• a² is short for a × a.
• When simplifying arithmetic or algebraic expressions, the order of operations is important.
  • If there are no brackets, do multiplication or division before addition and subtraction.
  • If there are brackets, first simplify the terms inside them.
• When removing brackets:
  • A positive sign outside the bracket (on the left hand side) does not change the sign of each term inside the bracket. For example:
    • 2 + (x + 2) = 2 + x + 2 = x + 4
    • 3x + (2y – 4) = 3x + 2y – 4
  • A negative sign outside the bracket (on the left hand side) does change the sign of each term inside the bracket. For example:
    • 2 – (x + 2) = 2 – x – 2 = -x
    • 3x – (2y – 4) = 3x – 2y + 4

Examples

1. 2a × 3
   • = 2 × a × 3
   • = 2 × 3 × a
   • = 6 × a
   • = 6a
2. 6b × 4b
   • = 6 × b × 4 × b
   • = 6 × 4 × b × b
   • = 24 × b²
   • = 24b²
3. 8ab × 7a
   • = 8 × a × b × 7 × a
   • = 8 × 7 × a × a × b
   • = 56 × a² × b
   • = 56a²b
4. ^14a/₇
   • = ^{14 × a}/₇
   • = ^{7 × 2a}/₇
   • = ^{1 × 2a}/₁
   • = 2a
5. ¹/₃ of 36c
   • = ^{36 × c}/₃
   • = ^{3 × 12c}/₃
   • = ^{1 × 12c}/₁
   • = 12c
6. 24d²e ÷ 3de
   • = ^{24 × d² × e}/_{3 × d × e}
   • = ^{3 × 8 × d × d × e}/_{3 × d × e}
   • = ^{1 × 8 × 1 × d × 1}/_{1 × 1 × 1}
   • = 8d
7. Find the value of 16 × 2 – 3 + 14 ÷ 7.
   • = (16 × 2) – 3 + (14 ÷ 7)
   • = 32 – 3 + 2
   • = 32 + 2 – 3
   • = 34 – 3
   • = 31
8. Simplify 7 × 3a – (3a + 5a) × 2.
   • = 7 × 3a – 8a × 2
   • = (7 × 3a) – (8a × 2)
   • = 21a – 16a
   • = 5a
9. Simplify (6x – 5y) + (3y + 4x)
   • = 6x – 5y + 3y + 4x
   • = 6x + 4x + 3y – 5y
   • = 10x – 2y
   • NOTE: There is no sign before the first bracket; we take it to be positive.
10. (6x – y) – (7x – 2y)
    • = 6x – y – 7x + 2y
    • = 6x – 7x + 2y – y
    • = -x + y or y – x
11. The greater of two consecutive numbers is x. (NOTE: Two whole numbers are consecutive when their difference is 1. For example, 5 and 6 are consecutive numbers; 49 and 50 are also consecutive. In algebra, x and x + 1 or y – 1 and y are consecutive, provided x and y are whole numbers)
    1. Find the sum of the two numbers.
       • If x is the greater of the two numbers, the lower number is x – 1.
       • ∴ The sum of the two numbers = x + (x – 1)
       •                                                            = x + x – 1
       • ∴ The sum of the two numbers = 2x – 1
    2. Subtract the sum of the two numbers from 5x.
       • = 5x – (2x – 1)
       • = 5x – 2x + 1
       • = 3x + 1