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Stage 9 of 20

Two-Digit Minus Single (No Borrow)

Build accurate no-borrow subtraction with place-value partitioning, addition-back checks, distance reasoning, worked models, and focused practice.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Identify when the available ones are sufficient for subtraction
  • Remove ones without altering the number of tens
  • Use related addition facts to calculate and verify differences
  • Explain why the answer remains in the same decade

Why This Matters

No-borrow subtraction handles small decreases quickly and teaches you to distinguish a local change in ones from a change that crosses a decade.

The Reasoning Behind Two-Digit Minus Single (No Borrow)

Subtraction removes value, but place value tells us where that value comes from. In 58 − 3, write 58 as 50 + 8. Removing 3 ones leaves 5 ones, so 50 + 5 = 55. All five tens remain because the eight loose ones were already enough; no ten needed to be opened.

The condition for no borrowing is simple: the ones digit of the starting number must be at least as large as the number subtracted. For 76 − 4, compare 6 and 4 before solving. Since 6 ≥ 4, the difference stays in the seventies. This prediction makes an answer such as 62 immediately suspicious.

Related addition offers a persuasive check. To solve 94 − 2, ask which ones fact completes 2 + ? = 4. The missing part is 2, giving 92. Then 92 + 2 = 94 restores the starting amount. Subtraction and addition undo each other, so this reverse operation provides mathematical justification rather than a guess.

Stage 7 added a small number while keeping the tens intact; this stage reverses that structure. Number bonds and single-digit subtraction from earlier stages now operate inside one chosen decade. Once this control is secure, Stage 10 will ask what to do when the loose ones are not sufficient and a ten must be regrouped.

Where You Will Use Two-Digit Minus Single (No Borrow)

A game account contains 87 tokens and spends 6. Because seven loose tokens cover the purchase, the eight bundles of ten remain sealed and one token stays loose: 81 tokens remain. The same reasoning tracks small withdrawals from stock or points.

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.

Remove only loose ones

67 − 4

  1. 1 Partition 67 as 60 + 7.
  2. 2 Subtract the ones: 7 − 4 = 3.
  3. 3 Recombine 60 + 3 to get 63.

67 − 4 = 63

Your turn — try it on new numbers

59 − 8 = ?

Think addition back

85 − 3

  1. 1 Ask, “3 plus what equals 5?”
  2. 2 The missing ones amount is 2.
  3. 3 Keep the 80 and form 82.

85 − 3 = 82

Your turn — try it on new numbers

62 − 2 = ?

Subtract to the decade

49 − 9

  1. 1 Nine ones are available, exactly matching the 9 removed.
  2. 2 Compute 9 − 9 = 0.
  3. 3 Keep four tens, producing 40.

49 − 9 = 40

Your turn — try it on new numbers

58 − 6 = ?

Verify a difference

73 − 2

  1. 1 Remove 2 from the 3 ones to leave 1.
  2. 2 Keep the seven tens, giving 71.
  3. 3 Check that 71 + 2 = 73.

73 − 2 = 71

Your turn — try it on new numbers

57 − 6 = ?

Self-Check: Errors to Avoid

Subtracting from the tens

Changing 68 − 5 into 18 removes five tens, not five ones. Self-correct by naming 68 as 60 + 8 and calculating 8 − 5.

Reversing the ones fact

For 74 − 2, computing 2 − 4 breaks the order of subtraction. Read it as four ones remove two ones, then evaluate 4 − 2.

Missing a decade boundary

The rule cannot solve 71 − 5 without regrouping because one loose one is insufficient. Compare the ones first; if it is smaller, use Stage 10 reasoning.

Pro Tips

  • • Compare the ones digit with the subtrahend before taking anything away.
  • • Use addition-back when the subtraction fact does not come immediately.
  • • Predict whether the result stays in the same decade.
  • • Separate “remove” from “compare”; both meanings produce the same difference.

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. 38 − 5 = ?
  2. 2. 76 − 2 = ?
  3. 3. 95 − 4 = ?
  4. 4. 64 − 3 = ?
  5. 5. 57 − 6 = ?
  6. 6. 89 − 7 = ?
  7. 7. 46 − 4 = ?
  8. 8. 72 − 1 = ?
  9. 9. 99 − 8 = ?
  10. 10. 35 − 5 = ?
  11. 11. 68 − 2 = ?
  12. 12. 83 − 3 = ?
  13. 13. 54 − 2 = ?
  14. 14. 77 − 4 = ?
  15. 15. 92 − 2 = ?
  16. 16. 61 − 1 = ?
  17. 17. 48 − 6 = ?
  18. 18. 26 − 3 = ?

Drill Stage 9 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses two-digit minus a single digit without borrowing. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

13 − 3 = ?

Stage 9 Questions

Can a no-borrow answer end in zero?

Yes. If the ones removed exactly equal the available ones, none remain, as in 35 − 5 = 30.

Why does the result usually stay in the same decade?

Enough loose ones are available, so no complete ten is removed. It reaches the lower decade only when zero ones remain.

Is counting backward a valid method?

Yes, especially for small subtrahends. Partitioning and addition-back are usually easier to explain and extend to harder problems.