Arithmetic System – Arithmetic Operations
Posted on: March 31, 2009
You definitely have done addition back in primary school.
So, let us now go through a few important arithmetic operations you have learnt.
Addition
When we talk about addition, we often talk about “something plus something”, and we get nice positive numbers. But sometimes when we do addition, we do not always get nice positive numbers.
When you learn how to add in the beginning, you are actually dealing with only positive numbers. “1” is not just “1”, but it is actually “+1” just that we do not include the “+” sign because of convention.
E.g.
3 + 8 = (+3) + (+8) = 11
Now, that was easy, wasn’t it? Take the “+” sign as you getting money; so you get $3, and you get another $8, so in total you will get $11, i.e. 11.
But how about adding negative numbers?
The idea is similar: take the “-” sign as you owing someone else money.
E.g.
(-1) + (-4) = (-5)
Brackets are usually placed around negative numbers to protect these special numbers. So looking at the example above, it seems that you owe someone $1, and then in addition you owe the same person $4, so in total you are actually owing the person $5, i.e. -5.
Subtraction
When you subtract a number from another, you are “removing” it from that number. However, subtraction can take many forms:
E.g.
9 – 5 = 4
The above is a very normal question, one you have seen a million times (well, maybe not a million times la…). However, the next example may scare you:
E.g.
-1 – 4 = -5
What happens here is that imagine you owe your friend $1, i.e. -1. You owe your friend $4 again, i.e. -4. So in total, you are actually owing her $5, i.e. -5.
If you read closely, this looks exactly like the 2nd example from “Addition”, i.e.
(-1) + (-4) = -1 – 4 = -5
When 2 signs next to each other are different, the resulting sign is a minus, i.e. (+) (-) = (-), or (-)(+) = (-).
Multiplication & Division
For the last 2 operations, they behave in a rather similar way.
Multiplying or dividing positive numbers is easy – just do what you used to do back in primary school!
E.g. Multiplying/dividing 2 positive numbers
However, when negative numbers enter the picture, sometimes it may just look confusing:
E.g. Multiplication & division, with 1 positive number and 1 negative number
OR
E.g. Multiplying/dividing 2 negative numbers
Just remember: when you see 2 signs that are the same, the resulting answer is positive.
2 different signs -> resulting answer is negative,
i.e.
Multiplication
Division
Hope this will help! This applies to all sorts of numbers; whole numbers, fractions, decimals etc.
Ms Sia's Realm of Maths 
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