Numbers: Variables and Functions

Variables and Functions

To understand variables, we need to understand constants also.

So we can see two facts:

1. Constant      2. Variables

1. Constants: All the numbers are constants. 

For Example: 2 has a value 2. Its value can not be changed. So it is a constant. All real numbers (Positive-Negative, Rational-Irrational, Integers-Fractions, Prime-Composite-Co-Prime, etc) are constants.

2. Variable

Variables are the symbols represented by normally alphanumeric and sometimes special characters to express some numbers. The values of these assumed characters may change time to time and according to situation and conditions. 

For example: In a condition a = 5 

and in other condition it is changed to a = 22. 

Therefore these are known as variables.

The mathematics for variables is same as the mathematics for numbers. It means they follows same sets of rules for addition, subtraction, multiplication, division, brackets, BODMAS, LCM, HCF, etc. So it is not a tough job to understand the operations on variables.

Let there are two variables x and y then

Addition:            x + y

Subtraction:       x - y

Multiplication:     x × y = xy

Division:             x ÷ y = x/y

When we find any value of x and y, then we can find the answer of these operations

Like let x = 24 and y = 6

Addition = 30,     

Subtraction = 18,   

Multiplication = 144    and   

Division = 4

Similarly we can solve for other operations like power and other expressions.

Let a constant 4 is operated with variable y, then

Addition: y + 4,   

Subtraction: y - 4,   

Multiplication: y × 4 = 4y,       and

Division: y ÷ 4 = y/4

Let a constant 4 is operated with variable 4y - 3, then

Addition: 4y - 3 + 4 = 4y + 1,                    

Subtraction: 4y - 3 - 4 = 4y - 7,   

Multiplication: (4y - 3) × 4 = 4y×4 - 4×3 = 16y - 12,       

Division: (4y - 3) ÷ 4 = 4y/4 - 3/4 = y - 3/4

Rules for doing problems related to the variables in the equation and questions

Variables follow all the mathematical operations and formula. For solving a variable in a equation, we have certain rules

If we transfer a number or variable from one side of equal to another side then,

+ is changed to – 

– is changed to +

× is changed to ÷

÷ is changed to ×

For Example: if x + 3 = 5;                 or         x = 5 – 3 = 2

                      if x – 4 = 7;                  or         x = 7 + 4 = 11

                      if x × 7 = 9;                 or          x = 9 ÷ 7 = 9/7 =  1.286

                      if x ÷ 7 = x / 7 = 3;       or         x = 3 × 7 = 21

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