Mixed Number Division

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Answer Key & Explanations

Mixed Number Division · Grade 6 · Worksheet 2

1. Liam is building a bookshelf and has a wooden board that is 3 1/4 feet long. He needs to cut it into smaller pieces that are each 5/8 of a foot long for the shelves. How many complete shelves can Liam cut from the board? Answer: 5 Solution: We have a board that is 3 1/4 feet long. We want to cut it into pieces that are each 5/8 of a foot long. We need to find how many *complete* shelves we can cut.
   Full step-by-step solution

   Step 1: Understand the problem. We have a board that is 3 1/4 feet long. We want to cut it into pieces that are each 5/8 of a foot long. We need to find how many *complete* shelves we can cut. --- Step 2: Convert the mixed number to an improper fraction. 3 1/4 = 3 + 1/4 3 = 12/4, so 12/4 + 1/4 = 13/4 feet. So the board length is 13/4 feet. --- Step 3: Divide the total board length by the length of one shelf to find how many shelves we can cut. Number of shelves = (13/4) ÷ (5/8) --- Step 4: Dividing fractions: multiply by the reciprocal. (13/4) ÷ (5/8) = (13/4) × (8/5) --- Step 5: Multiply the fractions. First multiply numerators: 13 × 8 = 104 Multiply denominators: 4 × 5 = 20 So we have 104/20. --- Step 6: Simplify the fraction. 104 ÷ 4 = 26, 20 ÷ 4 = 5, so 26/5. 26/5 = 5 1/5. --- Step 7: Interpret the result. 5 1/5 means we can cut 5 whole shelves, and there will be a leftover piece of 1/5 of a shelf length. Since the problem asks for *complete* shelves, the answer is 5. --- Final answer: 5

2. A community center is organizing a food drive and needs to divide their rice supply into care packages. They have 8 2/3 kilograms of rice available, and each care package should contain 1 1/4 kilograms of rice. How many complete care packages can they make with their current rice supply? Answer: 6 Solution: Convert 8 2/3 to an improper fraction: (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 Convert 1 1/4 to an improper fraction: (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 Divide the total rice by the amount per package: 26/3 ÷ 5/4 When dividing fractions, multiply by the reciprocal: 26/3 × 4/5 = (26 × 4)/(3 × 5) = 104/15…
   Full step-by-step solution

   Step 1: Convert 8 2/3 to an improper fraction: (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 Step 2: Convert 1 1/4 to an improper fraction: (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 Step 3: Divide the total rice by the amount per package: 26/3 ÷ 5/4 Step 4: When dividing fractions, multiply by the reciprocal: 26/3 × 4/5 = (26 × 4)/(3 × 5) = 104/15 Step 5: Convert 104/15 to a mixed number: 104 ÷ 15 = 6 with remainder 14, so 6 14/15 Step 6: Since we need complete packages, we take the whole number part: 6 The community center can make 6 complete care packages.

3. A community garden is planning to divide a large rectangular plot of land into equal sections for different vegetable types. The total plot measures 5 3/4 acres, and each vegetable section requires 1 1/3 acres. How many complete vegetable sections can the community garden create from this plot? Answer: 4 Solution: 5 3/4 = (5 × 4 + 3)/4 = 23/4 acres 1 1/3 = (1 × 3 + 1)/3 = 4/3 acres 23/4 ÷ 4/3 = 23/4 × 3/4 = 69/16 69 ÷ 16 = 4 remainder 5, so 69/16 = 4 5/16 Since we need complete sections, we take the whole number part The answer is 4 complete vegetable sections.
   Full step-by-step solution

   Step 1: Convert the mixed numbers to improper fractions 5 3/4 = (5 × 4 + 3)/4 = 23/4 acres 1 1/3 = (1 × 3 + 1)/3 = 4/3 acres Step 2: Divide the total area by the area per section 23/4 ÷ 4/3 = 23/4 × 3/4 = 69/16 Step 3: Convert the improper fraction to a mixed number 69 ÷ 16 = 4 remainder 5, so 69/16 = 4 5/16 Step 4: Since we need complete sections, we take the whole number part The answer is 4 complete vegetable sections.

4. Liam is building a bookshelf and has a wooden board that is 3 1/4 feet long. He needs to cut it into equal pieces that are each 5/8 of a foot long for the shelves. How many complete shelves can Liam cut from the board? Answer: 5 Solution: Liam has a board that is 3 1/4 feet long. He wants shelves that are each 5/8 of a foot long. We need to find how many complete shelves he can cut.
   Full step-by-step solution

   Step 1: Understand the problem Liam has a board that is 3 1/4 feet long. He wants shelves that are each 5/8 of a foot long. We need to find how many complete shelves he can cut. Step 2: Convert mixed number to improper fraction 3 1/4 feet = 3 + 1/4 3 = 12/4, so 12/4 + 1/4 = 13/4 feet. Step 3: Set up the division We divide the total board length by the length of one shelf: (13/4) ÷ (5/8) Step 4: Divide fractions Dividing by a fraction is the same as multiplying by its reciprocal: (13/4) × (8/5) Multiply numerators: 13 × 8 = 104 Multiply denominators: 4 × 5 = 20 So we have 104/20. Step 5: Simplify the fraction 104/20 = 52/10 = 26/5 26/5 = 5 1/5 Step 6: Interpret the result 5 1/5 means we can cut 5 full shelves, and there will be a small leftover piece (1/5 of a shelf length, which is less than one full shelf). Step 7: Final answer Liam can cut 5 complete shelves from the board.

