Mixed Number Division

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Mixed Number Division · Grade 6 · Worksheet 2

1. 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.

2. A construction crew needs to build a fence that is 48.75 meters long. Each fence panel measures 1.25 meters. How many panels does the crew need to complete the fence? Answer: 39 Solution: To find how many panels are needed, we need to divide the total length of the fence by the length of one panel. Write down the total length and the length of one panel. Total fence length = 48.75 meters Length of one panel = 1.25 meters Set up the division to find the number of panels.
   Full step-by-step solution

   To find how many panels are needed, we need to divide the total length of the fence by the length of one panel. Step 1: Write down the total length and the length of one panel. Total fence length = 48.75 meters Length of one panel = 1.25 meters Step 2: Set up the division to find the number of panels. Number of panels = Total length / Length per panel Number of panels = 48.75 / 1.25 Step 3: To make the division easier, we can multiply both the numerator and the denominator by 100. This moves the decimal point two places to the right for both numbers, turning them into whole numbers. This does not change the value of the division. 48.75 / 1.25 = (48.75 * 100) / (1.25 * 100) = 4875 / 125 Step 4: Now, perform the division 4875 ÷ 125. First, check how many times 125 fits into 487. 125 * 3 = 375 Subtract 375 from 487: 487 - 375 = 112 Step 5: Bring down the next digit, which is 5, making the new number 1125. Now, see how many times 125 fits into 1125. 125 * 9 = 1125 Subtract 1125 from 1125: 1125 - 1125 = 0 Step 6: Since the remainder is 0, the division is complete. 4875 ÷ 125 = 39 Therefore, the crew needs 39 panels to complete the fence.

3. Kai is building a model car track. The track needs to be 11 feet long, but the track pieces are each 11 feet long. How many track pieces does Kai need to buy? Answer: 1 Solution: The total track length needed is 11 feet. Each piece is 11 feet long. Divide the total length by the piece length: 11 ÷ 11 = 1 pieces.
   Full step-by-step solution

   Step 1: The total track length needed is 11 feet. Step 2: Each piece is 11 feet long. Step 3: Divide the total length by the piece length: 11 ÷ 11 = 1 pieces. The answer is 1.

4. A rectangular garden is divided into four equal triangular sections by drawing both diagonals. The garden measures 36 meters long by 28 meters wide. If the gardener plants vegetables in two adjacent triangular sections, what is the total area of the vegetable sections in square meters? Answer: 504 Solution: Find the total area of the rectangular garden. Area = length × width = 36 m × 28 m = 1008 square meters Determine how the diagonals divide the rectangle.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden. Area = length × width = 36 m × 28 m = 1008 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: Find the area of one triangular section. Area of one triangle = Total area ÷ 4 = 1008 ÷ 4 = 252 square meters Step 4: Calculate the area for two adjacent triangular sections. Two adjacent triangles = 2 × 252 = 504 square meters The answer is 504.

5. 4 2/3 ÷ 2 1/4 = ? Answer: 2 2/27 Solution: Convert 4 2/3 to an improper fraction: (4 × 3 + 2)/3 = (12 + 2)/3 = 14/3 Convert 2 1/4 to an improper fraction: (2 × 4 + 1)/4 = (8 + 1)/4 = 9/4 Rewrite the division as multiplication by the reciprocal: 14/3 ÷ 9/4 = 14/3 × 4/9 Multiply the fractions: (14 × 4)/(3 × 9) = 56/27 Convert 56/27 to a…
   Full step-by-step solution

   Step 1: Convert 4 2/3 to an improper fraction: (4 × 3 + 2)/3 = (12 + 2)/3 = 14/3 Step 2: Convert 2 1/4 to an improper fraction: (2 × 4 + 1)/4 = (8 + 1)/4 = 9/4 Step 3: Rewrite the division as multiplication by the reciprocal: 14/3 ÷ 9/4 = 14/3 × 4/9 Step 4: Multiply the fractions: (14 × 4)/(3 × 9) = 56/27 Step 5: Convert 56/27 to a mixed number: 56 ÷ 27 = 2 with remainder 2, so 2 2/27 The answer is 2 2/27.

6. 3 1/3 ÷ 2 1/2 = ? Answer: 1 1/3 Solution: Convert 3 1/3 to an improper fraction: 3 1/3 = (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Convert 2 1/2 to an improper fraction: 2 1/2 = (2 × 2 + 1)/2 = (4 + 1)/2 = 5/2 Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 5/2 = 10/3 × 2/5 Multiply the fractions: (10 × 2)/(3 × 5) = 20/15…
   Full step-by-step solution

   Step 1: Convert 3 1/3 to an improper fraction: 3 1/3 = (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Step 2: Convert 2 1/2 to an improper fraction: 2 1/2 = (2 × 2 + 1)/2 = (4 + 1)/2 = 5/2 Step 3: Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 5/2 = 10/3 × 2/5 Step 4: Multiply the fractions: (10 × 2)/(3 × 5) = 20/15 Step 5: Simplify the fraction: 20/15 = 4/3 Step 6: Convert to a mixed number: 4/3 = 1 1/3 The answer is 1 1/3.

7. 3 1/3 ÷ 1 1/4 = ? Answer: 2 2/3 Solution: Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Convert 1 1/4 to an improper fraction: (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 5/4 = 10/3 × 4/5 Multiply the fractions: (10 × 4)/(3 × 5) = 40/15 Simplify the fraction:…
   Full step-by-step solution

   Step 1: Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3 Step 2: Convert 1 1/4 to an improper fraction: (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4 Step 3: Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 5/4 = 10/3 × 4/5 Step 4: Multiply the fractions: (10 × 4)/(3 × 5) = 40/15 Step 5: Simplify the fraction: 40 ÷ 5 = 8, 15 ÷ 5 = 3, so 40/15 = 8/3 Step 6: Convert back to a mixed number: 8 ÷ 3 = 2 with remainder 2, so 8/3 = 2 2/3 The answer is 2 2/3.

8. 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.

9. 3 1/2 ÷ 2 1/4 = ? Answer: 1 5/9 Solution: Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Convert 2 1/4 to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 Rewrite the division as multiplication by the reciprocal: 7/2 ÷ 9/4 = 7/2 × 4/9 Multiply the fractions: (7 × 4)/(2 × 9) = 28/18 Simplify the fraction: 28/18 =…
   Full step-by-step solution

   Step 1: Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Step 2: Convert 2 1/4 to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4 Step 3: Rewrite the division as multiplication by the reciprocal: 7/2 ÷ 9/4 = 7/2 × 4/9 Step 4: Multiply the fractions: (7 × 4)/(2 × 9) = 28/18 Step 5: Simplify the fraction: 28/18 = 14/9 Step 6: Convert to a mixed number: 14/9 = 1 5/9 The answer is 1 5/9.