Multi-Digit Division

lessonbunny.com

Answer Key & Explanations

Multi-Digit Division · Grade 5 · Worksheet 1

1. The city park department is planting trees along a new bike path. They have 1,575 saplings that need to be distributed equally among 15 different park sections. How many trees will each section receive? Answer: 105 Solution: Step 1: Identify the total number of trees: 1,575 Step 2: Identify the number of park 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 park 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.

2. A rectangular garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. If the total area of the garden is 600 square feet, what is the area of each square plot? Answer: 50 Solution: Let’s go step by step. The garden is a rectangle divided into 12 equal square plots arranged in 3 rows and 4 columns. Total area of the garden is given as 600 square feet.
   Full step-by-step solution

   Let’s go step by step. Step 1: Understand the problem. The garden is a rectangle divided into 12 equal square plots arranged in 3 rows and 4 columns. So there are 3 × 4 = 12 square plots in total. Step 2: Total area of the garden is given as 600 square feet. Since the 12 plots are equal in area, we can find the area of one plot by dividing the total area by the number of plots. Step 3: Calculation. Area of one plot = Total area ÷ Number of plots Area of one plot = 600 ÷ 12 Step 4: Perform the division. 600 ÷ 12 = 50 Step 5: Conclusion. Each square plot has an area of 50 square feet. Final answer: 50

3. The city recreation department is organizing a summer reading program. They have 1,575 books that need to be distributed equally among 15 different community centers. How many books will each community center receive? Answer: 105 Solution: Identify the total number of books: 1,575 Identify the number of community centers: 15 Set up the division problem: 1,575 ÷ 15 Divide 1,575 by 15 15 × 100 = 1,500 1,575 - 1,500 = 75 15 × 5 = 75 75 - 75 = 0 Add the partial quotients: 100 + 5 = 105 Each community center will receive 105 books.
   Full step-by-step solution

   Step 1: Identify the total number of books: 1,575 Step 2: Identify the number of community centers: 15 Step 3: Set up the division problem: 1,575 ÷ 15 Step 4: Divide 1,575 by 15 15 × 100 = 1,500 1,575 - 1,500 = 75 15 × 5 = 75 75 - 75 = 0 Step 5: Add the partial quotients: 100 + 5 = 105 Step 6: Each community center will receive 105 books.

4. The city recreation department is organizing a summer sports camp. They have 1,575 basketballs that need to be distributed equally among 21 different community centers. How many basketballs will each community center receive? Answer: 75 Solution: Identify the total number of basketballs: 1,575 Identify the number of community centers: 21 Set up the division problem: 1,575 ÷ 21 Divide 1,575 by 21 21 × 75 = 1,575 Therefore, 1,575 ÷ 21 = 75 Each community center will receive 75 basketballs.
   Full step-by-step solution

   Step 1: Identify the total number of basketballs: 1,575 Step 2: Identify the number of community centers: 21 Step 3: Set up the division problem: 1,575 ÷ 21 Step 4: Divide 1,575 by 21 21 × 75 = 1,575 Step 5: Therefore, 1,575 ÷ 21 = 75 Each community center will receive 75 basketballs.

5. The school library is organizing its book collection and needs to distribute 1,248 books equally among 8 classrooms for their reading corners. How many books will each classroom receive? Answer: 156 Solution: We are dividing 1,248 books equally among 8 classrooms. This means we need to calculate 1,248 ÷ 8. Set up the division.
   Full step-by-step solution

   We are dividing 1,248 books equally among 8 classrooms. This means we need to calculate 1,248 ÷ 8. Step 1: Set up the division. We can think of it as: 8 × ? = 1,248 Step 2: Break down 1,248 into parts that are easier to divide by 8. First, 8 × 100 = 800. Subtract: 1,248 − 800 = 448. So far we have 100 books per classroom, with 448 left to divide. Step 3: Now divide 448 by 8. 8 × 50 = 400. Subtract: 448 − 400 = 48. Now we have an additional 50 books per classroom, so total so far is 100 + 50 = 150 per classroom, with 48 left. Step 4: Divide 48 by 8. 8 × 6 = 48. Subtract: 48 − 48 = 0. So that’s an extra 6 books per classroom. Step 5: Add up: 100 + 50 + 6 = 156. Thus, each classroom receives 156 books. Final answer: 156

