- Variables are the alphabets or letters used to represent unknown numbers/unknown quantities.
- These are also known as literals.
- Generally, we use \(x\) or \(y\) to represent unknown quantities, but any letter can be used as a variable.

**For example: **\(a,\;m,\;z,\) etc can be used as variables.

- Variables are mostly written in lower case.
- Sometimes, figures like \(\Box,\;\Delta,\) etc are used in place of variables.

- A variable can be used in any sort of mathematical expression.

- An expression having numbers with one or more operations and no equals sign is called mathematical expression.

**Example: **\(2(8+6)\)

- An expression having variables with one or more operations along with numbers and no equals sign is called variable expression/algebraic expression.

**Example:** \(6x+7,\;2z,\;3y-3\) etc.

A \(3(4+7)\)

B \(71(21\div7)\)

C \(2x+1\)

D \(27(21-17)\)

- A variable can be added to numbers.
- The addition is shown by a '\(+\)' sign in between a variable and a number.

**For example:** \(x+5\) can be written as

"A variable is added to \(5\)"

or

"Sum of a variable and \(5\)"

or

"\(5\) more than a variable"

- The addition is shown by using the keywords: 'added', 'sum' or 'more than'.

A \(10\) more than \(x\)

B \(10\) less than \(x\)

C \(10\) times \(x\)

D \(x\) less than \(10\)

- A literal can be subtracted from a number and vice-versa.
- The subtraction is shown by using a '\(-\)' sign between a variable and a number.

**Example: **\(x-5\) can be written as

"\(5\) less than a variable"

or

"\(5\) subtracted from \(x\)"

- The subtraction is shown by using the keywords: 'taken away', 'less than' or 'subtracted'.

**Note: **Always take care that \(5\) subtracted from \(x\) represents \((x-5)\). It is not same as \(x\) subtracted from \(5\) which is \((5-x)\).

A \(7\) less than \(x\)

B \(7\) more than \(x\)

C \(x\) less than \(7\)

D \(7\) times \(x\)

- A variable can be multiplied with numbers.
- The multiplication is shown either by '\(.\)' or '\(×\)' sign between them.

**For example:** \(7x\) can be written as

"\(7\) times \(x\)"

or

"\(7\) multiplied by \(x\)"

or

"Product of \(7\) and \(x\)"

- The multiplication is shown by using the keywords: 'times', 'multiplied' or 'product'.

**Note:** By commutative rule, \(xy\) is same as \(yx\).

A \(20\) times \(x\)

B \(20\) divides \(x\)

C \(x\) divides \(20\)

D \(x\) more than \(20\)

- A variable can be divided by a number and vice versa.

**For example:** \(\dfrac{10}{x}\) can be represented as

"\(10\) divided by \(x\)"

or

"\(10\) by \(x\)"

**Note:** It should be taken care that \(10\) by \(x\) represents \(\left(\dfrac{10}{x}\right)\). It is not same as \(x\) by 10 which is \(\left(\dfrac{x}{10}\right)\).

- The division is shown by using the keywords: 'by', 'divided by' or 'divides'.

A \(x\) divided by \(10\)

B \(10\) divided by \(x\)

C \(10\) times \(x\)

D \(x\) more than \(10\)