Multi-Digit Division

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Multi-Digit Division · Grade 5 · Worksheet 3

1. Olivia is organizing 72913 photographs into an album. Each page can hold exactly 93 photographs. How many full pages can Olivia fill? Answer: 784 Solution: Start with 72913 photographs. Divide by 93 photographs per page: 72913 ÷ 93 = 784 with a remainder. The number of full pages is the whole number part: 784.
   Full step-by-step solution

   Step 1: Start with 72913 photographs. Step 2: Divide by 93 photographs per page: 72913 ÷ 93 = 784 with a remainder. Step 3: The number of full pages is the whole number part: 784. The answer is 784.

2. The city park department is planting trees along a new walking trail. They have 1,575 tree saplings that need to be distributed equally among 15 different sections of the trail. How many trees will be planted in each section? Answer: 105 Solution: Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of sections: 15 Step 3: Divide the total trees by the number of sections: 1,575 ÷ 15 Step 4: Calculate 15 × 100 = 1,500 Step 5: Subtract: 1,575 - 1,500 = 75 Step 6: Calculate 15 × 5 = 75 Step 7: Add the partial…
   Full step-by-step solution

   Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of sections: 15 Step 3: Divide the total trees by the number of sections: 1,575 ÷ 15 Step 4: Calculate 15 × 100 = 1,500 Step 5: Subtract: 1,575 - 1,500 = 75 Step 6: Calculate 15 × 5 = 75 Step 7: Add the partial results: 100 + 5 = 105 Step 8: Verify: 15 × 105 = 1,575 The answer is 105 trees per section.

3. The city park department is creating a new community garden with 1,680 square feet of planting space. They want to divide it equally into 35 rectangular plots for local families. How many square feet will each family's garden plot be? Answer: 48 Solution: Identify the total area: 1,680 square feet Identify the number of equal plots: 35 plots Divide the total area by the number of plots: 1,680 ÷ 35 Calculate 35 × 48 = 1,680, so 1,680 ÷ 35 = 48 Each family's garden plot will be 48 square feet.
   Full step-by-step solution

   Step 1: Identify the total area: 1,680 square feet Step 2: Identify the number of equal plots: 35 plots Step 3: Divide the total area by the number of plots: 1,680 ÷ 35 Step 4: Calculate 35 × 48 = 1,680, so 1,680 ÷ 35 = 48 Step 5: Each family's garden plot will be 48 square feet.

4. Leo is organizing 48255 photographs into an album. Each page can hold exactly 84 photographs. How many full pages can Leo fill? Answer: 574 Solution: Start with 48255 photographs. Divide by 84 photographs per page: 48255 ÷ 84 = 574 with a remainder. The number of full pages is the whole number part: 574.
   Full step-by-step solution

   Step 1: Start with 48255 photographs. Step 2: Divide by 84 photographs per page: 48255 ÷ 84 = 574 with a remainder. Step 3: The number of full pages is the whole number part: 574. The answer is 574.

5. A rectangular garden is drawn on a coordinate plane with corners at (2, 1), (8, 1), (8, 5), and (2, 5). If the gardener wants to divide the garden into equal square sections by drawing vertical and horizontal lines, creating the largest possible squares without any leftover space, how many square sections will there be? Answer: 6 Solution: The corners are at (2, 1), (8, 1), (8, 5), and (2, 5). The side from (2, 1) to (8, 1) is horizontal, so the length is: 8 − 2 = 6 units. The side from (2, 1) to (2, 5) is vertical, so the height is: 5 − 1 = 4 units.
   Full step-by-step solution