6. A factory produces 1,248 identical toy cars and needs to pack them equally into boxes that hold 24 cars each. How many boxes will be completely filled? Answer: 52 Solution: We are told that the factory produces 1,248 identical toy cars and each box holds 24 cars. We need to find how many boxes will be completely filled.
   Full step-by-step solution

   We are told that the factory produces 1,248 identical toy cars and each box holds 24 cars. We need to find how many boxes will be completely filled. Step 1: Understand the problem. We need to divide the total number of cars by the number of cars per box to find the number of full boxes. Step 2: Write the division. Total cars = 1,248 Cars per box = 24 Number of boxes = 1248 ÷ 24 Step 3: Perform the division. First, check how many times 24 goes into 1248. We can break it down: 24 × 50 = 1200 Subtract: 1248 − 1200 = 48 Now, 24 × 2 = 48 So, 24 × 50 + 24 × 2 = 24 × 52 = 1248. Step 4: Interpret the result. Since 1248 ÷ 24 = 52 exactly, there is no remainder. This means all 1,248 cars fit perfectly into 52 boxes, with no leftover cars. Step 5: Conclusion. The number of boxes completely filled is 52. ANSWER: 52

7. 1,365 ÷ 15 = ? Answer: 91 Solution: Set up the division: 15 into 1,365 15 goes into 13 zero times, so consider 136 15 × 9 = 135, which fits into 136 Subtract: 136 - 135 = 1 Bring down the 5 to make 15 15 × 1 = 15, which fits exactly Subtract: 15 - 15 = 0 The quotient is 91 The answer is 91.
   Full step-by-step solution

   Step 1: Set up the division: 15 into 1,365 Step 2: 15 goes into 13 zero times, so consider 136 Step 3: 15 × 9 = 135, which fits into 136 Step 4: Subtract: 136 - 135 = 1 Step 5: Bring down the 5 to make 15 Step 6: 15 × 1 = 15, which fits exactly Step 7: Subtract: 15 - 15 = 0 Step 8: The quotient is 91 The answer is 91.

8. The city recreation department is organizing a community sports day. They have 1,680 bottles of water that need to be distributed equally among 24 different activity stations. How many bottles of water will each station receive? Answer: 70 Solution: Identify the total number of water bottles: 1,680 Identify the number of stations: 24 Set up the division problem: 1,680 ÷ 24 Divide 1,680 by 24 24 × 70 = 1,680 Therefore, 1,680 ÷ 24 = 70 The answer is 70.
   Full step-by-step solution

   Step 1: Identify the total number of water bottles: 1,680 Step 2: Identify the number of stations: 24 Step 3: Set up the division problem: 1,680 ÷ 24 Step 4: Divide 1,680 by 24 24 × 70 = 1,680 Step 5: Therefore, 1,680 ÷ 24 = 70 The answer is 70.

9. A rectangular garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. If the total area of the garden is 432 square meters, what is the area of each square plot? Answer: 36 Solution: 1. The garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. This means there are 3 × 4 = 12 plots in total.
   Full step-by-step solution

   Let's go step-by-step. 1. The garden is divided into 12 equal square plots arranged in 3 rows and 4 columns. This means there are 3 × 4 = 12 plots in total. 2. The total area of the garden is given as 432 square meters. Since all 12 plots are equal in area, we can find the area of one plot by dividing the total area by the number of plots. 3. Calculation: Area of one plot = Total area ÷ Number of plots Area of one plot = 432 ÷ 12 4. Perform the division: 432 ÷ 12 = 36 5. So, each square plot has an area of 36 square meters. Final answer: 36