Simple subtraction

Subtraction can be thought of as taking away one number from another, the difference between two numbers or what you have to add to one number to get to another. As with addition, many strategies that begin as pencil and paper tasks are also useful mental strategies. Also, the strategies outlined here can be extended to be used with larger numbers and with more than two numbers.

+ 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18

The addition table provided in an earlier section also highlights related subtractions. From the addition 5 + 8 = 13 we also get 13 − 5 = 8 and 13 − 8 = 5. It is useful to be fluent with these subtractions and the related addition.

Subtract a bit at a time

To subtract a single-digit number the procedure is straightforward. For example, 78 − 4 = 74.

If the number being subtracted is larger than nine, the process can be broken down into a number of more manageable steps.
For example:

\begin{align*} 197-28&= 197-20-8\\\\ &= 177-8\\\\ &=177-7-1\\\\ &= 170-1\\\\ &= 169\\\\ \end{align*}

Build up to the larger number

The building strategy also breaks the steps into more manageable parts. Keep track of what has been added.
For example:

\begin{align} &197-168\\\\ &168+2=170\ \text{(2 has been added)}\\\\ &170+20=190\ \text{(A total of 22 has been added)}\\\\ &190+7=197\ \text{(A total of 29 has been added)}\\\\ &197-168=29 \end{align}

Add the same to both numbers

Adding the same to each number does not change the difference between them. Add the most obvious number to both, then subtract as usual.
For example:

\begin{align*} 197-28 &= (197+2)-(28+2)\\\\ &= 199-30\\\\ &= 169\\\\ \end{align*}