## Order of Operations and Integers

In calculations involving several operations, the word BEDMAS shows the order in which each operation should be carried out.

### BEDMAS

BEDMAS means:

 Brackets: Work out the value of any expressions inside brackets. Exponents: Work out the value of any numbers or expressions with exponents or indices. Sometimes shown as 'of ' meaning multiply. Division Multiplication If these two operations occur together, work from left to right. Addition Subtraction If these two operations occur together, work from left to right.

 Examples Answers Calculate: a. 3 + 4 × 5 a. 3 + 4 × 5 = 3 + 20 = 23 b. 4 + (6 − 2) b. 4 + (6 − 2) = 4 + 4 = 8 c. 13 − 2 × 5 + 4 c. 13 − 2 × 5 + 4 = 13 − 10 + 4 = 7 d. 3 × 6 2 d. 3 × 6 2 = 3 × 36 = 108

Care should be taken when using a calculator to do calculations of this type.

### Integers

Integers are positive and negative whole numbers and include zero.
Use a number line when adding and subtracting integers.
The first integer is the starting point on the number line.

• When adding a positive integer, move to the right.

e.g. 4 + 2 = 6 • When adding a negative integer, move to the left.

e.g. 4 + − 2 = 2 Subtraction

• When subtracting a positive integer, move to the left.

e.g. 4 − 2 = 2 • When subtracting a negative integer, move to the right

e.g. 4 − − 2 = 6 Multiplication and division

The rule is the same for both multiplying and dividing two integers.

• If the signs of the two integers are the same, the answer is positive.
• If the signs of the two integers are different, the answer is negative.

The table illustrates these rules:

 ×/÷ +ve -ve +ve + − -ve − +

Examples:

 For multiplication For division 4 × 2 = 8 4 ÷ 2 = 2 - 4 × − 2 = 8 - 4 ÷ − 2 = 2 4 × − 2 = − 8 4 ÷ − 2 = − 2 - 4 × 2 = − 8 - 4 ÷ 2 = − 2

For practice with integer calculations − 