Negative numbers are awkward but need not be too much of a nuisance. Most children spot the concept through the use of a thermometer which drops to sub-zero levels. However, manipulating the numbers can be a bit confusing. The key is to remember that adding and subtracting are opposites of each other and that if you 'subtract' a negative number you are saying 'minus a minus' which is the equivalent of adding.
Most numbers we deal with are positive. A sum such as '3 + 5' really means 'positive 3 add positive 5' or '+3 + +5'.
When you use a minus in any calculation you need to think logically. '-3 + 5' means that we should start at -3 on our number line and add five to it. It takes us to positive 2.
However, '-3 - 5' will take us from -3 on the number line and head 5 further into the negatives. The answer is minus 8. ( -8 )
If you try adding a negative number you must take it away as the '+' sign is just saying 'put together with...' or '...altogether'.
3 + (-5) means that we have to put 3 together with the -5. That leaves -2 altogether.
Similarly, if we subtract a negative number, we are doing the OPPOSITE of subtracting and therefore add it.
3 - (-5) = 3 + 5 = 8
Remember, 'minus a minus is a plus'.
We have seen how adding and subtracting negative numbers can be logical but difficult to understand at first. Multiplying and dividing is equally logical but again, you need to be aware which way the answer will be expressed - will it be negative or positive?
If I were to take 5 and multiply it by 6 I would have 30. However, if I multiply 5 by -6 the answer becomes -30.
In effect you are saying '5 lots of -6' which will be -30.
When you multiply a positive by a negative, the answer is negative.
If BOTH numbers become negative, you are going to create a positive number. You are effectively doing the opposite of the opposite and therefore end up back where you started. Think of the 'double negative' in speech - 'I am not not going' means I am going.
If I were to multiply -4 by -10 then I would get the answer positive 40.
When you multiply a negative by a negative, you get a positive.
Division is exactly the same. If you divide a negative number by a positive one, or a positive number by a negative one, the answer will be negative.
-8 ÷ 2 = -4 and 8 ÷ -2 = -4
When we divide a negative number by another negative number, we are going to end up with a positive number.
-8 ÷ -2 = 4
Effectively we are saying 'how many lots of -2 fit into -8?' and the answer will be 4.