Multi-Digit Operations

Grade 4 Β· mathematics Β· 85 practice problems Β· read aloud

πŸ”Š Listen to this explanation

Multi-Digit Operations: Adding & Subtracting Big Numbers

πŸ” What Is It & Why Learn It?

Multi-digit operations are when we add or subtract numbers that have more than one digit, like 345 + 178 or 602 - 437. We use this all the time in real life, like when we're figuring out how much money we have, how many points our team scored, or how many miles we've traveled! It helps us work with bigger numbers confidently.

πŸ“ Step-by-Step Guide

The secret is to line up the numbers by their place value (ones, tens, hundreds) and work from right to left!

  1. Write it down: Stack the numbers so the digits line up in columns.
  2. Start on the right: Add or subtract the ones column first.
  3. Regroup if needed: If the ones add up to 10 or more, carry the tens digit to the next column. If you can't subtract, borrow from the next column.
  4. Move left: Repeat for the tens, then hundreds column.

✨ Visual Examples

Example 1: Addition with Carrying
Let's solve 427 + 158.

Β Β 427
+Β 158
Β Β 585

Steps: 7 ones + 8 ones = 15 ones. Write down the 5, carry the 1 ten. 1 ten + 2 tens + 5 tens = 8 tens. 4 hundreds + 1 hundred = 5 hundreds.

Example 2: Subtraction with Borrowing
Let's solve 503 - 267.

Β 4Β 9Β 13
Β 5ΜΆ0ΜΆΒ³3
-Β 2Β 6Β 7
Β Β 2Β 3Β 6

Steps: Can't do 3 - 7. Borrow from the tens, but the tens is 0! So borrow from the hundreds. 5 hundreds becomes 4 hundreds, 0 tens becomes 10 tens. Then borrow 1 ten to make 13 ones. 13 - 7 = 6. 9 tens - 6 tens = 3 tens. 4 hundreds - 2 hundreds = 2 hundreds.

⚠️ Common Mistakes

  • Forgetting to regroup: Always check if you need to carry or borrow!
  • Misaligned columns: If your ones, tens, and hundreds aren't lined up, your answer will be wrong. Use graph paper to help.
  • Borrowing confusion: Remember, when you borrow, you're taking 10, not 1. And don't forget to cross out and reduce the number you borrowed from.

πŸ’‘ Tips & Tricks

  • Check your work! For addition, subtract one of the numbers from your answer to see if you get the other. For subtraction, add your answer to the number you subtracted to see if you get the original number.
  • Estimate first: Round the numbers (427 β‰ˆ 430, 158 β‰ˆ 160). 430 + 160 = 590. Your real answer (585) should be close!
  • Use a highlighter to mark the columns you are currently working on to help you stay focused.

🎯 Practice Makes Perfect

Here's how you can become a multi-digit master:

  • Start with 2-digit problems, then move to 3-digit.
  • Create your own problems about things you like (sports scores, video game points).
  • Ask a friend or family member to give you five problems a day.
  • Use online math games that focus on addition and subtraction with regrouping.

Practice problems

6 of the 85, worked through step by step β€” try them before opening the answer.

1 347 Γ— 6 = ?

Hint: Multiply each digit in the larger number by the single-digit multiplier, remembering to carry over when necessary.

Show the answer

Answer: 2082

  1. Multiply 6 by the units digit (7). 6 Γ— 7 = 42 Write down 2 in the units place, carry over 4 to the tens column.
  2. Multiply 6 by the tens digit (4). 6 Γ— 4 = 24 Add the carried over 4: 24 + 4 = 28 Write down 8 in the tens place, carry over 2 to the hundreds column.
  3. Multiply 6 by the hundreds digit (3). 6 Γ— 3 = 18 Add the carried over 2: 18 + 2 = 20 Write down 0 in the hundreds place and 2 in the thousands place. So the result is 2082. Final check: 347 Γ— 6 = (300 Γ— 6) + (40 Γ— 6) + (7 Γ— 6) = 1800 + 240 + 42 = 1800 + 282 = 2082 ANSWER: 2082

Let's multiply 347 by 6 step-by-step. We can write it as: 347 Γ— 6 ------

2 324 Γ— 17 = ?

