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Level 2Grade 2skill: sub_within_100· 6 min read

Subtraction Within 100

In short: To subtract within 100, line up tens over tens and ones over ones, then start at the ones. If the top ones digit is too small, borrow one ten (add 10 to the ones, drop the tens digit by one) before you subtract. When both numbers have two digits, the ones column is the only place that can force a borrow.

How to subtract within 100

Line the two numbers up so the tens sit over tens and the ones sit over ones. Then you always work the same direction: start at the ones column on the right, finish at the tens on the left. Never start on the left.

Here is the whole game in one sentence: look at the top ones digit. If it is big enough to subtract from, subtract straight down. If it is too small, you borrow one ten from the tens column — that turns the ten into 10 ones, so the top ones digit grows by 10 and the top tens digit drops by 1.

  1. Write the bigger number on top, the number you take away underneath, ones under ones.
  2. Look at the ones column. Is the top digit big enough? If yes, subtract it. If no, borrow: cross out the tens digit, make it one less, and add 10 to the ones.
  3. Subtract the ones column and write that digit underneath.
  4. Subtract the tens column (using the crossed-out, reduced digit if you borrowed).
  5. Read your answer: tens digit then ones digit.

Why the ones column runs the whole show Why it works

No borrow
Top ones digit is big enough, so both columns subtract straight down.

47 − 23: 7 − 3 = 4, then 4 − 2 = 2, giving 24.

Borrow one ten
Top ones digit is too small, so trade one ten for 10 ones before subtracting.

52 − 38: 2 is too small, so 12 − 8 = 4, then (5 becomes 4) 4 − 3 = 1, giving 14.

Borrow across a zero
When the top has a 0 in the ones, you always borrow — 0 is never big enough.

80 − 45: 0 is too small, so 10 − 5 = 5, then (8 becomes 7) 7 − 4 = 3, giving 35.

Look back at the three patterns above. In every one, the decision — subtract straight down or trade a ten first — was settled the instant you compared the two ones digits; the tens column never made that call, it only cleaned up afterward. So when both numbers have two digits, do one thing before you write anything: compare the ones. Smaller digit on top means a borrow is coming. (The single exception is taking a number away from 100 itself, where the tens is 0 too — see the FAQ.) That one glance decides the whole problem.

Worked examples

47 − 23 = 24
  1. Ones: 7 − 3 = 4. No borrow needed.
  2. Tens: 4 − 2 = 2.
52 − 38 = 14
  1. Ones: 2 is smaller than 8, so borrow. The 5 tens become 4, and the 2 becomes 12.
  2. Ones: 12 − 8 = 4.
  3. Tens: 4 − 3 = 1.
63 − 27 = 36
  1. Ones: 3 is smaller than 7, so borrow. The 6 tens become 5, and the 3 becomes 13.
  2. Ones: 13 − 7 = 6.
  3. Tens: 5 − 2 = 3.
70 − 48 = 22
  1. Ones: 0 is smaller than 8, so borrow. The 7 tens become 6, and the 0 becomes 10.
  2. Ones: 10 − 8 = 2.
  3. Tens: 6 − 4 = 2.

Common mistakes and how to fix them

Taking the smaller digit from the bigger, whichever is on top

✗ 44

In 63 − 27, the ones are 3 (top) and 7 (bottom). A common slip is to ignore which one is on top and just do the easy 7 − 3 = 4, then 6 − 2 = 4, landing on 44. But you must subtract down: 3 − 7 isn't possible without borrowing.

Fix: Always subtract the bottom digit from the top digit. If the top is too small, that is your signal to borrow — never flip the order to dodge it. Correct answer: 36.

place_value_slip

Borrowing the ten but forgetting to make it one less

✗ 46

In 63 − 27, you correctly turn 3 into 13 and get 13 − 7 = 6. But if you forget to drop the top tens digit from 6 to 5, you do 6 − 2 = 4 and write 46. You borrowed the ten but never paid it back.

Fix: When you borrow, cross out the tens digit right away and write the smaller number above it. Do it before you subtract the ones so you can't forget. Correct answer: 36.

missed_carry

A miscount in the ones by one

✗ 65

In 85 − 19, you borrow to get 15 − 9. If you miscount and say 15 − 9 = 5 instead of 6, the whole answer slides down by one to 65.

Fix: Slow down on the borrow subtraction and check it: 9 + 6 = 15, so 15 − 9 must be 6, not 5. Add your answer back to the bottom number to test it. Correct answer: 66.

off_by_one

Adding when the problem says subtract

✗ 112

In 74 − 38, reading too fast and adding gives 74 + 38 = 112 — a number bigger than you started with, which can't happen when you take away.

Fix: Check the sign before the first step, and sanity-check the size: after subtracting, the answer must be smaller than the top number. 112 is bigger than 74, so it must be wrong. Correct answer: 36.

wrong_operation

Practice subtraction within 100

Work through a mix of problems — some with borrowing, some without, and a few tricky ones like subtracting from 100. Take each one column at a time, starting with the ones.

Related skills

First, make sure of

Frequently asked questions

How do I know when I need to borrow?

Look only at the ones column. If the top ones digit is smaller than the bottom one — like the 2 over the 8 in 52 − 38 — you borrow one ten. If the top ones digit is equal or bigger, you subtract straight down with no borrow.

What does borrowing actually do?

It trades one ten for ten ones. You cross out the top tens digit and make it one smaller, and you add 10 to the top ones digit. The number's value doesn't change — you've just rearranged it so the ones column has enough to subtract from.

How do I subtract from 100?

Taking a number away from 100 is the one case where the tens column can also force a borrow, because both the ones and the tens on top are 0. Borrow from the hundred to make the tens 10, then borrow one of those tens for the ones: you end up with 9 tens and 10 ones, so 10 − 4 = 6 and 9 − 6 = 3, giving 36 for 100 − 64. A quick shortcut: ask 'what adds up to 100?'

How can I check my answer is right?

Add your answer back to the number you took away — you should get the number you started with. For 74 − 38 = 36, check 36 + 38 = 74. If it doesn't match, you slipped somewhere, often a miscount or a missed borrow.

Do I always start from the ones?

Yes. Always begin with the ones column on the right and move left to the tens. Starting from the left doesn't work, because you can't tell whether the tens will need to give up a ten until you've looked at the ones.