Content description

Simplify algebraic expressions involving the four operations (ACMNA192)

Elaboration

• understanding that the laws used with numbers can also be used with algebra.

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

Addition

Any two numbers can be added. When two or more numbers are added, the result is called the sum. The order in which we add two or more numbers does not matter. Adding them in any order will give the same answer.

Example 1

21 + 34 = 34 + 21 = 55

21 + 34 + 45 = 55 + 45 = 21 + 79 = 100

Remember that pronumerals are numbers so:

\(x+2=2+x,\ x+y=y+x\)

\(x+y+z=(x+y)+z=x+(y+z)\) 

\(3x+2y+6x=3x+6x+2y=9x+2y\) 

All of these examples illustrate the any-order property for addition. It states that a list of numbers can be added together in any order to give the sum of the numbers. This property summarises the commutative and associative laws for addition.

Subtraction

Subtraction gives the difference between two numbers. For example, the difference between 8 and 5 is 3 and this is written 8 − 5 = 3.

The same rule applies when using pronumerals.

Example 2

The difference between \(x\) and \(y\) is \(x-y\).

The difference between \(7x\) and \(2x\) is \(7x-2x=5x\).