Mixed Number Division

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Mixed Number Division · Grade 6 · Worksheet 3

1. Liam is building a bookshelf and has a wooden board that is 3 1/2 feet long. He needs to cut it into smaller pieces that are each 5/8 of a foot long to make the shelves. How many complete shelves can he cut from the board? Answer: 5 Solution: Liam has a board that is 3 1/2 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 1/2 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 1/2 = 3 + 1/2 = 6/2 + 1/2 = 7/2 feet. Step 3: Set up the division To find how many pieces of length 5/8 fit into 7/2, we divide: (7/2) ÷ (5/8) Step 4: Dividing fractions rule Dividing by a fraction is the same as multiplying by its reciprocal: (7/2) ÷ (5/8) = (7/2) × (8/5) Step 5: Multiply the fractions Multiply numerators: 7 × 8 = 56 Multiply denominators: 2 × 5 = 10 So we get 56/10. Step 6: Simplify the fraction 56/10 = 28/5 = 5 3/5. Step 7: Interpret the result 5 3/5 means 5 whole shelves and a leftover piece (3/5 of a shelf length). The problem asks for complete shelves, so we take the whole number part: 5. Step 8: Final answer Liam can cut 5 complete shelves from the board.

2. A rectangular garden is divided into four equal triangular sections by drawing both diagonals from opposite corners. The garden measures 32 meters long by 24 meters wide. If the gardener plants vegetables in one of these triangular sections, what is the area of the vegetable section in square meters? Answer: 192 Solution: Find the total area of the rectangular garden. Area = length × width = 32 m × 24 m = 768 square meters Determine how many equal triangular sections the diagonals create.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden. Area = length × width = 32 m × 24 m = 768 square meters Step 2: Determine how many equal triangular sections the diagonals create. The two diagonals divide the rectangle into 4 equal triangles. Step 3: Calculate the area of one triangular section. Area of one triangle = Total area ÷ 4 = 768 ÷ 4 = 192 square meters The area of the vegetable section is 192 square meters.

3. Liam is building a bookshelf and needs to cut a wooden board that is 8 3/4 feet long into equal sections that are each 1 1/4 feet long. How many complete sections can he cut from the board? Answer: 7 Solution: We have a board that is 8 3/4 feet long. We want to cut it into sections each 1 1/4 feet long. We need the number of *complete* sections.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the problem** We have a board that is 8 3/4 feet long. We want to cut it into sections each 1 1/4 feet long. We need the number of *complete* sections. --- **Step 2: Convert mixed numbers to improper fractions** 8 3/4 = (8 × 4 + 3)/4 = (32 + 3)/4 = 35/4 1 1/4 = (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 So the board length is 35/4 feet, and each section is 5/4 feet. --- **Step 3: Divide total length by section length** Number of sections = (35/4) ÷ (5/4) Dividing fractions: (35/4) × (4/5) = (35 × 4) / (4 × 5) Cancel the 4's: 35/5 = 7. --- **Step 4: Interpret the result** The division gives exactly 7, meaning we can cut 7 full sections of 1 1/4 feet each with no leftover wood that can make another full section. --- **Step 5: Check** 7 sections × 1 1/4 feet = 7 × 5/4 = 35/4 = 8 3/4 feet. This exactly matches the board length, so there is no leftover. --- **Final Answer:** 7

4. A community garden is planning to create rectangular planting beds using wooden planks. They have a long plank that measures 8 2/3 feet in length. Each planting bed requires side pieces that are exactly 1 1/4 feet long. How many complete side pieces can they cut from the full plank? Answer: 6 Solution: 8 2/3 = (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 1 1/4 = (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 We need to divide 26/3 by 5/4 Apply the division rule for fractions (multiply by the reciprocal) 26/3 ÷ 5/4 = 26/3 × 4/5 (26 × 4)/(3 × 5) = 104/15 104 ÷ 15 = 6 with remainder 14, so 104/15 = 6 14/15 Since we need…
   Full step-by-step solution

   Step 1: Convert the mixed numbers to improper fractions 8 2/3 = (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 1 1/4 = (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 Step 2: Set up the division problem We need to divide 26/3 by 5/4 Step 3: Apply the division rule for fractions (multiply by the reciprocal) 26/3 ÷ 5/4 = 26/3 × 4/5 Step 4: Multiply the fractions (26 × 4)/(3 × 5) = 104/15 Step 5: Convert the improper fraction to a mixed number 104 ÷ 15 = 6 with remainder 14, so 104/15 = 6 14/15 Step 6: Since we need complete pieces, we take the whole number part 6 complete side pieces can be cut The answer is 6.