5. A school is organizing a science fair and needs to divide 4 1/2 liters of liquid nitrogen equally among several demonstration stations. Each station requires exactly 3/4 of a liter for their experiment. How many complete demonstration stations can be supplied with liquid nitrogen? Answer: 6 Solution: Convert the mixed number to an improper fraction: 4 1/2 = (4 × 2 + 1)/2 = 9/2 We need to divide the total liquid nitrogen by the amount per station: 9/2 ÷ 3/4 When dividing fractions, multiply by the reciprocal: 9/2 × 4/3 Multiply the numerators: 9 × 4 = 36 Multiply the denominators: 2 × 3 = 6…
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction: 4 1/2 = (4 × 2 + 1)/2 = 9/2 Step 2: We need to divide the total liquid nitrogen by the amount per station: 9/2 ÷ 3/4 Step 3: When dividing fractions, multiply by the reciprocal: 9/2 × 4/3 Step 4: Multiply the numerators: 9 × 4 = 36 Step 5: Multiply the denominators: 2 × 3 = 6 Step 6: Simplify the fraction: 36/6 = 6 Step 7: Since we're asked for complete stations, and 6 is a whole number, we have exactly 6 complete stations. The answer is 6.

6. A community center is organizing a food drive and needs to divide a large donation of rice into family-sized portions. They have 8 2/3 pounds of rice and want to create bags that each contain 5/6 of a pound. How many complete family-sized bags can they make from the rice donation? Answer: 10 Solution: Convert the mixed number 8 2/3 to an improper fraction 8 2/3 = (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 We need to divide 26/3 by 5/6 26/3 ÷ 5/6 = 26/3 × 6/5 (26 × 6)/(3 × 5) = 156/15 156 ÷ 3 = 52, 15 ÷ 3 = 5, so 156/15 = 52/5 52 ÷ 5 = 10 with remainder 2, so 52/5 = 10 2/5 Since we're looking for…
   Full step-by-step solution

   Step 1: Convert the mixed number 8 2/3 to an improper fraction 8 2/3 = (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 Step 2: Set up the division problem We need to divide 26/3 by 5/6 Step 3: Apply the rule for dividing fractions 26/3 ÷ 5/6 = 26/3 × 6/5 Step 4: Multiply the fractions (26 × 6)/(3 × 5) = 156/15 Step 5: Simplify the fraction 156 ÷ 3 = 52, 15 ÷ 3 = 5, so 156/15 = 52/5 Step 6: Convert to a mixed number 52 ÷ 5 = 10 with remainder 2, so 52/5 = 10 2/5 Step 7: Since we're looking for complete bags, we take the whole number part The community center can make 10 complete family-sized bags. The answer is 10.

7. A rectangular garden is divided into four equal triangular sections by two diagonal paths that cross at the center. The garden measures 24 meters long by 18 meters wide. If the gardener plants roses in one of these triangular sections, what is the area of the rose section in square meters? Answer: 108 Solution: Calculate the total area of the rectangular garden. Area = length × width = 24 m × 18 m = 432 square meters. Determine how the diagonals divide the rectangle.
   Full step-by-step solution

   Step 1: Calculate the total area of the rectangular garden. Area = length × width = 24 m × 18 m = 432 square meters. Step 2: Determine how the diagonals divide the rectangle. The two diagonals crossing at the center divide the rectangle into four triangles of equal area. Step 3: Calculate the area of one triangular section. Area of one triangle = Total area ÷ 4 = 432 ÷ 4 = 108 square meters. Step 4: Since the rose section is one of these triangles, its area is 108 square meters. The answer is 108.

8. A community center is organizing a food drive and needs to distribute 5 3/4 kilograms of rice equally among families. If each family receives 2/5 of a kilogram of rice, how many complete family portions can be made from the available rice? Answer: 14 Solution: Convert the mixed number to an improper fraction. 5 3/4 = (5 × 4 + 3)/4 = (20 + 3)/4 = 23/4 kilograms. To find how many portions of 2/5 kg fit into 23/4 kg, divide: (23/4) ÷ (2/5).
   Full step-by-step solution

   Step 1: Convert the mixed number to an improper fraction. 5 3/4 = (5 × 4 + 3)/4 = (20 + 3)/4 = 23/4 kilograms. Step 2: To find how many portions of 2/5 kg fit into 23/4 kg, divide: (23/4) ÷ (2/5). Step 3: Dividing fractions means multiplying by the reciprocal: (23/4) × (5/2) = (23 × 5)/(4 × 2) = 115/8. Step 4: Convert 115/8 to a mixed number: 115 ÷ 8 = 14 remainder 3, so 115/8 = 14 3/8. Step 5: Since the question asks for complete portions, we take the whole number part: 14. The answer is 14 complete family portions.