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Mixed Number Division

Grade 6 · Mathematics · Worksheet 3

  1. A construction company is building a new community garden and needs to divide a large plot of land into equal sections for different vegetable types. The total plot measures 4 1/2 acres, and each vegetable section requires 3/4 of an acre. How many complete vegetable sections can the company create from this plot? Answer: ______________
  2. Mere is training for a relay race. The total distance of the race is 12 miles. The team has 3 runners, and each runner runs the same distance. If Mere runs one leg of the race, how many miles does Mere run? Answer: ______________
  3. A construction company is building a new playground and needs to install safety fencing around the perimeter. They have a roll of fencing that is 15 3/4 meters long. Each section of the playground requires fencing pieces that are 1 1/8 meters long. How many complete fencing sections can they cut from the full roll? Answer: ______________
  4. 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: ______________
  5. 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: ______________
  6. 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: ______________
  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: ______________
  8. A rectangular garden is divided into four equal triangular flower beds by drawing both diagonals from opposite corners. The garden measures 32 meters long by 24 meters wide. What is the area of one triangular flower bed in square meters? Answer: ______________
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Answer Key & Explanations

Mixed Number Division · Grade 6 · Worksheet 3

  1. A construction company is building a new community garden and needs to divide a large plot of land into equal sections for different vegetable types. The total plot measures 4 1/2 acres, and each vegetable section requires 3/4 of an acre. How many complete vegetable sections can the company create from this plot? Answer: 6 Solution: Convert the mixed number 4 1/2 to an improper fraction: 4 1/2 = (4 × 2 + 1)/2 = 9/2 Set up the division problem: (9/2) ÷ (3/4) To divide fractions, multiply by the reciprocal: (9/2) × (4/3) Multiply the numerators: 9 × 4 = 36 Multiply the denominators: 2 × 3 = 6 Simplify the fraction: 36/6 = 6…
    Full step-by-step solution

    Step 1: Convert the mixed number 4 1/2 to an improper fraction: 4 1/2 = (4 × 2 + 1)/2 = 9/2 Step 2: Set up the division problem: (9/2) ÷ (3/4) Step 3: To divide 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 the question asks for complete sections, we use the whole number part: 6 The company can create 6 complete vegetable sections.

  2. Mere is training for a relay race. The total distance of the race is 12 miles. The team has 3 runners, and each runner runs the same distance. If Mere runs one leg of the race, how many miles does Mere run? Answer: 4 Solution: The total distance is 12 miles. Divide the distance equally among 3 runners: 12 ÷ 3 = 4 miles.
    Full step-by-step solution

    Step 1: The total distance is 12 miles. Step 2: Divide the distance equally among 3 runners: 12 ÷ 3 = 4 miles. The answer is 4 miles.

  3. A construction company is building a new playground and needs to install safety fencing around the perimeter. They have a roll of fencing that is 15 3/4 meters long. Each section of the playground requires fencing pieces that are 1 1/8 meters long. How many complete fencing sections can they cut from the full roll? Answer: 14 Solution: 15 3/4 = (15 × 4 + 3)/4 = (60 + 3)/4 = 63/4 1 1/8 = (1 × 8 + 1)/8 = (8 + 1)/8 = 9/8 63/4 ÷ 9/8 Change division to multiplication by the reciprocal 63/4 × 8/9 63/9 = 7 and 8/4 = 2 So we have 7 × 2 = 14 63/4 × 8/9 = (63 × 8)/(4 × 9) = 504/36 = 14 The answer is 14 complete fencing sections.
    Full step-by-step solution

    Step 1: Convert the mixed numbers to improper fractions 15 3/4 = (15 × 4 + 3)/4 = (60 + 3)/4 = 63/4 1 1/8 = (1 × 8 + 1)/8 = (8 + 1)/8 = 9/8 Step 2: Set up the division problem 63/4 ÷ 9/8 Step 3: Change division to multiplication by the reciprocal 63/4 × 8/9 Step 4: Simplify before multiplying 63/9 = 7 and 8/4 = 2 So we have 7 × 2 = 14 Step 5: Verify the multiplication 63/4 × 8/9 = (63 × 8)/(4 × 9) = 504/36 = 14 The answer is 14 complete fencing sections.

  4. 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.

  5. 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.

  6. 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.

  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 rectangular garden is divided into four equal triangular flower beds by drawing both diagonals from opposite corners. The garden measures 32 meters long by 24 meters wide. What is the area of one triangular flower bed in square meters? Answer: 192 Solution: Calculate the total area of the rectangular garden Area of rectangle = length × width = 32 m × 24 m = 768 square meters When both diagonals are drawn in a rectangle, they divide it into four equal triangles Since there are four equal triangles, each triangle has area = total area ÷ 4 Area of one…
    Full step-by-step solution

    Step 1: Calculate the total area of the rectangular garden Area of rectangle = length × width = 32 m × 24 m = 768 square meters Step 2: Determine how the diagonals divide the rectangle When both diagonals are drawn in a rectangle, they divide it into four equal triangles Step 3: Calculate the area of one triangular flower bed Since there are four equal triangles, each triangle has area = total area ÷ 4 Area of one triangle = 768 ÷ 4 = 192 square meters The answer is 192 square meters.