🔢 MathGrade 2Lesson 15
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Subtract with Borrowing

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What you will learn

  • 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 (regroup) 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 take the bottom ones digit away from the new, larger ones number.
  • 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.

Words to know

Borrow

To take a ten from the tens column when the ones column needs more

e.g. I had to borrow because 3 was less than 7.

Tens column

The column to the left of the ones, where tens digits go

e.g. I crossed out 8 in the tens column to borrow.

Ones column

The right-most column where the ones digits go

e.g. After borrowing, the ones column had 13.

Difference

The answer to a subtraction problem

e.g. The difference of 83 − 47 is 36.

Cross out

To draw a line through a digit when it changes

e.g. I crossed out 8 and wrote 7 above it.

Regroup

To rearrange tens and ones to make subtracting possible

e.g. Regrouping helps when the top ones digit is too small.

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."

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