### Simplifications

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__Simplification__

Order of Operations - BODMAS Rule

BODMAS rule defines the correct sequence in which operations are to be performed in a given mathematical expression to find its value.

In BODMAS,

B = Bracket,

O = Order (Powers, Square Roots, etc.)

DM = Division and Multiplication (left-to-right)

AS = Addition and Subtraction (left-to-right)

This means, to simplify an expression, the following order must be followed.

i. Do operations in Brackets first, strictly in the order (), {} and []

ii. Evaluate exponents (Powers, Roots, etc.)

iii. Perform division and multiplication, working from left to right. (division and multiplication rank equally and done left to right).

iv. Perform addition and subtraction, working from left to right. (addition and subtraction rank equally and done left to right).

Examples

12 + 22 / 11 * (18 / 3)2 - 10

= 12 + 22 / 11 * 62 - 10 ( Brackets first)

= 12 + 22 / 11 * 36 - 10 ( exponents)

= 12 + 2 * 36 - 10 = 12 + 72 - 10 ( division and multiplication, left to right)

= 84 - 10 = 74 ( Addition and Subtraction, left to right)

In BODMAS,

B = Bracket,

O = Order (Powers, Square Roots, etc.)

DM = Division and Multiplication (left-to-right)

AS = Addition and Subtraction (left-to-right)

This means, to simplify an expression, the following order must be followed.

i. Do operations in Brackets first, strictly in the order (), {} and []

ii. Evaluate exponents (Powers, Roots, etc.)

iii. Perform division and multiplication, working from left to right. (division and multiplication rank equally and done left to right).

iv. Perform addition and subtraction, working from left to right. (addition and subtraction rank equally and done left to right).

Examples

12 + 22 / 11 * (18 / 3)2 - 10

= 12 + 22 / 11 * 62 - 10 ( Brackets first)

= 12 + 22 / 11 * 36 - 10 ( exponents)

= 12 + 2 * 36 - 10 = 12 + 72 - 10 ( division and multiplication, left to right)

= 84 - 10 = 74 ( Addition and Subtraction, left to right)

Modulus of a Real Number

For any real number x, the absolute value or modulus of x is denoted by |x| and is defined as

Hence, the Modulus(absolute value) of x is always either positive or zero, but never negative

Example

|5| = |-5| = 5

Hence, the Modulus(absolute value) of x is always either positive or zero, but never negative

Example

|5| = |-5| = 5