ALGEBRA

The Four Operations

In addition and subtraction, like terms can be added together or subtracted.

Examples:

1. 4m-m+2m
= 4m + 2m - m
= 6m - m
= 5m

2. 6k+3k-k-4k
= 9 - 5k
= 4k

In addition and subtraction, unlike terms cannot be simplified.

Examples:

1. 5x+ 3y-4x-y
= 5x- 4x + 3y- y (Put the like terms together. Then add/subtract like terms)
= x + 2y

2. 6c - 4d + 4c- d- c+ 2d
= 6c + 4c - c + 2d - d - 4d
= 10c - c + 2d - 5d
= 9c - 3d

In multiplication and division, we can combine the like and unlike terms together.

Examples:

1. 4x x 3y
= 12xy

2. 24x ÷  8y
= 24x
     y
= 3x
    y

3. 12ab x 6c
      4c      3a
= 12 x a x b x 6 x c
      4 x c         3xa
= 6b

4. 8ab ÷ 16b
    4bc    12c
= 8 x a x b x 12 x c
   4 x b x c    16 x b
= 3a
   2b 

Substitution

After substituting the values for the letters, work out in this order:
(a) what is in the brackets first,
(b)multiply or divide from left to right, add or subtract from left to right.

Examples:

1. If x= 11 and y= 6, find by substitution the value of n in n =  sqrt(5x – y) .
                                                                                                 2
n = sqrt(5x – y - 6)
                2
= sqrt(55 – 6)
              2
= sqrt(49)
       2
= 7
    2
= 3 1/2

2. Solve 3b + a² - 2z, when a=6, b=9 and c=3.
3b + a² - 2z
= 3 x 9 + 6² - 2 x 3
= 27 + 36 - 6
= 63 – 6
= 57