SOMATH Math Enrichment · Regrouping · Medium Level

20 Regrouping Practice Questions — SOMATH Math Enrichment

A focused 20-question multiple-choice practice set from SOMATH Math Enrichment on regrouping — the moment in math when a column overflows (carrying) or runs short (borrowing). Every addition question below requires at least one carry. Every subtraction question requires at least one borrow. Every multiplication is 2-digit by 2-digit. Each explanation walks through the algorithm one column at a time.

· By the SOMATH team · 226 W 79th St, UWS

What's in this practice set

  1. Regrouping — carrying, borrowing, and 2-digit multiplication
  2. Addition with carrying (Questions 1–7)
  3. Subtraction with borrowing (Questions 8–14)
  4. 2-digit × 2-digit multiplication (Questions 15–20)
  5. Show all answers & explanations
  6. How SOMATH Math Enrichment builds these skills

Regrouping — the idea behind carrying, borrowing, and multi-digit multiplication

Every number we write is a bundle of ones, tens, hundreds, and thousands. The digit 2 in the tens place isn't really a "2" — it's 2 tens, which means 20 ones. The whole reason our number system works is that any time a column has 10 or more, we can trade it in for one of the next-bigger unit. That trade is called regrouping, and it shows up in three different disguises below.

1. Carrying (in addition)

When two digits in the same column add up to 10 or more, we can't fit the whole answer in that column. So we keep only the ones digit in that column and carry the extra 1 to the next column to the left. Example: 347 + 286.

The rule is always the same, no matter how many digits: if a column overflows, carry the extra to the next column. Get that idea, and 3-digit + 3-digit isn't harder than 2-digit + 2-digit — just longer.

2. Borrowing (in subtraction)

Borrowing is carrying in reverse. When the top digit is smaller than the bottom digit in a column, we can't subtract yet. So we borrow 1 from the next column to the left, which adds 10 to the current column. Example: 623 − 178.

When the top number has a zero in the middle (like 805 − 267), borrowing works the same way — the zero borrows from the hundreds first, then the ones borrows from the (now non-zero) tens.

3. 2-digit × 2-digit multiplication

Multiplying 47 × 18 looks scary until you break it into two easier problems. Split the second number into its tens and ones: 18 = 10 + 8. Then multiply each part by 47 and add.

This is exactly what the standard multi-digit multiplication algorithm does — one line for the ones, one line for the tens (shifted over by a zero), then add. Once a student sees the shift-a-zero step, 2 × 2 digit multiplication clicks.

How to use this practice set: Work each problem on paper using the standard algorithm — line up the digits by place, carry/borrow as needed, and add. Try each one before revealing the explanation. When you're stuck, click Show answer under that question — the explanation walks column by column. Finish all 20, then hit Show all answers & explanations at the bottom to review everything at once.

Addition · Questions 1–7 · Every problem has at least one carry

Addition with carrying

Line up the digits by place. Add the ones column first. If the sum is 10 or more, carry the 1 to the tens. Then add the tens (including any carry). Then add the hundreds (including any carry).

Question 1

What is 347 + 286?

  1. 633
  2. 693
  3. 609
  4. 596

Answer: A — 633

Ones: 7 + 6 = 13 — write 3, carry 1. Tens: 4 + 8 + 1 (carried) = 13 — write 3, carry 1. Hundreds: 3 + 2 + 1 (carried) = 6 — write 6. Answer: 347 + 286 = 633.

Question 2

What is 528 + 394?

  1. 1016
  2. 1020
  3. 922
  4. 871

Answer: C — 922

Ones: 8 + 4 = 12 — write 2, carry 1. Tens: 2 + 9 + 1 (carried) = 12 — write 2, carry 1. Hundreds: 5 + 3 + 1 (carried) = 9 — write 9. Answer: 528 + 394 = 922.

Question 3

What is 146 + 275?

  1. 377
  2. 383
  3. 421
  4. 475

Answer: C — 421

Ones: 6 + 5 = 11 — write 1, carry 1. Tens: 4 + 7 + 1 (carried) = 12 — write 2, carry 1. Hundreds: 1 + 2 + 1 (carried) = 4 — write 4. Answer: 146 + 275 = 421.

Question 4

What is 683 + 549?

  1. 1142
  2. 1390
  3. 1232
  4. 1322

Answer: C — 1232

Ones: 3 + 9 = 12 — write 2, carry 1. Tens: 8 + 4 + 1 (carried) = 13 — write 3, carry 1. Hundreds: 6 + 5 + 1 (carried) = 12 — write 2, carry 1 into the thousands. Answer: 683 + 549 = 1232.