5. 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.

6. A community garden is planning to divide a large rectangular plot of land into individual gardening beds. The total plot measures 8 3/4 acres, and each gardening bed requires 1 1/4 acres of space. How many complete gardening beds can the community create from this plot? Answer: 7 Solution: 8 3/4 = (8 × 4 + 3)/4 = (32 + 3)/4 = 35/4 1 1/4 = (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 35/4 ÷ 5/4 = 35/4 × 4/5 35/4 × 4/5 = (35 × 4)/(4 × 5) = 35/5 35/5 = 7 Since we're looking for complete beds, and 7 is a whole number, we have exactly 7 complete beds.
   Full step-by-step solution

   Step 1: Convert the mixed numbers to improper fractions 8 3/4 = (8 × 4 + 3)/4 = (32 + 3)/4 = 35/4 1 1/4 = (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 Step 2: Divide the total area by the area per bed 35/4 ÷ 5/4 = 35/4 × 4/5 Step 3: Simplify the fractions 35/4 × 4/5 = (35 × 4)/(4 × 5) = 35/5 Step 4: Calculate the result 35/5 = 7 Step 5: Since we're looking for complete beds, and 7 is a whole number, we have exactly 7 complete beds. The community can create 7 complete gardening beds.

7. A community center is organizing a food drive and needs to divide their rice supply into family-sized portions. They have 8 2/3 kilograms of rice available, and each family should receive 5/6 of a kilogram. How many complete family portions can they prepare from their rice supply? Answer: 10 Solution: Convert 8 2/3 to an improper fraction: 8 2/3 = (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 Divide the total rice by the portion size: 26/3 ÷ 5/6 When dividing fractions, multiply by the reciprocal: 26/3 × 6/5 Multiply the numerators: 26 × 6 = 156 Multiply the denominators: 3 × 5 = 15 Simplify the…
   Full step-by-step solution

   Step 1: Convert 8 2/3 to an improper fraction: 8 2/3 = (8 × 3 + 2)/3 = (24 + 2)/3 = 26/3 Step 2: Divide the total rice by the portion size: 26/3 ÷ 5/6 Step 3: When dividing fractions, multiply by the reciprocal: 26/3 × 6/5 Step 4: Multiply the numerators: 26 × 6 = 156 Step 5: Multiply the denominators: 3 × 5 = 15 Step 6: Simplify the fraction: 156/15 = 52/5 = 10 2/5 Step 7: Since we need complete portions, we take the whole number part: 10 The community center can prepare 10 complete family portions.

8. A community center is organizing a food drive and needs to divide their rice supply into family-sized portions. They have 8 2/3 kilograms of rice and want to create packages that each contain 5/6 of a kilogram. How many complete family-sized packages can they make? Answer: 10 Solution: Convert 8 2/3 to an improper fraction: 8 × 3 = 24, 24 + 2 = 26, so 8 2/3 = 26/3 Set up the division problem: 26/3 ÷ 5/6 To divide fractions, multiply by the reciprocal: 26/3 × 6/5 Multiply numerators: 26 × 6 = 156 Multiply denominators: 3 × 5 = 15 Simplify the fraction: 156/15 = 10 6/15 = 10 2/5…
   Full step-by-step solution

   Step 1: Convert 8 2/3 to an improper fraction: 8 × 3 = 24, 24 + 2 = 26, so 8 2/3 = 26/3 Step 2: Set up the division problem: 26/3 ÷ 5/6 Step 3: To divide fractions, multiply by the reciprocal: 26/3 × 6/5 Step 4: Multiply numerators: 26 × 6 = 156 Step 5: Multiply denominators: 3 × 5 = 15 Step 6: Simplify the fraction: 156/15 = 10 6/15 = 10 2/5 Step 7: Since we need complete packages, we take the whole number part: 10 They can make 10 complete family-sized packages.