Hint: Break this into smaller multiplication problems and add the partial products together

Show the answer

Answer: 5508

  1. Break 17 into 10 + 7. We will multiply 324 by 10 and 324 by 7, then add the results.
  2. Multiply 324 by 10. 324 Γ— 10 = 3240.
  3. Multiply 324 by 7. First, 300 Γ— 7 = 2100. Then, 20 Γ— 7 = 140. Then, 4 Γ— 7 = 28. Add them: 2100 + 140 = 2240, then 2240 + 28 = 2268.
  4. Add the results from Step 2 and
  5. 3240 + 2268. First, add the thousands: 3000 + 2000 = 5000. Then add the hundreds: 240 + 268 = 508. Now combine: 5000 + 508 = 5508. Final answer: 5508.

Let's multiply 324 by 17 step by step.

3 347 Γ— 26 = ?

Hint: Break the problem into smaller parts by multiplying each digit separately, then combine the results

Show the answer

Answer: 9022

  1. Break 26 into 20 + 6. We will multiply 347 by 6 first, then 347 by 20, and add the results.
  2. Multiply 347 by 6. 347 Γ— 6: 7 Γ— 6 = 42 β†’ write 2, carry 4 4 Γ— 6 = 24, plus carried 4 = 28 β†’ write 8, carry 2 3 Γ— 6 = 18, plus carried 2 = 20 β†’ write 20 So 347 Γ— 6 = 2082.
  3. Multiply 347 by 20. 347 Γ— 20 = 347 Γ— 2 Γ— 10 First, 347 Γ— 2: 7 Γ— 2 = 14 β†’ write 4, carry 1 4 Γ— 2 = 8, plus carried 1 = 9 β†’ write 9 3 Γ— 2 = 6 β†’ write 6 So 347 Γ— 2 = 694. Now multiply by 10: 694 Γ— 10 = 6940. So 347 Γ— 20 = 6940.
  4. Add the two results. 2082 + 6940: 2082 + 6940 --- 9022
  5. Final answer. 347 Γ— 26 = 9022.

Let's multiply 347 by 26 step by step.

4 245 Γ— 36 = ?

Hint: Break this into smaller multiplication problems and then add the results together. Think about multiplying by the tens place and ones place separately.

Show the answer

Answer: 8820

  1. Break 36 into 30 + 6. We will multiply 245 by 6, then 245 by 30, and add the results.
  2. Multiply 245 Γ— 6. 245 Γ— 6: 5 Γ— 6 = 30 β†’ write 0, carry 3 4 Γ— 6 = 24, plus carried 3 = 27 β†’ write 7, carry 2 2 Γ— 6 = 12, plus carried 2 = 14 β†’ write 14 So 245 Γ— 6 = 1470.
  3. Multiply 245 Γ— 30. 245 Γ— 30 = 245 Γ— 3 Γ— 10 First, 245 Γ— 3: 5 Γ— 3 = 15 β†’ write 5, carry 1 4 Γ— 3 = 12, plus carried 1 = 13 β†’ write 3, carry 1 2 Γ— 3 = 6, plus carried 1 = 7 β†’ write 7 So 245 Γ— 3 = 735. Now multiply by 10: 735 Γ— 10 = 7350.
  4. Add the two results. 1470 + 7350: 0 + 0 = 0 7 + 5 = 12 β†’ write 2, carry 1 4 + 3 = 7, plus carried 1 = 8 β†’ write 8 1 + 7 = 8 β†’ write 8 So total = 8820. Final answer: 8820

Let's multiply 245 Γ— 36 step by step.

5 1,248 Γ— 37 = ?

Hint: Break this into smaller multiplication problems by multiplying each digit of the first number by the second number, then add the partial products together.

Show the answer

Answer: 46,176

  1. Multiply 1,248 by 7 (the ones digit of 37) 1,248 Γ— 7 = 8,736
  2. Multiply 1,248 by 30 (the tens digit of 37) 1,248 Γ— 30 = 37,440
  3. Add the partial products together 8,736 + 37,440 = 46,176

The answer is 46,176.

6 2,156 Γ— 43 = ?

Hint: Break this into smaller multiplication problems and then add the results together

Show the answer

Answer: 92708

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

The answer is 92,708.

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