The commutative law of addition. This law states that for any numbers a and b, a + b = b + aIn other words the result is the same no matter which number is considered to be the “first number” and which number is considered to be the “added on” number. |
The associative law of addition. If we need to add three or more numbers together then we do this by adding two at a time. The associative law of addition says that the result is the same no matter which two we choose to start with. It states that for any numbers a, b and c, (a + b) + c = a + (b + c) |
Zero. The number 0 is called the additive identity because adding it to any number a just gives back a : a + 0 = aFor every number a there is a number −a, called the additive inverse. Added together they give zero: a + (−a) = 0 |
Another way to view subtraction is to use the idea that we subtract to find out how different two numbers are. (This is why the result is called the difference!) Thus the difference between 5 and 2 is 3. The trouble with this method is that we have to be careful which number we subtract from which.
replace this subtraction by this addition of an opposite 2 − 5 = − 3 2 + (−5) = − 3 −5 − 3 = − 8 −5 + (−3) = − 8 −8 − (−2) = − 6 −8 + 2 = − 6
Addition and subtraction of expressions,
Addition and subtraction of algebraic fractions.