Whole ÷ Fraction

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Whole ÷ Fraction · Grade 5 · Worksheet 2

1. 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.

2. A school is organizing a field trip and needs to prepare snack bags. They have 8 kilograms of trail mix to distribute equally among the students. If each snack bag should contain 2/5 of a kilogram of trail mix, how many complete snack bags can they make? Answer: 20 Solution: We need to divide the total trail mix by the amount per bag: 8 ÷ (2/5) Dividing by a fraction is the same as multiplying by its reciprocal: 8 × (5/2) Multiply the whole number by the numerator: 8 × 5 = 40 Divide by the denominator: 40 ÷ 2 = 20 Since we're asked for complete snack bags, and 20 is…
   Full step-by-step solution

   Step 1: We need to divide the total trail mix by the amount per bag: 8 ÷ (2/5) Step 2: Dividing by a fraction is the same as multiplying by its reciprocal: 8 × (5/2) Step 3: Multiply the whole number by the numerator: 8 × 5 = 40 Step 4: Divide by the denominator: 40 ÷ 2 = 20 Step 5: Since we're asked for complete snack bags, and 20 is a whole number, we have exactly 20 complete snack bags. The answer is 20 complete snack bags.

3. Liam is making friendship bracelets for his class. He has 6 meters of colorful yarn. If each bracelet requires 3/4 of a meter of yarn, how many complete bracelets can Liam make? Answer: 8 Solution: We are told Liam has 6 meters of yarn and each bracelet uses 3/4 of a meter. We want to find how many complete bracelets he can make.
   Full step-by-step solution

   We are told Liam has 6 meters of yarn and each bracelet uses 3/4 of a meter. We want to find how many complete bracelets he can make. Step 1: Understand the problem We need to divide the total yarn length by the yarn length per bracelet: Total bracelets possible = (Total yarn) ÷ (Yarn per bracelet) Step 2: Write the division Total yarn = 6 meters Yarn per bracelet = 3/4 meter So: 6 ÷ (3/4) Step 3: Dividing by a fraction 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 4: Multiply 6 × (4/3) = (6 × 4) / 3 = 24 / 3 Step 5: Simplify 24 / 3 = 8 Step 6: Interpret the result This means 8 complete bracelets can be made, with no yarn leftover for a 9th bracelet. Final answer: 8

4. 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.

5. A rectangular garden is divided into equal sections for different vegetables. The garden is 12 meters long and 3/4 meter wide. If each vegetable section must be exactly 1/6 meter wide, how many complete vegetable sections can fit across the width of the garden? Answer: 4 Solution: The total width of the garden is 3/4 meter. Each vegetable section is 1/6 meter wide.
   Full step-by-step solution

   Step 1: The total width of the garden is 3/4 meter. Step 2: Each vegetable section is 1/6 meter wide. Step 3: To find how many sections fit across the width, divide the total width by the section width: 3/4 ÷ 1/6 Step 4: Dividing by a fraction is the same as multiplying by its reciprocal: 3/4 × 6/1 Step 5: Multiply the numerators: 3 × 6 = 18 Step 6: Multiply the denominators: 4 × 1 = 4 Step 7: Simplify the fraction: 18/4 = 9/2 = 4.5 Step 8: Since we need complete sections, we take the whole number part: 4 The answer is 4 complete vegetable sections.

6. Sophia has 9 meters of ribbon to make hair bows for her friends. Each hair bow requires 1/5 of a meter of ribbon. How many hair bows can Sophia make in total? Answer: 45 Solution: We have 9 meters of ribbon, and each bow needs 1/5 of a meter. Step 2: To find how many 1/5-meter pieces are in 9 meters, divide 9 by 1/5.
   Full step-by-step solution

   Step 1: We have 9 meters of ribbon, and each bow needs 1/5 of a meter. Step 2: To find how many 1/5-meter pieces are in 9 meters, divide 9 by 1/5. Step 3: Dividing by a unit fraction is the same as multiplying by the denominator. So 9 ÷ (1/5) = 9 × 5. Step 4: 9 × 5 = 45. Step 5: Therefore, Sophia can make 45 hair bows. The answer is 45.

7. Hana is designing a large rectangular mural that is 24 feet wide. She plans to divide the width into equal vertical sections, where each section is exactly 1/8 of a foot wide. How many complete sections can she fit across the width of the mural? Answer: 192 Solution: We need to find how many 1/8-foot sections fit into 24 feet. This is a division problem: 24 divided by 1/8. 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 1/8-foot sections fit into 24 feet. This is a division problem: 24 divided by 1/8. Step 2: Dividing by a unit fraction is the same as multiplying by its denominator. So, 24 divided by 1/8 = 24 multiplied by 8. Step 3: Multiply: 24 x 8 = 192. Step 4: So, 192 sections, each 1/8 foot wide, fit across the 24-foot width. The answer is 192.

8. Liam is making friendship bracelets and 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: We are told Liam has 6 meters of yarn and each bracelet uses 3/4 meter of yarn. We want to find how many complete bracelets he can make. Write the problem as a division.
   Full step-by-step solution

   We are told Liam has 6 meters of yarn and each bracelet uses 3/4 meter of yarn. We want to find how many complete bracelets he can make. Step 1: Write the problem as a division. Total yarn = 6 meters Yarn per bracelet = 3/4 meter Number of bracelets = Total yarn ÷ Yarn per bracelet So: 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 6 by 4/3. First, multiply 6 by 4: 6 × 4 = 24 Then divide by 3: 24 ÷ 3 = 8 Step 4: Interpret the result. The calculation gives exactly 8, which is a whole number. That means Liam can make 8 bracelets with no yarn left over. Final answer: 8 complete bracelets.