Skip to main content

About this free course

Download this course

Share this free course

Numbers, units and arithmetic
Numbers, units and arithmetic

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

3.17 Subtraction of negative numbers

Next consider subtraction of a negative number. In terms of Thomas’s piggy bank, subtracting a negative number is the same as taking away one of his IOUs. If his mother says ‘you have been a good boy today so I’ll take away that IOU for £3’ this is equivalent to him being given £3.

So, − (3) = 3. Does this correspond with the number line interpretation of subtracting a negative number?

Consider the evaluation of 8 − 3. Continue to think of subtraction as undoing addition: adding 3 to 11 gives 8, and so subtracting3 from the answer, 8, gets back to 11. So, in terms of the number line, subtracting 3 from 8 means starting at 8 and moving 3 units to the right.

But moving 3 units to the right is the same as adding 3. So

   8 − 3 = 8 + 3 = 11.

If on one occasion Thomas's piggy bank is worth £8 in total (cash and IOUs) and his mother takes away a £3 IOU, the value of the piggy bank is 8 − 3 = 8 + 3 = 11.

Subtracting a negative number is the same as adding the corresponding positive number.