2. Mathematical rules for addition and subtraction
Commutative law
Addition is commutative which means that it is possible to change the order of the operands when adding. We all know that for example
5 + 6 = 6 + 5
In mathematics we say that whatever two numerical values designated by a and b, we have
a + b = b + a
Let's apply this rule to an example:
14 + 25 + 6 = 14 + 6 + 25
I have switched the values 6 and 25. The aim is to put the 6 with 14 to make the calculation easier:
14 + 6 + 25 = 20 + 25 = 45
If there is a subtraction in the expression, you can always change the order of the values, but only if you move the + or - sign before each value. For example :
28 - 15 + 12 = 28 + 12 - 15
I have moved the value 12 with the + sign before it and the value 15 with the - sign before it
28 + 12 – 15 = 40 -15 = 25
Associative law
Addition is associative, which means that it is possible to perform addition in any order.
We say in mathematics that whatever three numerical values denoted by a, b and c, we have
(a + b) + c = a + (b + c)
The parentheses signify the order in which the addition is performed. In the first expression, b is added to a, then c is added to the result. In the second expression c is added to b, then the result is added to a.
Let's take an example:
37 + 78 = 30 + 7 + 70 + 8
I apply the commutativity rule
30 + 7 + 70 + 8 = 30 + 70 + 7 + 8
I apply the associativity rule; I start by adding 70 to 30 on the one hand and adding 8 to 7 on the other
30 + 70 + 7 + 8 = (30 + 70) + (7 + 8) = 100 + 15 = 115
Add and subtract the same value when adding
For example, the following addition operation:
85 + 28
I will add 15 to 85 and subtract 15 from 28
85 + 28 = (85 + 15) + (28 -15) = 100 + 13 = 113
Add the same value to both operands in case of subtraction
Subtraction example:
74 – 58
I add 2 to each of the two operands:
74 – 58 = (74+2) – (58+2) = 76 – 60 = 16
Case of direct calculation
In some cases it is appropriate to use a direct calculation of an operation. This means doing the operation without the help of a complement or other trick. In mental arithmetic, we prefer in these cases to do the calculation from left to right.
For example, 258+376
We say, 2+3=5, so 500, and 5+7=12, so 620. And 8+6=14, so 634.