__maths__>__Introduction to Algebra, Polynomials, and Identities__>__Algebra: Variables and Expressions__### Introduction to Variables

In this page, it is explained that a variable is a symbol that represents a number.

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How many yellow flowers are shown in the figure?

- `1`
- `1`
- `2`

The answer is '`1`'

How many petals does the yellow flower have?

- `4`
- `8`
- `8`

The answer is '`8`'

How many yellow flowers are shown in the figure?

- `1`
- `4`
- `4`

The answer is '`4`'

How many petals do all the four yellow flowers have?

- `8xx4`
- `8xx4`
- `8`

The answer is '`8xx4`'

If a person has `2` yellow flowers of the kind shown in the figure, how many petals do those `2` flowers have?

- `8`
- `8 xx 2 = 16`
- `8 xx 2 = 16`

The answer is '`8xx2= 16`'

A person has `x` yellow flowers of the kind shown in the figure. The `x` can be any number.

The number of petals from `x` flowers is `8x`.

• if `x` is `2` then the number of petals is `8 xx 2 = 16`

• if `x` is `6` then the number of petals is `8xx6 = 48`

• etc. In this, the number of flowers is considered as a symbol `x` and the number of petals is derived as an expression `8x`. *The letter `x` in the expression is called a variable.*

How many cherry flowers are shown in the figure?

- `1`
- `1`
- `2`

The answer is '`1`'

How many petals does the cherry flower have?

- `4`
- `5`
- `5`

The answer is '`5`'

How many cherry flowers are shown in the figure?

- `1`
- `3`
- `3`

The answer is '`3`'

How many petals do all the three cherry flowers have?

- `5xx3`
- `5xx3`
- `5`

The answer is '`5xx3`'

If a person has `y` cherry flowers of the kind shown in the figure, how many petals do those `y` flowers have?

- `5`
- `5y`
- `5y`

The answer is '`5y`'.

If a person has `2` yellow blossom flowers and `3` cherry flowers of the kinds shown in the figure, how many petals do all the flowers have?

- `8+5 = 13`
- `8xx2 + 5xx3`
- `8xx2 + 5xx3`

The answer is '`8xx2 + 5xx3`'

If a person has `x` yellow blossom flowers and `y` cherry flowers of the kinds shown in the figure, how many petals do all the flowers have?

- `8+5 = 13`
- `8xx x + 5xx y`
- `8xx x + 5xx y`

The answer is '`8xx x + 5xx y`'. `x` and `y` are two variables.

In the examples, it is clearly given that

• an unknown number can be represented using a symbol. eg: `x` flowers.

• a symbol, which is used in place of a number, can take a value based on the problem. eg: the number of flowers is taken as `x` and in a particular basket the number of flowers is `3`; then `x=3` for that basket.

The symbol is called a *variable*.

Which of the following is a meaning for the word 'variable'?

- that varies or changes in value
- that varies or changes in value
- that easily gets angry

The answer is 'that varies or changes in value'.

What is the term used to refer to quantities represented with a letter?

- Pronunciation : Say the answer once

Spelling: Write the answer once

The answer is 'variable'.

a variable is a quantity that can assume different numerical values.

**Variable: ** is a representation of a numerical quantity with a letter or a symbol.

example: number of dogs `x` and number of cats `y`.

*Solved Exercise Problem: *

How many legs will a group of dogs have? Note: The number of dogs in the group is not given, so take the number of dogs as a variable.

- `4`
- if the group has `x` dogs, the number of legs ` = 4x`
- if the group has `x` dogs, the number of legs ` = 4x`

The answer is 'if the group has `x` dogs, the number of legs ` = 4x`'

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