   Let's go step by step. --- **Step 1: Understand the rectangle's dimensions** The corners are at (2, 1), (8, 1), (8, 5), and (2, 5). The side from (2, 1) to (8, 1) is horizontal, so the length is: 8 − 2 = 6 units. The side from (2, 1) to (2, 5) is vertical, so the height is: 5 − 1 = 4 units. So the rectangle is 6 units wide and 4 units high. --- **Step 2: Interpret the problem** We want to divide the rectangle into equal square sections by drawing vertical and horizontal lines, creating the largest possible squares without leftover space. That means we need the largest square size that divides both the length (6) and the width (4) evenly. --- **Step 3: Find the largest possible square size** The largest square that can evenly divide both 6 and 4 means the side length of the square must be the greatest common divisor (GCD) of 6 and 4. GCD(6, 4) = 2. So the largest possible square has side length 2 units. --- **Step 4: Determine the number of squares** If each square is 2×2, then: - Along the width (6 units): number of squares = 6 ÷ 2 = 3 squares. - Along the height (4 units): number of squares = 4 ÷ 2 = 2 squares. Total squares = 3 × 2 = 6. --- **Step 5: Conclusion** The gardener can make 6 equal square sections, each of side 2 units. --- **Final answer:** 6

6. The city park department is planning to plant trees along a new walking trail. They have 1,575 young trees to plant equally along 15 sections of the trail. How many trees will be planted in each section? Answer: 105 Solution: Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of sections: 15 Step 3: Divide the total trees by the number of sections: 1,575 ÷ 15 Step 4: Calculate the division: 15 × 100 = 1,500, and 1,575 - 1,500 = 75 Step 5: 15 × 5 = 75, so 100 + 5 = 105 Step 6: Verify: 105 ×…
   Full step-by-step solution

   Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of sections: 15 Step 3: Divide the total trees by the number of sections: 1,575 ÷ 15 Step 4: Calculate the division: 15 × 100 = 1,500, and 1,575 - 1,500 = 75 Step 5: 15 × 5 = 75, so 100 + 5 = 105 Step 6: Verify: 105 × 15 = 1,575 The answer is 105 trees per section.

7. The city recreation department is organizing a community sports day. They have 1,575 participants who need to be divided equally among 21 different activity stations. How many participants will be assigned to each station? Answer: 75 Solution: Identify the total number of participants: 1,575 Identify the number of activity stations: 21 Set up the division problem: 1,575 ÷ 21 Divide 1,575 by 21 21 × 75 = 1,575 Therefore, 1,575 ÷ 21 = 75 The answer is 75 participants per station.
   Full step-by-step solution

   Step 1: Identify the total number of participants: 1,575 Step 2: Identify the number of activity stations: 21 Step 3: Set up the division problem: 1,575 ÷ 21 Step 4: Divide 1,575 by 21 Step 5: 21 × 75 = 1,575 Step 6: Therefore, 1,575 ÷ 21 = 75 The answer is 75 participants per station.

8. The school art club is preparing for their annual exhibition. They have 1,728 colorful beads that they want to divide equally among 24 students to make identical friendship bracelets. How many beads will each student receive for their bracelet project? Answer: 72 Solution: We are told there are 1,728 beads total and 24 students. We want to divide the beads equally among the students. Set up the division.
   Full step-by-step solution

   We are told there are 1,728 beads total and 24 students. We want to divide the beads equally among the students. Step 1: Set up the division. Total beads ÷ Number of students = Beads per student So we need to compute: 1728 ÷ 24 Step 2: One way to solve 1728 ÷ 24 is to break it into simpler steps. First, note that 24 = 8 × 3. We can divide 1728 by 8 first, then divide the result by 3. Step 3: Divide 1728 by 8. 8 × 200 = 1600 1728 − 1600 = 128 8 × 16 = 128 So 8 × (200 + 16) = 8 × 216 = 1728. Thus, 1728 ÷ 8 = 216. Step 4: Now divide 216 by 3. 3 × 70 = 210 216 − 210 = 6 3 × 2 = 6 So 3 × (70 + 2) = 3 × 72 = 216. Thus, 216 ÷ 3 = 72. Step 5: Conclusion. Each student will receive 72 beads. Answer: 72