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Stage 12 of 20

Two-Digit Addition (With Carry)

Master two-digit addition with carrying through regrouping, place-value reasoning, estimation, and flexible mental strategies with checked practice.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Recognize when ten or more ones must be regrouped as one ten
  • Add two two-digit numbers accurately when one or both columns overflow
  • Choose between column regrouping, partitioning, and round-and-adjust methods
  • Estimate and use subtraction to check whether a sum is reasonable

The Reasoning Behind Two-Digit Addition (With Carry)

Carrying works because our number system groups ten ones as one ten. In 38 + 47, the ones total 8 + 7 = 15: five ones remain in the ones place and the other ten joins the tens. This is not an extra “1” appearing from nowhere; it is one new group of ten.

Stage 11 separated tens and ones when both columns stayed below ten. The same partitioning still applies here, but regrouping connects the columns. For 56 + 39, combine 50 + 30 and 6 + 9. The 15 ones become 10 + 5, so 80 + 10 + 5 = 95.

A left-to-right method can reduce memory load. Add the tens first, then the ones: 67 + 28 becomes 67 + 20 = 87, followed by 87 + 8 = 95. The Stage 8 skill of bridging to the next ten makes the last move efficient: 87 needs 3, leaving 5.

Round-and-adjust is especially useful when an addend lies near a multiple of ten. Replace 49 with 50, calculate 36 + 50 = 86, then remove the extra 1 to obtain 85. The adjustment preserves equality because the temporary change is reversed.

Estimate before accepting an answer. Rounding 68 + 75 to 70 + 80 predicts about 150, so 143 is plausible but 1,430 is not. A precise inverse check—143 − 75 = 68—reuses the subtraction relationship learned in earlier stages.

Why This Skill Matters

Carried addition appears whenever totals cross a bundle, decade, or place-value boundary: combining prices, scores, distances, and inventories. Understanding the regrouping prevents the common habit of following a written rule without knowing what the carried digit represents.

Where You Will Use Two-Digit Addition (With Carry)

Suppose a school club sold 68 tickets online and 57 at the door. Add 50 to 68, then 7: 118 + 7 = 125 tickets. An estimate of 70 + 60 = 130 confirms the total is sensible.

See the Strategy in Action

Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.

Regroup the ones

38 + 47

  1. 1 Add the ones: 8 + 7 = 15.
  2. 2 Keep 5 ones and regroup 10 ones as 1 ten.
  3. 3 Add tens: 3 + 4 + 1 = 8 tens.

38 + 47 = 85

Your turn — try it on new numbers

34 + 36 = ?

Cross into the hundreds

68 + 75

  1. 1 The ones make 8 + 5 = 13, so keep 3 and carry 1 ten.
  2. 2 The tens make 6 + 7 + 1 = 14 tens.
  3. 3 Fourteen tens equal 1 hundred and 4 tens.

68 + 75 = 143

Your turn — try it on new numbers

29 + 34 = ?

Add in parts

57 + 48

  1. 1 Add 40 to 57 to reach 97.
  2. 2 Split 8 as 3 + 5; add 3 to reach 100.
  3. 3 Add the remaining 5.

57 + 48 = 105

Your turn — try it on new numbers

13 + 39 = ?

Round and compensate

46 + 29

  1. 1 Treat 29 as 30 − 1.
  2. 2 Calculate 46 + 30 = 76.
  3. 3 Subtract the extra 1.

46 + 29 = 75

Your turn — try it on new numbers

56 + 37 = ?

Self-Check: Errors to Avoid

Forgetting the regrouped ten

Writing 8 + 7 = 15 and then adding only 3 + 4 loses ten. Mark or say “one extra ten” before adding the tens column.

Writing 15 in the ones place

A place holds one digit. Keep the 5 ones and move the value 10—not the digit 1 without meaning—to the tens.

Adjusting in the wrong direction

If 49 was rounded up to 50, the temporary sum is one too large. Subtract 1; do not add another 1.

Pro Tips

  • • Say “ten ones become one ten” rather than memorizing “carry the one.”
  • • Estimate with rounded tens before doing exact work.
  • • For an addend ending in 8 or 9, test round-and-adjust.
  • • Check a sum by subtracting either addend from the total.

Practice Exercises

Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.

  1. 1. 27 + 48 = ?
  2. 2. 36 + 57 = ?
  3. 3. 49 + 28 = ?
  4. 4. 65 + 37 = ?
  5. 5. 58 + 46 = ?
  6. 6. 74 + 19 = ?
  7. 7. 68 + 67 = ?
  8. 8. 39 + 54 = ?
  9. 9. 47 + 66 = ?
  10. 10. 85 + 29 = ?
  11. 11. 56 + 78 = ?
  12. 12. 99 + 38 = ?
  13. 13. 44 + 77 = ?
  14. 14. 69 + 45 = ?
  15. 15. 88 + 27 = ?
  16. 16. 73 + 58 = ?
  17. 17. 96 + 17 = ?
  18. 18. 59 + 59 = ?

Drill Stage 12 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses two-digit plus two-digit with carrying. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

47 + 24 = ?

Stage 12 Questions

Must I always add the ones first?

No. Ones-first suits written columns, while left-to-right partitioning often suits mental work. Both must account for the new ten.

Why can a sum of two two-digit numbers have three digits?

Their combined tens can reach ten or more tens. For example, 68 + 75 makes 14 tens and 3 ones, or 143.

How do I know whether carrying is needed?

Inspect the ones digits: a sum of 10 or more creates a new ten. The tens may then also reach 10 and create a hundred.