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Subtraction

Subtraction is harder than addition for most children, and the reason is usually borrowing. It helps to know that subtraction answers two different questions — how many are left, and how far apart are they — and that counting up is often easier than taking away.

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Two-digit subtraction with borrowing

52 - 27

  1. Line the numbers up, ones above ones and tens above tens.
  2. Look at the ones: you cannot take 7 from 2, so borrow a ten. The 5 tens become 4 tens, and the 2 ones become 12 ones.
  3. Take the ones: 12 - 7 is 5.
  4. Take the tens: 4 - 2 is 2.
  5. The answer is 25.

Worth knowing. Saying "fifty-two is four tens and twelve ones" out loud is worth more than any amount of crossing out. The borrowing is a trade, not a trick.

Counting up instead of taking away

203 - 198

  1. The numbers are close together, so counting up is quicker than the column method.
  2. From 198 to 200 is 2.
  3. From 200 to 203 is 3.
  4. Add the jumps: 2 + 3 is 5. The answer is 5.

Worth knowing. Column subtraction on 203 - 198 means borrowing across a zero, which is genuinely awkward. Choosing the easier method is a real skill, not a shortcut.

Where it usually goes wrong

  • Taking the smaller digit from the larger one in each column regardless of which is on top, so 52 - 27 comes out as 35.
  • Forgetting to reduce the tens digit after borrowing from it.
  • Getting stuck borrowing across a zero, as in 300 - 148.

When the numbers are close together, the Professor counts up instead of taking away. It is the same answer with less work.

Practise it

All level paths

Questions teachers and parents ask

Why is subtraction so much harder than addition?

Order matters, so it cannot be done in whichever direction is easier. Borrowing runs right to left while children read left to right. And subtraction facts are usually taught after addition facts, so there has been less practice.

Should I teach borrowing or counting up?

Both, and when to choose. Counting up is faster when the numbers are close together or when there are zeros to borrow across. The column method is more reliable when they are far apart. A child who only knows one method will use it in the situation it is worst at.

What about answers below zero?

Below grade 6 the answer is normally kept at zero or above, and a bigger number is always on top. Negative answers belong with integers, which is a separate topic and a different idea.

Where this shows up

Standards

  • K.OA · Operations and algebraic thinking
  • 1.OA · Operations and algebraic thinking
  • 1.NBT · Number and operations in base ten
  • 2.OA · Operations and algebraic thinking
  • 2.NBT · Number and operations in base ten
  • 3.NBT · Number and operations in base ten
  • 4.NBT · Number and operations in base ten

Formats