Multi-Digit Operations

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Answer Key & Explanations

Multi-Digit Operations · Grade 4 · Worksheet 3

1. A rectangular garden is drawn on a grid where each square represents 1 square meter. The garden spans 8 squares along its length and 5 squares along its width. What is the total area of the garden in square meters? Answer: 40 Solution: The garden is drawn on a grid where each square represents 1 square meter. The length spans 8 squares, so the length is 8 meters. The width spans 5 squares, so the width is 5 meters.
   Full step-by-step solution

   Step 1: Understand the problem. The garden is drawn on a grid where each square represents 1 square meter. The length spans 8 squares, so the length is 8 meters. The width spans 5 squares, so the width is 5 meters. Step 2: Recall the formula for the area of a rectangle. Area = length × width Step 3: Substitute the given values into the formula. Area = 8 × 5 Step 4: Perform the multiplication. 8 × 5 = 40 Step 5: State the final answer with units. The total area of the garden is 40 square meters.

2. 32,762 + 47,217 = ? Answer: 79,979 Solution: Write the numbers vertically, aligning by place value: 32,762 + 47,217 Add the ones column: 2 + 7 = 9. Write 9 in the ones place. Add the tens column: 6 + 1 = 7.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning by place value: 32,762 + 47,217 -------- Step 2: Add the ones column: 2 + 7 = 9. Write 9 in the ones place. Step 3: Add the tens column: 6 + 1 = 7. Write 7 in the tens place. Step 4: Add the hundreds column: 7 + 2 = 9. Write 9 in the hundreds place. Step 5: Add the thousands column: 2 + 7 = 9. Write 9 in the thousands place. Step 6: Add the ten-thousands column: 3 + 4 = 7. Write 7 in the ten-thousands place. Step 7: Combine the results: 79,979. The answer is 79,979.

3. Emma is planning a school field trip to the science museum. The museum charges $12 per student for admission. If 28 students from Emma's class are going on the trip, how much money will they need to pay for all the student admissions? Answer: 336 Solution: Identify the cost per student: $12 Identify the number of students: 28 Multiply the cost per student by the number of students: 12 × 28 Calculate 12 × 20 = 240 Calculate 12 × 8 = 96 Add the partial products: 240 + 96 = 336 The total cost for all student admissions is $336.
   Full step-by-step solution

   Step 1: Identify the cost per student: $12 Step 2: Identify the number of students: 28 Step 3: Multiply the cost per student by the number of students: 12 × 28 Step 4: Calculate 12 × 20 = 240 Step 5: Calculate 12 × 8 = 96 Step 6: Add the partial products: 240 + 96 = 336 Step 7: The total cost for all student admissions is $336.

4. Liam is organizing his trading card collection. He has 347 baseball cards and 285 basketball cards. He gives his friend 120 cards that he already has duplicates of. How many cards does Liam have left in his collection? Answer: 512 Solution: First, find the total number of cards Liam has before giving any away. He has 347 baseball cards and 285 basketball cards. 347 + 285 = 632 So, Liam starts with 632 cards.
   Full step-by-step solution

   First, find the total number of cards Liam has before giving any away. He has 347 baseball cards and 285 basketball cards. Add them: 347 + 285 = 632 So, Liam starts with 632 cards. Next, he gives his friend 120 duplicate cards. Subtract the cards he gives away from the total: 632 - 120 = 512 Therefore, Liam has 512 cards left in his collection.

5. 2,847 - 1,539 = ? Answer: 1308 Solution: 2,847 - 1,539 Subtract the ones place: 7 - 9 (can't do, so regroup) Borrow 1 ten from the tens place, making 4 tens become 3 tens The 7 ones become 17 ones 17 - 9 = 8 Subtract the tens place: 3 - 3 = 0 Subtract the hundreds place: 8 - 5 = 3 Subtract the thousands place: 2 - 1 = 1 Combine the…
   Full step-by-step solution

   Step 1: Write the problem vertically: 2,847 - 1,539 Step 2: Subtract the ones place: 7 - 9 (can't do, so regroup) Borrow 1 ten from the tens place, making 4 tens become 3 tens The 7 ones become 17 ones 17 - 9 = 8 Step 3: Subtract the tens place: 3 - 3 = 0 Step 4: Subtract the hundreds place: 8 - 5 = 3 Step 5: Subtract the thousands place: 2 - 1 = 1 Step 6: Combine the results: 1,000 + 300 + 0 + 8 = 1,308 The answer is 1,308.

6. Olivia is looking at a rectangular garden plot drawn on a grid where each square represents 1 square meter. The plot is 45 meters long and 30 meters wide. A rectangular flower bed in one corner measures 15 meters by 10 meters. What is the area of the garden that is not covered by the flower bed? Answer: 1200 Solution: Find the total area of the rectangular garden plot. Area of rectangle = length × width = 45 × 30 = 1350 square meters. Find the area of the rectangular flower bed.
   Full step-by-step solution

   Step 1: Find the total area of the rectangular garden plot. Area of rectangle = length × width = 45 × 30 = 1350 square meters. Step 2: Find the area of the rectangular flower bed. Area of rectangle = length × width = 15 × 10 = 150 square meters. Step 3: Subtract the area of the flower bed from the total area to find the area not covered. 1350 - 150 = 1200 square meters. The answer is 1200.

7. Liam is organizing his book collection. He has 248 fiction books and 175 non-fiction books. If he donates 89 books to the library, how many books does Liam have left? Answer: 334 Solution: Find the total number of books Liam has initially. He has 248 fiction books and 175 non-fiction books. So, total books = 248 + 175.
   Full step-by-step solution

   Step 1: Find the total number of books Liam has initially. He has 248 fiction books and 175 non-fiction books. So, total books = 248 + 175. Let's add: 248 + 175 = 423. So, initially Liam has 423 books. Step 2: Subtract the number of books he donates. He donates 89 books. So, books left = 423 − 89. Let's subtract: 423 − 89 = 334. Step 3: Conclusion. After donating 89 books, Liam has 334 books left.