# Order of Operation

The order of operations used throughout mathematics… such as..

i. exponents and roots

ii. multiplication and division

Exponents and roots takes the first place in the order of operations. Then multiplication and division, thereafter addition and subtraction. The commutative and associative laws of addition and multiplication allow adding terms in any order, and multiplying factors in any order—but mixed operations must obey the standard order of operations.

This can be clearly explained with the help of BODMAS rule.

 B Brackets first O Orders (i.e. Powers and Square Roots, etc.) DM Division and Multiplication (left-to-right) AS Addition and Subtraction (left-to-right)

According to BODMAS you must do brackets first, then division, then multiplication, then addition and subtraction. When doing addition and subtraction it is best to go left to right. In some examples the rule will be applied more than once.

Example:

(1) 5 +  (6 x 8) – 10

Solution:

According to BODMAS RULE you must do brackets first, then division, then multiplication, then addition and subtraction. When doing addition and subtraction it is best to go left to right.

Thus, 5 + (6 x 8) – 10   [start inside the bracket first]

= 5 + (14) – 10 [multiplied]

= 5 + 14 – 10 [now addition]

= 19 – 10 [finally subtraction]

= 9

Therefore, 5 + (6 x 8) – 10 = 9

(2) 72 – 6² + (√25 x 5 +5) ÷ 6

Solution:

According to BODMAS RULE you must do brackets first, then division, then multiplication, then addition and subtraction. When doing addition and subtraction it is best to go left to right.

We have, 72 – 6² + (√25 x 5 +5) ÷ 6, {solve the terms inside the brackets first}

= 72 – 6² + (5 x 5 + 5) ÷ 6,  {now multiply inside the bracket}

= 72 – 6² + (25 + 5) ÷ 6 ,  {now add the terms inside the bracket}

= 72 – 6² + (30) ÷ 6, {6² = 36}

= 72 – 36 + 30 ÷ 6, {Then division according to BODMAS rule}

= 72 – 36 + 5, {addition}

= 72 – 31, {subtraction at the end}

= 41