🔢 MathGrade 2Lesson 15
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Subtract with Borrowing

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Learning Objectives

  • 1Subtract two 2-digit numbers that require borrowing
  • 2Cross out the tens digit, reduce it by 1
  • 3Add 10 to the ones column
  • 4Identify subtractions that do not require borrowing
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Mini Lesson

When the top ones digit is smaller than the bottom ones digit, you cannot subtract yet. You need to borrow a ten from the tens column to make the ones large enough.

The four-step borrowing method

  • Step 1 — Check the ones: Is the top ones digit smaller than the bottom? If yes, borrow.
  • Step 2 — Borrow from the tens: Cross out the top tens digit and write one less above it. Write a small 1 in front of the top ones digit (making it 10 more).
  • Step 3 — Subtract the ones: Now subtract the (new, larger) ones digit minus the bottom ones digit.
  • Step 4 — Subtract the tens: Subtract the (reduced) tens digits.

Worked example: 83 − 47

  • Ones: 3 < 7, so borrow. Cross out 8, write 7 above it. Ones becomes 13.
  • 13 − 7 = 6. Write 6 in the ones answer.
  • Tens: 7 − 4 = 3. Write 3 in the tens answer.
  • Difference: 36.

When do you NOT need to borrow?

  • If the top ones digit is equal to or greater than the bottom ones digit, just subtract normally.
  • Example: 75 − 32 → ones: 5 ≥ 2 → no borrow → 5 − 2 = 3, tens: 7 − 3 = 4 → 43.
Column subtraction 83 minus 47 with borrowingVertical column subtraction. 83 on top, 47 below, minus sign on the left. The 8 tens digit is crossed out and replaced with 7. The ones digit 3 becomes 13 after borrowing. 13 minus 7 equals 6 in the ones. 7 minus 4 equals 3 in the tens. Answer: 36.83 − 47 = ?TO8713−4736Ones: 3<7 → borrow → 13−7 = 6Tens: 7−4 = 3 → Difference = 36
Column subtraction 83 − 47. The 8 is crossed out and reduced to 7; the 3 becomes 13. Then 13 − 7 = 6 (ones) and 7 − 4 = 3 (tens), giving 36.
Borrowing decision: is the top ones digit smaller than the bottom?A decision diamond: Is the top ones digit smaller than the bottom? Yes: borrow a ten — cross out tens, add 10 to ones. No: subtract directly. Two examples shown.Top ones < bottom ones?Borrow?YES−1 from tens+10 to onesNOSubtractdirectly75−32: ones 5≥2No borrow → 4383−47: ones 3<7Borrow → 36Always check the ones column first!
A decision diamond — if the top ones digit is smaller than the bottom, borrow (reduce tens by 1, add 10 to ones); otherwise subtract directly.
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Ask yourself: "Is the top ones digit smaller than the bottom ones digit? If yes, I need to borrow."

Vocabulary
Borrow
To take a ten from the tens column when the ones column needs moree.g. I had to borrow because 3 was less than 7.
Tens column
The column to the left of the ones, where tens digits goe.g. I crossed out 8 in the tens column to borrow.
Ones column
The right-most column where the ones digits goe.g. After borrowing, the ones column had 13.
Difference
The answer to a subtraction probleme.g. The difference of 83 − 47 is 36.
Cross out
To draw a line through a digit when it changese.g. I crossed out 8 and wrote 7 above it.
Regroup
To rearrange tens and ones to make subtracting possiblee.g. Regrouping helps when the top ones digit is too small.
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