Question 5

What is 259 + 468?

  1. 737
  2. 727
  3. 715
  4. 672

Answer: B — 727

Ones: 9 + 8 = 17 — write 7, carry 1. Tens: 5 + 6 + 1 (carried) = 12 — write 2, carry 1. Hundreds: 2 + 4 + 1 (carried) = 7 — write 7. Answer: 259 + 468 = 727.

Question 6

What is 417 + 195?

  1. 612
  2. 538
  3. 583
  4. 593

Answer: A — 612

Ones: 7 + 5 = 12 — write 2, carry 1. Tens: 1 + 9 + 1 (carried) = 11 — write 1, carry 1. Hundreds: 4 + 1 + 1 (carried) = 6 — write 6. Answer: 417 + 195 = 612.

Question 7

What is 738 + 596?

  1. 1335
  2. 1420
  3. 1234
  4. 1334

Answer: D — 1334

Ones: 8 + 6 = 14 — write 4, carry 1. Tens: 3 + 9 + 1 (carried) = 13 — write 3, carry 1. Hundreds: 7 + 5 + 1 (carried) = 13 — write 3, carry 1 into the thousands. Answer: 738 + 596 = 1334.

Subtraction · Questions 8–14 · Every problem needs at least one borrow

Subtraction with borrowing

Line up the digits by place. Start with the ones column. If the top digit is smaller than the bottom, borrow 1 from the next column to the left (that borrow adds 10 to your current column). Then subtract.

Question 8

What is 623 − 178?

  1. 435
  2. 509
  3. 459
  4. 445

Answer: D — 445

Ones: 3 is smaller than 8, so borrow 1 from the tens. Now the ones are 13 and the tens digit of the top number drops from 2 to 1. Then 13 − 8 = 5. Tens: 1 is smaller than 7, so borrow 1 from the hundreds. Now the tens are 11 and the hundreds digit drops from 6 to 5. Then 11 − 7 = 4. Hundreds: 5 − 1 = 4. Answer: 623 − 178 = 445. Check: 178 + 445 = 623. ✓

Question 9

What is 805 − 267?

  1. 498
  2. 538
  3. 528
  4. 503

Answer: B — 538

Ones: 5 is smaller than 7, so borrow 1 from the tens. Now the ones are 15 and the tens digit of the top number drops from 0 to -1. Then 15 − 7 = 8. Tens: -1 is smaller than 6, so borrow 1 from the hundreds. Now the tens are 9 and the hundreds digit drops from 8 to 7. Then 9 − 6 = 3. Hundreds: 7 − 2 = 5. Answer: 805 − 267 = 538. Check: 267 + 538 = 805. ✓

Question 10

What is 712 − 348?

  1. 365
  2. 355
  3. 385
  4. 364

Answer: D — 364

Ones: 2 is smaller than 8, so borrow 1 from the tens. Now the ones are 12 and the tens digit of the top number drops from 1 to 0. Then 12 − 8 = 4. Tens: 0 is smaller than 4, so borrow 1 from the hundreds. Now the tens are 10 and the hundreds digit drops from 7 to 6. Then 10 − 4 = 6. Hundreds: 6 − 3 = 3. Answer: 712 − 348 = 364. Check: 348 + 364 = 712. ✓

Question 11

What is 500 − 173?

  1. 317
  2. 355
  3. 287
  4. 327

Answer: D — 327

Ones: 0 is smaller than 3, so borrow 1 from the tens. Now the ones are 10 and the tens digit of the top number drops from 0 to -1. Then 10 − 3 = 7. Tens: -1 is smaller than 7, so borrow 1 from the hundreds. Now the tens are 9 and the hundreds digit drops from 5 to 4. Then 9 − 7 = 2. Hundreds: 4 − 1 = 3. Answer: 500 − 173 = 327. Check: 173 + 327 = 500. ✓

Question 12

What is 934 − 587?

  1. 348
  2. 356
  3. 347
  4. 357

Answer: C — 347

Ones: 4 is smaller than 7, so borrow 1 from the tens. Now the ones are 14 and the tens digit of the top number drops from 3 to 2. Then 14 − 7 = 7. Tens: 2 is smaller than 8, so borrow 1 from the hundreds. Now the tens are 12 and the hundreds digit drops from 9 to 8. Then 12 − 8 = 4. Hundreds: 8 − 5 = 3. Answer: 934 − 587 = 347. Check: 587 + 347 = 934. ✓

Question 13

What is 461 − 285?

