lane is 3/4 meter wide.
   Full step-by-step solution

   Step 1: The pool is 15 meters wide and each lane is 3/4 meter wide. Step 2: To find how many lanes fit, divide the total width by the width of one lane: 15 ÷ (3/4) Step 3: Dividing by a fraction is the same as multiplying by its reciprocal: 15 × (4/3) Step 4: Multiply: 15 × 4 = 60 Step 5: Divide by 3: 60 ÷ 3 = 20 Step 6: Since we're asked for complete lanes, and 20 is a whole number, we have exactly 20 complete lanes. The answer is 20.

2. A school is organizing a field trip and needs to pack lunches. They have 8 large pizzas to divide equally among students. If each student gets 2/5 of a pizza, how many students can receive a portion? Answer: 20 Solution: We need to find how many 2/5 portions are in 8 whole pizzas. To divide a whole number by a fraction, we multiply the whole number by the reciprocal of the fraction. The reciprocal of 2/5 is 5/2.
   Full step-by-step solution

   Step 1: We need to find how many 2/5 portions are in 8 whole pizzas. Step 2: To divide a whole number by a fraction, we multiply the whole number by the reciprocal of the fraction. Step 3: The reciprocal of 2/5 is 5/2. Step 4: Multiply 8 × 5/2 = 40/2 = 20. Step 5: Therefore, 20 students can receive a portion of pizza. The answer is 20.

3. Kai has 6 cups of flour for baking cookies. Each batch of cookies needs 1/4 cup of flour. How many batches of cookies can Kai make? Answer: 24 Solution: We need to find how many 1/4 cup portions are in 6 cups. This means we divide 6 by 1/4. Dividing by a unit fraction is the same as multiplying by the denominator: 6 ÷ 1/4 = 6 × 4 = 24.
   Full step-by-step solution

   Step 1: We need to find how many 1/4 cup portions are in 6 cups. This means we divide 6 by 1/4. Step 2: Dividing by a unit fraction is the same as multiplying by the denominator: 6 ÷ 1/4 = 6 × 4 = 24. Step 3: So Kai can make 24 batches of cookies. The answer is 24.

4. 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.

5. Liam is making friendship bracelets for his class. He has 6 meters of colorful yarn. Each bracelet requires 3/4 of a meter of yarn. How many complete bracelets can Liam make? Answer: 8 Solution: Liam has 6 meters of yarn. Each bracelet requires 3/4 of a meter. To find how many complete bracelets he can make, we need to divide the total yarn by the yarn per bracelet.
   Full step-by-step solution

   Liam has 6 meters of yarn. Each bracelet requires 3/4 of a meter. To find how many complete bracelets he can make, we need to divide the total yarn by the yarn per bracelet. Step 1: Write the division problem. 6 ÷ (3/4) Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. So, 6 ÷ (3/4) = 6 × (4/3) Step 3: Multiply the numbers. 6 × 4 = 24 Then divide by 3: 24 ÷ 3 = 8 Step 4: Interpret the result. The calculation gives exactly 8, which means Liam can make 8 complete bracelets with no yarn left over. Answer: 8

6. A factory needs to package 840 kilograms of flour into bags that each hold 3/5 of a kilogram. How many bags will they be able to fill completely? Answer: 1400 Solution: We need to find how many bags of 3/5 kg can be filled with 840 kg of flour. This means we need to calculate 840 ÷ (3/5). Dividing by a fraction is the same as multiplying by its reciprocal.
   Full step-by-step solution

   Step 1: We need to find how many bags of 3/5 kg can be filled with 840 kg of flour. This means we need to calculate 840 ÷ (3/5). Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/5 is 5/3. Step 3: So we calculate 840 × (5/3). Step 4: First, 840 ÷ 3 = 280 Step 5: Then, 280 × 5 = 1400 Step 6: The factory will be able to fill 1400 bags completely. The answer is 1400.

7. The school cafeteria is making fruit salad for a special event. They have 8 cups of chopped pineapple to use. If each serving of fruit salad requires 2/3 cup of pineapple, how many complete servings can they make? Answer: 12 Solution: Identify what we're dividing: 8 cups total divided by 2/3 cup per serving Write the division problem: 8 ÷ (2/3) Remember that dividing by a fraction is the same as multiplying by its reciprocal The reciprocal of 2/3 is 3/2 Multiply: 8 × (3/2) = 24/2 Simplify: 24/2 = 12 Check if we can make…
   Full step-by-step solution

   Step 1: Identify what we're dividing: 8 cups total divided by 2/3 cup per serving Step 2: Write the division problem: 8 ÷ (2/3) Step 3: Remember that dividing by a fraction is the same as multiplying by its reciprocal Step 4: The reciprocal of 2/3 is 3/2 Step 5: Multiply: 8 × (3/2) = 24/2 Step 6: Simplify: 24/2 = 12 Step 7: Check if we can make complete servings: 12 is a whole number, so yes The cafeteria can make 12 complete servings of fruit salad.

8. Noah has 540 feet of rope for a school outdoor adventure activity. He needs to cut the rope into pieces that are each 1/3 of a foot long for a team-building exercise. How many pieces of rope can Noah cut from the entire length? Answer: 1620 Solution: We need to find how many 1/3-foot pieces are in 540 feet. This means we divide 540 by 1/3. Dividing by a unit fraction is the same as multiplying by its denominator.
   Full step-by-step solution

   Step 1: We need to find how many 1/3-foot pieces are in 540 feet. This means we divide 540 by 1/3. Step 2: Dividing by a unit fraction is the same as multiplying by its denominator. So 540 ÷ (1/3) = 540 × 3. Step 3: Multiply: 540 × 3 = 1620. Step 4: Check: 1620 pieces × 1/3 foot each = 1620/3 = 540 feet. The answer is 1620.

9. 24 ÷ 3/4 = ? Answer: 32 Solution: Write the division problem: 24 ÷ 3/4 Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3.
   Full step-by-step solution

   Step 1: Write the division problem: 24 ÷ 3/4 Step 2: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3. Step 3: Rewrite the problem as multiplication: 24 × 4/3 Step 4: Multiply 24 by the numerator: 24 × 4 = 96 Step 5: Divide by the denominator: 96 ÷ 3 = 32 Step 6: The answer is 32.