Mixed Number Division

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Mixed Number Division · Grade 6 · Worksheet 1

1. Ethan is building a model bridge using wooden planks. Each section of the bridge needs 6 meters of wood. Ethan has a total of 8 meters of wood. How many full sections can Ethan build? Answer: 1 Solution: Note the total length of wood: 8 meters. Note the length needed per section: 6 meters. Divide the total length by the length per section: 8 ÷ 6 = 1.
   Full step-by-step solution

   Step 1: Note the total length of wood: 8 meters. Step 2: Note the length needed per section: 6 meters. Step 3: Divide the total length by the length per section: 8 ÷ 6 = 1. Ethan can build 1 full sections of the bridge.

2. 3 1/2 ÷ 1 3/4 = ? Answer: 2 Solution: Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2 Convert 1 3/4 to an improper fraction: 1 3/4 = (1 × 4 + 3)/4 = 7/4 Rewrite the division: 7/2 ÷ 7/4 Change division to multiplication by the reciprocal: 7/2 × 4/7 Multiply the fractions: (7 × 4)/(2 × 7) = 28/14 Simplify the…
   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 1 3/4 to an improper fraction: 1 3/4 = (1 × 4 + 3)/4 = 7/4 Step 3: Rewrite the division: 7/2 ÷ 7/4 Step 4: Change division to multiplication by the reciprocal: 7/2 × 4/7 Step 5: Multiply the fractions: (7 × 4)/(2 × 7) = 28/14 Step 6: Simplify the fraction: 28 ÷ 14 = 2 The answer is 2.

3. 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.

4. Kaia is designing a mosaic for a community art project. She has a rectangular board that measures 15 3/4 inches long by 10 1/2 inches wide. She wants to divide the board into equal square sections by drawing a grid. The side length of each square section must be 1 3/4 inches. Into how many square sections will the board be divided? Answer: 54 Solution: Find the number of squares along the length. Length = 15 3/4 inches. Square side = 1 3/4 inches.
   Full step-by-step solution

   Step 1: Find the number of squares along the length. Length = 15 3/4 inches. Square side = 1 3/4 inches. Convert to improper fractions: 15 3/4 = (15*4 + 3)/4 = 63/4. 1 3/4 = (1*4 + 3)/4 = 7/4. Divide: (63/4) ÷ (7/4) = (63/4) * (4/7) = (63 * 4) / (4 * 7) = 63/7 = 9 squares along the length. Step 2: Find the number of squares along the width. Width = 10 1/2 inches. Convert to improper fraction: 10 1/2 = (10*2 + 1)/2 = 21/2. Divide: (21/2) ÷ (7/4) = (21/2) * (4/7) = (21 * 4) / (2 * 7) = 84/14 = 6 squares along the width. Step 3: Find the total number of square sections. Total squares = squares along length * squares along width = 9 * 6 = 54 square sections. The answer is 54.

5. A rectangular garden is divided into two triangular sections by a diagonal path. The garden measures 12 meters long by 5 meters wide. If one triangular section is planted with flowers, what is the area of the flower section in square meters? Answer: 30 Solution: We have a rectangular garden that is 12 meters long and 5 meters wide. A diagonal divides it into two equal triangles. One triangular section is planted with flowers.
   Full step-by-step solution

   Step 1: Understand the problem. We have a rectangular garden that is 12 meters long and 5 meters wide. A diagonal divides it into two equal triangles. One triangular section is planted with flowers. We need the area of that triangular flower section. Step 2: Recall the area of a rectangle. Area of rectangle = length × width = 12 × 5. Step 3: Calculate the area of the rectangle. 12 × 5 = 60 square meters. Step 4: Understand the diagonal's effect. A diagonal of a rectangle splits it into two congruent (identical) triangles. So each triangle has half the area of the rectangle. Step 5: Find the area of one triangular section. Area of flower section = (Area of rectangle) / 2 = 60 / 2 = 30 square meters. Step 6: Final answer. The flower section has an area of 30 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. Liam is making a special trail mix for his hiking club. He has 2 1/4 cups of almonds and wants to divide them equally into small snack bags. If each bag can hold 3/8 cup of almonds, how many full snack bags can Liam make? Answer: 6 Solution: Liam has 2 1/4 cups of almonds. Each bag holds 3/8 cup. We want to find how many full bags he can make.
   Full step-by-step solution

   Step 1: Understand the problem Liam has 2 1/4 cups of almonds. Each bag holds 3/8 cup. We want to find how many full bags he can make. Step 2: Convert mixed number to improper fraction 2 1/4 = 2 + 1/4 = 8/4 + 1/4 = 9/4 cups. Step 3: Set up the division Number of bags = (total almonds) ÷ (almonds per bag) Number of bags = (9/4) ÷ (3/8) Step 4: Divide fractions Dividing by a fraction is the same as multiplying by its reciprocal. (9/4) ÷ (3/8) = (9/4) × (8/3) Step 5: Multiply the fractions Multiply numerators: 9 × 8 = 72 Multiply denominators: 4 × 3 = 12 Result = 72/12 Step 6: Simplify 72 ÷ 12 = 6 Step 7: Interpret the result The division gives exactly 6, meaning Liam can make 6 full snack bags with no almonds left over. Final answer: 6

8. 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.