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Stage 8 of 20

Two-Digit Plus Single (With Carry)

Master two-digit plus one-digit addition with carrying by bridging through tens, regrouping ones, explaining each trade, and checking results.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Predict when an ones sum will form a new group of ten
  • Split an addend to bridge efficiently through the next ten
  • Regroup ten ones as one ten without changing the total
  • Defend an answer using inverse subtraction and estimation

How Two-Digit Plus Single (With Carry) Works

In 47 + 8, seven ones and eight ones make fifteen ones. Fifteen ones are not written as a single ones digit: they regroup into one ten and five ones. The four existing tens become five tens, producing 55. Carrying is therefore an exchange of equal value, because ten ones and one ten both represent 10.

Bridging through a friendly ten often feels lighter than holding 15. Forty-seven needs 3 to reach 50, so split the 8 into 3 + 5. First move 47 + 3 to 50, then add the remaining 5. The split is legitimate because 3 + 5 still equals the original addend, 8.

A place-value chart explains why both digits may change. For 68 + 7, the ones total is 15: write 5 in the ones place and move one group to the tens. Six tens plus the new ten become seven tens, so the result is 75. Checking 75 − 7 = 68 confirms both the regrouping and the direction of change.

Stage 7 trained you to inspect the ones before operating. Keep that habit, but respond differently when the sum reaches 10. Earlier complement-of-ten work is useful too: the complement of 8 is 2, so 58 + 6 becomes 60 + 4. This bridge prepares you to carry within two-digit plus two-digit addition later.

Why This Skill Matters

Crossing a ten occurs constantly in elapsed time, scores, prices, and inventory. Understanding the exchange prevents carrying from becoming an unexplained written trick.

Mental Walkthroughs

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.

Bridge to fifty

46 + 7

  1. 1 Notice that 46 needs 4 to reach 50.
  2. 2 Split 7 into 4 + 3.
  3. 3 Calculate 46 + 4 = 50, then 50 + 3 = 53.

46 + 7 = 53

Your turn — try it on new numbers

57 + 7 = ?

Regroup fifteen ones

68 + 7

  1. 1 Combine the ones: 8 + 7 = 15.
  2. 2 Exchange 10 ones for 1 ten, leaving 5 ones.
  3. 3 Combine 6 tens and the new ten to make 75.

68 + 7 = 75

Your turn — try it on new numbers

36 + 4 = ?

Cross into a new hundred

96 + 8

  1. 1 Use 4 of the 8 to move from 96 to 100.
  2. 2 There are 4 left because 8 = 4 + 4.
  3. 3 Add the remainder: 100 + 4 = 104.

96 + 8 = 104

Your turn — try it on new numbers

68 + 3 = ?

Check a carried answer

79 + 5

  1. 1 Add 1 first to reach 80.
  2. 2 Add the remaining 4 to get 84.
  3. 3 Check by subtracting: 84 − 5 = 79.

79 + 5 = 84

Your turn — try it on new numbers

58 + 2 = ?

Watch for These Missteps

Keeping all fifteen in the ones place

Writing 615 for 68 + 7 ignores place value. Self-correct by exchanging ten of the fifteen ones for one ten and leaving only 5 ones.

Forgetting the leftover amount

After using 3 to move 47 to 50, stopping loses 5 of the original 8. State the split aloud—“3 and 5”—and add both parts.

Adding an extra carried ten

Changing 56 + 7 to 73 carries twice. Mark one exchange only: 6 + 7 = 13 means one new ten and 3 ones, giving 63.

Two-Digit Plus Single (With Carry) in Everyday Life

A bus has 58 passengers and picks up 7 more. Two passengers fill the next group of ten, and the other five bring the count to 65. Bridging to 60 makes the capacity change easy to track without written work.

Pro Tips

  • • Ask how many are needed to reach the next ten before splitting the addend.
  • • Keep both pieces of a split visible mentally so none is lost.
  • • Say “one new ten” instead of memorizing “carry one.”
  • • Estimate the new decade first; 67 + 8 must land in the seventies.

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 + 6 = ?
  2. 2. 48 + 5 = ?
  3. 3. 59 + 4 = ?
  4. 4. 36 + 8 = ?
  5. 5. 74 + 9 = ?
  6. 6. 85 + 7 = ?
  7. 7. 68 + 6 = ?
  8. 8. 93 + 8 = ?
  9. 9. 45 + 6 = ?
  10. 10. 77 + 5 = ?
  11. 11. 29 + 3 = ?
  12. 12. 56 + 9 = ?
  13. 13. 88 + 7 = ?
  14. 14. 39 + 8 = ?
  15. 15. 67 + 7 = ?
  16. 16. 95 + 9 = ?
  17. 17. 18 + 4 = ?
  18. 18. 82 + 9 = ?

Drill Stage 8 with unlimited problems

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

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Problem 1

22 + 8 = ?

Stage 8 Questions

Is bridging different from carrying?

They describe the same place-value change. Bridging splits the addend mentally; carrying records the newly formed ten.

What happens when the answer passes 99?

Ten tens regroup as one hundred. For example, 96 + 8 reaches 104, with one hundred, zero tens, and four ones.

Should I always add the ones first?

Not mentally. You may bridge to a round ten first, provided every part of the original addend is included.