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Stage 14 of 20

Two-Digit Subtraction (With Borrow)

Master two-digit subtraction with borrowing through regrouping, counting up, constant differences, estimation, and inverse-operation checks.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Explain borrowing as exchanging one ten for ten ones without changing value
  • Subtract accurately when the top ones digit is smaller than the bottom one
  • Select regrouping, counting up, or constant difference for a given problem
  • Estimate and verify differences through addition

How Two-Digit Subtraction (With Borrow) Works

Borrowing is a place-value exchange, not a loan that changes the number. In 72 − 38, rename 72 as 60 + 12. Twelve ones can supply eight ones, and the total still equals 72 because one of the seven tens became ten ones.

Now subtract by place: 12 − 8 = 4 and 60 − 30 = 30, giving 34. Stage 13 already established independent column subtraction; the only new action is preparing enough ones before applying that familiar process.

Counting up treats subtraction as distance. From 38, jump 2 to 40, 30 to 70, and 2 to 72. The jumps total 34. This method is often clearer when the subtrahend lies near a friendly ten and directly uses complements learned in Stage 5.

Constant difference can remove an awkward ones comparison. Add 2 to both numbers in 72 − 38 to obtain 74 − 40. Their gap remains 34 because shifting both endpoints equally does not alter the distance between them.

An estimate controls the process. Since 72 is about 70 and 38 is about 40, expect roughly 30. A result of 34 fits; 44 suggests the regrouped ten was not reduced. Finally, add 38 + 34 to ensure the original 72 returns.

Why This Skill Matters

Regrouping makes subtraction useful across decade boundaries: calculating change, elapsed distance, stock reductions, and score differences. Understanding the exchange is safer than memorizing crossed-out digits.

The same principle later handles zeros and larger numbers. Each exchange always trades one unit of a place for ten units of the place to its right.

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.

Exchange one ten

72 − 38

  1. 1 Rename 72 as 60 + 12.
  2. 2 Subtract ones: 12 − 8 = 4.
  3. 3 Subtract tens: 60 − 30 = 30; combine 30 + 4.

72 − 38 = 34

Your turn — try it on new numbers

20 − 11 = ?

Borrow across a zero ones place

80 − 47

  1. 1 Rename 80 as 70 + 10.
  2. 2 Take 7 ones from 10, leaving 3.
  3. 3 Subtract 4 tens from 7 tens, leaving 3 tens.

80 − 47 = 33

Your turn — try it on new numbers

28 − 19 = ?

Count upward

61 − 27

  1. 1 Jump 27 to 30: 3.
  2. 2 Jump 30 to 60: 30.
  3. 3 Jump 60 to 61: 1; total the jumps.

61 − 27 = 34

Your turn — try it on new numbers

37 − 19 = ?

Shift both endpoints

53 − 29

  1. 1 Add 1 to both numbers to preserve the gap.
  2. 2 Compute the friendlier 54 − 30.
  3. 3 Subtract three tens from 54.

53 − 29 = 24

Your turn — try it on new numbers

44 − 28 = ?

Watch for These Missteps

Adding ten ones without removing a ten

Changing 72 to “70 + 12” creates 82. The correct rename is 60 + 12: one fewer ten, ten more ones.

Reversing the ones subtraction

Calculating 8 − 2 because it is easier changes the problem. Regroup first, then calculate 12 − 8.

Counting endpoints twice

When counting 38 to 40, the distance is 2, not 3. Track jumps or additions, not the number of spoken endpoints.

Two-Digit Subtraction (With Borrow) in Everyday Life

If you pay $80 for a $47 purchase, rename the eighty dollars as seven tens and ten ones. The change is $33. Counting from 47 to 50 and then to 80 reaches the same answer.

A runner planned 91 kilometres over several weeks and completed 48. The remaining 43 kilometres is plausible because 90 − 50 is about 40.

Pro Tips

  • • Say the rename explicitly: “72 is 60 plus 12.”
  • • Use counting up when the lower number is near a multiple of ten.
  • • Round first so you know the expected decade of the answer.
  • • Add the difference back to the subtrahend to check.

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. 74 − 28 = ?
  2. 2. 63 − 19 = ?
  3. 3. 82 − 47 = ?
  4. 4. 50 − 26 = ?
  5. 5. 91 − 58 = ?
  6. 6. 67 − 29 = ?
  7. 7. 73 − 46 = ?
  8. 8. 84 − 57 = ?
  9. 9. 60 − 38 = ?
  10. 10. 52 − 17 = ?
  11. 11. 95 − 68 = ?
  12. 12. 71 − 36 = ?
  13. 13. 43 − 18 = ?
  14. 14. 86 − 49 = ?
  15. 15. 90 − 54 = ?
  16. 16. 64 − 27 = ?
  17. 17. 81 − 65 = ?
  18. 18. 55 − 38 = ?

Drill Stage 14 with unlimited problems

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

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Problem 1

76 − 17 = ?

Stage 14 Questions

Does borrowing make the top number smaller?

No. It renames the same value: 72 and 60 + 12 are equal. Only the distribution among places changes.

Is counting up valid for every subtraction?

Yes, because subtraction measures a difference. It is most convenient when a few friendly jumps connect the numbers.

Which method should I use mentally?

Choose the method with the fewest secure steps: regrouping for clear place work, counting up near round numbers, or equal shifts for friendly endpoints.