Mixed Number Division

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Answer Key & Explanations

Mixed Number Division · Grade 6 · Worksheet 1

1. 2 3/4 ÷ 1 1/2 = ? Answer: 1 5/6 Solution: Convert 2 3/4 to an improper fraction: 2 × 4 + 3 = 11, so 2 3/4 = 11/4 Convert 1 1/2 to an improper fraction: 1 × 2 + 1 = 3, so 1 1/2 = 3/2 Rewrite the division as multiplication by the reciprocal: 11/4 ÷ 3/2 = 11/4 × 2/3 Multiply the fractions: (11 × 2)/(4 × 3) = 22/12 Simplify the fraction:…
   Full step-by-step solution

   Step 1: Convert 2 3/4 to an improper fraction: 2 × 4 + 3 = 11, so 2 3/4 = 11/4 Step 2: Convert 1 1/2 to an improper fraction: 1 × 2 + 1 = 3, so 1 1/2 = 3/2 Step 3: Rewrite the division as multiplication by the reciprocal: 11/4 ÷ 3/2 = 11/4 × 2/3 Step 4: Multiply the fractions: (11 × 2)/(4 × 3) = 22/12 Step 5: Simplify the fraction: 22/12 = 11/6 Step 6: Convert to a mixed number: 11 ÷ 6 = 1 with remainder 5, so 11/6 = 1 5/6 The answer is 1 5/6.

2. A school is organizing a field trip and needs to divide students equally among buses. There are 156 students going on the trip, and each bus can hold 24 students. How many full buses will be needed to transport all the students? Answer: 6 Solution: Identify the total number of students: 156 Identify how many students each bus can hold: 24 Divide the total students by the bus capacity: 156 ÷ 24 Calculate 24 × 6 = 144 Since 24 × 7 = 168 (which is more than 156), we can only fill 6 full buses The remaining 12 students (156 - 144 = 12) would…
   Full step-by-step solution

   Step 1: Identify the total number of students: 156 Step 2: Identify how many students each bus can hold: 24 Step 3: Divide the total students by the bus capacity: 156 ÷ 24 Step 4: Calculate 24 × 6 = 144 Step 5: Since 24 × 7 = 168 (which is more than 156), we can only fill 6 full buses Step 6: The remaining 12 students (156 - 144 = 12) would need a partial bus, but the question asks for full buses only Step 7: Therefore, 6 full buses are needed The answer is 6.

3. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 24 meters long by 18 meters wide. If the owner plants flowers in one triangular section and vegetables in the other, what is the area of the vegetable section in square meters? Answer: 216 Solution: We have a rectangular garden 24 m long and 18 m wide. A diagonal divides it into two equal triangles. One triangle is for vegetables, the other for flowers.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular garden 24 m long and 18 m wide. A diagonal divides it into two equal triangles. One triangle is for vegetables, the other for flowers. Step 2: Find the area of the whole rectangle. Area of rectangle = length × width Area = 24 × 18 Step 3: Calculate 24 × 18. 24 × 10 = 240 24 × 8 = 192 240 + 192 = 432 So, area of rectangle = 432 square meters. Step 4: Determine the area of one triangular section. Since the diagonal splits the rectangle into two equal triangles, each triangle has half the area of the rectangle. Area of one triangle = 432 ÷ 2 Step 5: Perform the division. 432 ÷ 2 = 216 Step 6: Conclusion. The vegetable section is one of these triangles, so its area is 216 square meters. Final answer: 216

4. A school is organizing a field trip to the science museum and needs to divide students equally among chaperones. There are 48 students attending, and the school policy requires 1 chaperone for every 3 1/2 students. How many complete chaperone groups can be formed? Answer: 13 Solution: Convert the mixed number 3 1/2 to an improper fraction: 3 1/2 = 7/2 Divide the total number of students (48) by the group size (7/2): 48 ÷ 7/2 Dividing by a fraction is the same as multiplying by its reciprocal: 48 × 2/7 Multiply: 48 × 2 = 96 Divide: 96 ÷ 7 = 13 with remainder 5 Since we need…
   Full step-by-step solution

   Step 1: Convert the mixed number 3 1/2 to an improper fraction: 3 1/2 = 7/2 Step 2: Divide the total number of students (48) by the group size (7/2): 48 ÷ 7/2 Step 3: Dividing by a fraction is the same as multiplying by its reciprocal: 48 × 2/7 Step 4: Multiply: 48 × 2 = 96 Step 5: Divide: 96 ÷ 7 = 13 with remainder 5 Step 6: Since we need complete groups, we take the whole number part: 13 The answer is 13 complete chaperone groups.

5. 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 feet long for the shelves. How many complete shelf pieces 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 feet long. We need to find how many *complete* pieces we can get.
   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 feet long. We need to find how many *complete* pieces we can get. --- Step 2: Convert mixed number to improper fraction The board length is 3 1/4 feet. 3 1/4 = 3 + 1/4 = 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 piece: (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 get 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 make 5 full pieces, and there will be a leftover piece of 1/5 of the shelf length. But 1/5 of a shelf length is (1/5) × (5/8) = 1/8 foot leftover wood, which is not enough for another full shelf (since a full shelf needs 5/8 foot). --- Step 7: Final answer The number of complete shelf pieces is 5.

6. Liam is building a bookshelf and has a board that is 3 1/2 feet long. He needs to cut it into pieces that are each 5/8 of a foot long for the shelves. How many complete shelves can he cut from this board? Answer: 5 Solution: We have a board that is 3 1/2 feet long. We need to cut it into pieces each 5/8 of a foot long. We want the number of complete shelves, so any leftover piece that is shorter than 5/8 foot does not count.
   Full step-by-step solution

   Step 1: Understand the problem. We have a board that is 3 1/2 feet long. We need to cut it into pieces each 5/8 of a foot long. We want the number of complete shelves, so any leftover piece that is shorter than 5/8 foot does not count. Step 2: Convert the mixed number to an improper fraction. 3 1/2 = 3 + 1/2 = 6/2 + 1/2 = 7/2 feet. Step 3: Divide the total board length by the length of one shelf to find how many shelves we can get. Number of shelves = (Total length) ÷ (Length per shelf) = (7/2) ÷ (5/8) Step 4: Dividing fractions: multiply by the 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 have 56/10. Step 6: Simplify 56/10. 56/10 = 28/5 = 5 3/5. Step 7: Interpret the result. 5 3/5 means 5 whole shelves and 3/5 of a shelf left over. Since we can only use complete shelves, the answer is 5. Final answer: 5

7. 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.

8. Liam is making a special trail mix for his hiking club. He has 3 1/2 cups of almonds and wants to divide them equally into small bags that each hold 1/4 cup. How many full bags of almonds can Liam make? Answer: 14 Solution: Liam has 3 1/2 cups of almonds. Each bag holds 1/4 cup. We want to know how many *full* bags he can make.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the problem** Liam has 3 1/2 cups of almonds. Each bag holds 1/4 cup. We want to know how many *full* bags he can make. --- **Step 2: Convert mixed number to improper fraction** 3 1/2 cups = 3 + 1/2 = 6/2 + 1/2 = 7/2 cups. --- **Step 3: Set up the division** We need to divide total almonds by amount per bag: (7/2) ÷ (1/4) --- **Step 4: Perform the division** Dividing by 1/4 is the same as multiplying by 4/1: (7/2) × (4/1) = (7 × 4) / (2 × 1) = 28 / 2 = 14. --- **Step 5: Interpret the result** 14 means 14 full bags, each holding 1/4 cup, can be made. No remainder, so all almonds are used exactly. --- **Final Answer:** 14