  1. 181
  2. 164
  3. 176
  4. 185

Answer: C — 176

Ones: 1 is smaller than 5, so borrow 1 from the tens. Now the ones are 11 and the tens digit of the top number drops from 6 to 5. Then 11 − 5 = 6. Tens: 5 is smaller than 8, so borrow 1 from the hundreds. Now the tens are 15 and the hundreds digit drops from 4 to 3. Then 15 − 8 = 7. Hundreds: 3 − 2 = 1. Answer: 461 − 285 = 176. Check: 285 + 176 = 461. ✓

Question 14

What is 802 − 456?

  1. 346
  2. 355
  3. 345
  4. 331

Answer: A — 346

Ones: 2 is smaller than 6, so borrow 1 from the tens. Now the ones are 12 and the tens digit of the top number drops from 0 to -1. Then 12 − 6 = 6. Tens: -1 is smaller than 5, so borrow 1 from the hundreds. Now the tens are 9 and the hundreds digit drops from 8 to 7. Then 9 − 5 = 4. Hundreds: 7 − 4 = 3. Answer: 802 − 456 = 346. Check: 456 + 346 = 802. ✓

Multiplication · Questions 15–20 · 2-digit × 2-digit

2-digit × 2-digit multiplication

Split the second number into its tens and ones. Multiply the first number by each part, then add the two partial products. Remember: the "tens-line" always ends in a zero because you're multiplying by a full ten.

Question 15

What is 23 × 15?

  1. 401
  2. 407
  3. 345
  4. 354

Answer: C — 345

Break 15 into its tens and ones: 15 = 10 + 5. Multiply 23 by each part. First, 23 × 5 = 115 (this is the ones-line). Next, 23 × 10 = 230 (this is the tens-line, which ends in a 0 because we're multiplying by a full ten). Now add the two partial products: 115 + 230 = 345. So 23 × 15 = 345.

Question 16

What is 34 × 26?

  1. 974
  2. 955
  3. 884
  4. 852

Answer: C — 884

Break 26 into its tens and ones: 26 = 20 + 6. Multiply 34 by each part. First, 34 × 6 = 204 (this is the ones-line). Next, 34 × 20 = 680 (this is the tens-line, which ends in a 0 because we're multiplying by a full ten). Now add the two partial products: 204 + 680 = 884. So 34 × 26 = 884.

Question 17

What is 47 × 18?

  1. 954
  2. 899
  3. 846
  4. 728

Answer: C — 846

Break 18 into its tens and ones: 18 = 10 + 8. Multiply 47 by each part. First, 47 × 8 = 376 (this is the ones-line). Next, 47 × 10 = 470 (this is the tens-line, which ends in a 0 because we're multiplying by a full ten). Now add the two partial products: 376 + 470 = 846. So 47 × 18 = 846.

Question 18

What is 56 × 32?

  1. 1628
  2. 1456
  3. 2055
  4. 1792

Answer: D — 1792

Break 32 into its tens and ones: 32 = 30 + 2. Multiply 56 by each part. First, 56 × 2 = 112 (this is the ones-line). Next, 56 × 30 = 1680 (this is the tens-line, which ends in a 0 because we're multiplying by a full ten). Now add the two partial products: 112 + 1680 = 1792. So 56 × 32 = 1792.

Question 19

What is 68 × 24?

  1. 1331
  2. 1632
  3. 1631
  4. 1856

Answer: B — 1632

Break 24 into its tens and ones: 24 = 20 + 4. Multiply 68 by each part. First, 68 × 4 = 272 (this is the ones-line). Next, 68 × 20 = 1360 (this is the tens-line, which ends in a 0 because we're multiplying by a full ten). Now add the two partial products: 272 + 1360 = 1632. So 68 × 24 = 1632.

Question 20

What is 79 × 43?

  1. 2987
  2. 3014
  3. 3261
  4. 3397

Answer: D — 3397

Break 43 into its tens and ones: 43 = 40 + 3. Multiply 79 by each part. First, 79 × 3 = 237 (this is the ones-line). Next, 79 × 40 = 3160 (this is the tens-line, which ends in a 0 because we're multiplying by a full ten). Now add the two partial products: 237 + 3160 = 3397. So 79 × 43 = 3397.

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How SOMATH Math Enrichment builds these skills

At SOMATH, regrouping is one of the most important moments in a student's math foundation — and one of the easiest ones to accidentally skip. Kids who never fully internalize why the carry is a 1 (and not some other number), or why the tens-line in a 2×2 multiplication has a zero on the end, will hit a wall when they get to long division, fractions, and eventually algebra.

Here's how we teach these ideas differently:

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