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