Multi-Digit Operations

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Multi-Digit Operations · Grade 4 · Worksheet 2

1. Liam is organizing his baseball card collection. He has 347 cards in his main binder and his friend gives him 125 more cards. How many baseball cards does Liam have in total now? Answer: 472 Solution: Start with the number of cards in his main binder. Liam has 347 cards. Add the number of cards his friend gives him.
   Full step-by-step solution

   Let's add the number of baseball cards Liam has. Step 1: Start with the number of cards in his main binder. Liam has 347 cards. Step 2: Add the number of cards his friend gives him. His friend gives him 125 more cards. Step 3: Write the addition problem. 347 + 125 Step 4: Add the ones place. 7 ones + 5 ones = 12 ones. 12 ones = 1 ten and 2 ones. Write down 2 in the ones place and carry over 1 to the tens place. Step 5: Add the tens place. 4 tens + 2 tens = 6 tens, plus the carried over 1 ten = 7 tens. Write down 7 in the tens place. Step 6: Add the hundreds place. 3 hundreds + 1 hundred = 4 hundreds. Write down 4 in the hundreds place. Step 7: Write the final number. The total is 472. So, Liam now has 472 baseball cards in total.

2. 12,345 + 67,890 = ? Answer: 80,235 Solution: Write the numbers vertically, aligning by place value: 12,345 + 67,890 Add the ones column: 5 + 0 = 5. Write 5. Add the tens column: 4 + 9 = 13.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning by place value: 12,345 + 67,890 -------- Step 2: Add the ones column: 5 + 0 = 5. Write 5. Step 3: Add the tens column: 4 + 9 = 13. Write 3, carry over 1 to the hundreds column. Step 4: Add the hundreds column: 3 + 8 + 1 (carried) = 12. Write 2, carry over 1 to the thousands column. Step 5: Add the thousands column: 2 + 7 + 1 (carried) = 10. Write 0, carry over 1 to the ten-thousands column. Step 6: Add the ten-thousands column: 1 + 6 + 1 (carried) = 8. Write 8. Step 7: Combine the digits: 80,235. The answer is 80,235.

3. A farmer harvested 3,475 pounds of apples from her orchard. She sold 1,892 pounds to a grocery store and 758 pounds to a farmers market. How many pounds of apples does she have left? Answer: 825 Solution: The farmer started with 3,475 pounds of apples. She sold some to a grocery store and some to a farmers market. We need to find how many pounds are left.
   Full step-by-step solution

   Let's solve this step-by-step. Step 1: Understand the problem. The farmer started with 3,475 pounds of apples. She sold some to a grocery store and some to a farmers market. We need to find how many pounds are left. Step 2: Add up the total pounds she sold. Sold to grocery store: 1,892 pounds Sold to farmers market: 758 pounds Total sold = 1,892 + 758 First, add the ones place: 2 + 8 = 10 → write 0, carry 1. Next, the tens place: 9 + 5 = 14, plus carried 1 = 15 → write 5, carry 1. Next, the hundreds place: 8 + 7 = 15, plus carried 1 = 16 → write 6, carry 1. Next, the thousands place: 1 + 0 = 1, plus carried 1 = 2. So, total sold = 2,650 pounds. Step 3: Subtract the total sold from the initial amount. Initial apples = 3,475 pounds Total sold = 2,650 pounds Apples left = 3,475 − 2,650 Subtract step-by-step: Ones place: 5 − 0 = 5 Tens place: 7 − 5 = 2 Hundreds place: 4 − 6 → we can't do directly, so borrow from thousands. 3,475 becomes 3 thousands and 4 hundreds → borrow 1 thousand → 2 thousands and 14 hundreds. Now hundreds: 14 − 6 = 8 Thousands place: 2 − 2 = 0 So, result = 825 pounds. Step 4: Conclusion. The farmer has 825 pounds of apples left. Answer: 825

4. 2,156 × 43 = ? Answer: 92708 Solution: Step 1: Multiply 2,156 by 3 (ones place): 2,156 × 3 = 6,468 Step 2: Multiply 2,156 by 40 (tens place): 2,156 × 40 = 86,240 Step 3: Add the two products: 6,468 + 86,240 = 92,708 Step 4: Verify: 6,468 + 86,240 = 92,708 The answer is 92,708.
   Full step-by-step solution

   Step 1: Multiply 2,156 by 3 (ones place): 2,156 × 3 = 6,468 Step 2: Multiply 2,156 by 40 (tens place): 2,156 × 40 = 86,240 Step 3: Add the two products: 6,468 + 86,240 = 92,708 Step 4: Verify: 6,468 + 86,240 = 92,708 The answer is 92,708.

5. 6,842 + 3,958 = ? Answer: 10800 Solution: Write the numbers vertically, aligning by place value: 6,842 + 3,958 Add the ones column: 2 + 8 = 10. Write 0, carry 1 to the tens column. Add the tens column: 4 + 5 + 1 (carried) = 10.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning by place value: 6,842 + 3,958 -------- Step 2: Add the ones column: 2 + 8 = 10. Write 0, carry 1 to the tens column. Step 3: Add the tens column: 4 + 5 + 1 (carried) = 10. Write 0, carry 1 to the hundreds column. Step 4: Add the hundreds column: 8 + 9 + 1 (carried) = 18. Write 8, carry 1 to the thousands column. Step 5: Add the thousands column: 6 + 3 + 1 (carried) = 10. Write 0, carry 1 to the ten-thousands column. Step 6: Write the carried 1 in the ten-thousands place. Step 7: The result is 10,800. The answer is 10,800.

6. Olivia is looking at a rectangular playground drawn on a grid where each square represents 1 square meter. The playground has a length of 35 meters and a width of 20 meters. A rectangular sandbox in one corner measures 5 meters by 10 meters. What is the total area of the playground that is NOT covered by the sandbox? Answer: 650 Solution: Find the area of the entire rectangular playground. Area = length × width = 35 × 20 = 700 square meters. Find the area of the rectangular sandbox.
   Full step-by-step solution

   Step 1: Find the area of the entire rectangular playground. Area = length × width = 35 × 20 = 700 square meters. Step 2: Find the area of the rectangular sandbox. Area = length × width = 5 × 10 = 50 square meters. Step 3: Subtract the sandbox area from the total playground area to find the area not covered by the sandbox. 700 - 50 = 650 square meters. The answer is 650.

7. Tane is looking at a rectangular sports field drawn on a grid. Each square on the grid represents 1 square meter. The length of the field spans 1,234 squares and the width spans 567 squares. What is the difference between the length and the width of the field in meters? Answer: 667 Solution: Identify the length and width. Length = 1,234 meters, Width = 567 meters. Subtract the width from the length to find the difference: 1,234 - 567.
   Full step-by-step solution

   Step 1: Identify the length and width. Length = 1,234 meters, Width = 567 meters. Step 2: Subtract the width from the length to find the difference: 1,234 - 567. Step 3: Subtract the hundreds: 1,200 - 500 = 700. Step 4: Subtract the tens: 30 - 60 = -30 (need to regroup). Alternatively, do the standard subtraction: 1,234 - 567. Step 5: Regroup: 1,234 = 1,200 + 34. Borrow 1 hundred to make 34 into 134. Then 1,200 becomes 1,100. So 1,100 + 134 = 1,234. Step 6: Subtract 567 from 1,234: 1,234 - 567 = 667. The answer is 667.