- 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 equal 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 \(27(21-17)\)

- Different operations can be performed on variables.
- To write an expression for a given statement, follow three steps:

(i) Identify the given number.

(ii) Identify any operations involved.

(iii) Identify the variable.

- A variable can be added to numbers.
- The addition is shown by a '\(+\)' sign in between a variable and a number.
- Words like, 'added to', 'sum', 'more than', 'increased', 'altogether', indicate addition.

**For example:**

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

Here, **added to** indicates addition.

Thus, it can be written as \(x+5\).

2. "The sum of a variable and \(7\) "

Here, **sum** indicates addition.

Thus, it can be written as \(x+7\).

3. "\(y\) more than \(x\)"

Here, **more than** indicates addition.

Thus, it can be written as \(x+y\).

Note: - By commutative property \(x+y\) is same as \(y+x\).

A \(10x\)

B \(10+x\)

C \(10-x\)

D \(\dfrac{10}{x}\)

- Different operations can be performed on variables.
- To write an expression for a given statement, follow three steps:

(i) Identify the given number.

(ii) Identify any operations involved.

(iii) Identify the variable.

- The variables can be subtracted from numbers and vice-versa.
- The subtraction can be shown by using a '–' sign between the variables and numbers.
- Words like, 'less than', 'taken away', 'subtracted', 'decreased', indicate subtraction.

**For example:**

(1) "\(5\) less than a variable \(x\)"

Here, **less than** indicates subtraction.

Thus, it can be written as \(x-5\).

(2) "\(y\) is taken away/fewer than \(x\)"

Here, **taken away/fewer than** indicate subtraction.

Thus, it can be written as \(x-y\).

(3) "\(2\) subtracted from \(y\)"

Here, **subtracted** indicates subtraction.

Thus, it can be written as \(y-2\).

**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 \(10-x\)

B \(x-10\)

C \(x+10\)

D \(10\,x\)

- Different operations can be performed on variables.
- To write an expression for a given statement, follow three steps:

(i) Identify the given number.

(ii) Identify any operations involved.

(iii) Identify the variable.

- A variable can be multiplied by a number.
- The multiplication is shown by either '\(.\)' or ' \(×\) ' sign between a literal and a number.
- In algebra, we don't use multiplication symbol \((×)\) between numbers and letters because that can be very confusing with the variable \(x\).
- Words like, 'product', 'times', indicate multiplication.

**For example:**

1. "\(4\) times \(x\)"

Here, **times** indicates multiplication.

Thus, it can be written as \(4x\).

2. "The product of \(x\) and \(y\)"

Here, **product** indicates multiplication.

Thus, it can be written as \(xy\).

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

A \(1.7x\)

B \(1.7+x\)

C \(1.7-x\)

D \(\dfrac{1.7}{x}\)

- Different operations can be performed on variables.
- To write an expression for a given statement, follow three steps:

(i) Identify the given number.

(ii) Identify any operations involved.

(iii) Identify the variable.

- A variable can be divided by a number and vice-versa.
- The division is shown either by a '\(\div\)' sign or by a fraction bar \((-)\).
- Words like, 'by', 'divided', indicate division.

**For example:**

1. "\(x\) divided by \(y\)"

Here, **divided** indicates division.

Thus, it can be written as \(\dfrac{x}{y}\).

2. "\(x\) by \(7\)"

Here, **by** indicates division.

Thus, it can be written as \(\dfrac{x}{7}\).

3. "\(30\) divided by \(x\)"

Here, **divided** indicates division.

Thus, it can be written as \(\dfrac{30}{x}\).

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

A \(2x\)

B \(2+x\)

C \(\dfrac{2}{x}\)

D \(2-x\)