tfarrejfm
Stage 10 of 20

Two-Digit Minus Single (With Borrow)

Understand two-digit minus one-digit borrowing through fair place-value exchanges, add-up strategies, rigorous checks, examples, and practice.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Recognize when the ones place lacks enough units to subtract
  • Exchange one ten for ten ones while preserving total value
  • Choose sensibly between regrouping and counting up
  • Confirm a borrowed subtraction result using addition

Understanding Two-Digit Minus Single (With Borrow)

Suppose 52 − 7 is represented by five tens and two ones. Two ones cannot supply seven ones, so exchange one of the tens for ten ones. The quantity is still 52, now arranged as four tens and twelve ones. Remove seven from twelve to leave five; four tens and five ones make 45.

Borrowing changes the representation, not the number. Algebraically, 50 + 2 equals 40 + 12 because 10 was moved from one place-value unit to another. After the exchange, every part is accounted for: 12 − 7 = 5 and the remaining four tens contribute 40. This conservation of value is the reason the procedure works.

Counting up is a useful alternative when the decade is nearby. For 63 − 8, measure the distance from 8 to 63: 8 to 10 is 2, 10 to 60 is 50, and 60 to 63 is 3; together that is 55. A shorter mental route is 63 − 3 = 60, then subtract the remaining 5 to get 55.

Stage 9 kept every ten intact because enough ones were available. Here, the initial comparison exposes the new need: in 63 − 8, 3 < 8. Earlier teen subtraction facts now become the inner calculation, since regrouping creates 13 − 8. Mastering this single exchange prepares you to borrow during two-digit subtraction.

Why This Skill Matters

Regrouping reveals that decimal notation is flexible: one ten can become ten ones whenever needed. That idea underlies change-making and every longer subtraction algorithm.

Worked Examples: Think It Through

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.

Trade a ten fairly

43 − 8

  1. 1 Rewrite 43 as 30 + 13.
  2. 2 Subtract 8 from 13 to get 5.
  3. 3 Combine 30 + 5 to make 35.

43 − 8 = 35

Your turn — try it on new numbers

47 − 8 = ?

Subtract through a round ten

61 − 4

  1. 1 Use 1 of the 4 to move from 61 to 60.
  2. 2 Three still must be removed.
  3. 3 Calculate 60 − 3 = 57.

61 − 4 = 57

Your turn — try it on new numbers

22 − 5 = ?

Open a ten at zero ones

70 − 6

  1. 1 Exchange one of seven tens: 70 becomes 60 + 10.
  2. 2 Remove 6 from 10, leaving 4.
  3. 3 Rejoin 60 + 4 to get 64.

70 − 6 = 64

Your turn — try it on new numbers

16 − 9 = ?

Prove with inverse addition

82 − 9

  1. 1 Regroup 82 as 70 + 12.
  2. 2 Compute 12 − 9 = 3, giving 73.
  3. 3 Verify that 73 + 9 = 82.

82 − 9 = 73

Your turn — try it on new numbers

14 − 7 = ?

Common Mistakes and How to Fix Them

Creating ten ones without reducing tens

Treating 52 as five tens and twelve ones creates 62. Self-correct by crossing out one ten: the equal form is four tens and twelve ones.

Subtracting only to the decade

For 63 − 8, reaching 60 uses only 3 of the 8. Record the split 8 = 3 + 5, then remove the remaining 5.

Reversing a teen subtraction

After regrouping 41 − 6, calculating 6 − 11 is incorrect. Keep the original order: eleven available ones minus six leaves five.

Two-Digit Minus Single (With Borrow) in Everyday Life

Paying $7 from $42 demonstrates the exchange physically. Trade one ten-dollar bill for ten one-dollar coins; then seven coins can be paid, leaving three coins and three tens, or $35. The money changed form but never changed value during the trade.

Time subtraction uses the same boundary reasoning. Nine minutes before 3:04 is five minutes before 3:00, or 2:55: remove four minutes to reach the hour, then the remaining five.

Pro Tips

  • • State the equivalent form, such as “54 is 40 plus 14,” before subtracting.
  • • When near a decade, split the amount removed into two manageable parts.
  • • Draw tens sticks and ones dots until the exchange feels concrete.
  • • Add the subtracted amount back to test both digits of the answer.

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. 42 − 7 = ?
  2. 2. 51 − 6 = ?
  3. 3. 63 − 8 = ?
  4. 4. 30 − 4 = ?
  5. 5. 74 − 9 = ?
  6. 6. 92 − 5 = ?
  7. 7. 61 − 7 = ?
  8. 8. 83 − 6 = ?
  9. 9. 40 − 8 = ?
  10. 10. 55 − 9 = ?
  11. 11. 72 − 4 = ?
  12. 12. 31 − 5 = ?
  13. 13. 64 − 7 = ?
  14. 14. 20 − 3 = ?
  15. 15. 86 − 9 = ?
  16. 16. 53 − 8 = ?
  17. 17. 71 − 2 = ?
  18. 18. 94 − 6 = ?

Drill Stage 10 with unlimited problems

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

Correct
0 / 0
Accuracy
—
Best streak
0
Time
0:00

Problem 1

25 − 8 = ?

Stage 10 Questions

Does borrowing make the starting number smaller?

No. It only renames one ten as ten ones; for example, 50 + 2 and 40 + 12 are both 52.

When is counting up easier than regrouping?

It is often convenient when the subtrahend or a nearby decade provides a short, obvious sequence of jumps.

How do I subtract from a number ending in zero?

Exchange one ten for ten ones. Thus 60 becomes 50 + 10 before the ones subtraction begins.