# Absolute value of integer

## What is Absolute Value?

The actual value of any integer without considering its sign is called Absolute Value.

Integers are number with positive or negative sign.

Absolute value tells the value of integer disregarding its sign.

For Example;

⟹ Absolute value of +3 is 3

⟹ Absolute value of -3 is 3

## Symbols representing Absolute Value

The absolute value is represented by two horizontal lines ” | | “ placed on either side of integer.

The integer with horizontal lines are called Mod.

For Example;
⟹ The absolute value of -10 is represented as | -10 |
| -10 | is called Mod of -10.

⟹ Similarly absolute value of + 10 is represented as | + 10 |
| + 10 | is called Mod of 10.

Summary
Absolute value considers the value and ignores the sign.
It is represented by two horizontal line ” | | “
The symbol of absolute value is called Mod

## Significance of Absolute value

Absolute value helps in finding the distance of the number from origin on the number line.

Practically, negative numbers create lots of confusion regarding its actual distance from number 0.

Absolute value offers great help by removing the signs from the digits and focusing on its actual value.

Example 01
Using absolute value, represent -10 on number line.

Solution
Absolute value of -10 is represented as | -10 |

We know that absolute value ignores the sign and considers the original value.

| -10 | ⟹ 10

Representing 10 in number line.

## Absolute Value of Integer – Solved Examples

(01) Find the absolute value of following numbers.

(a) -35

The absolute value is represented as | -35 |

The value of | -35 | is 35.

i.e. | -35 | = 35
Hence, the absolute value of -35 is 35

(b) + 25

The absolute value is represented as | +25 |

The value of | +25 | is 25.

i.e. |+ 25 | = 25
Hence, the absolute value of + 25 is 25.

(c) + 63

⟹ |+ 63 | = 63
Hence absolute value of + 63 is 63

(d) -75

i.e. | -75 | = 75
Hence, absolute value of -75 is 75

(e) -30

i.e. | -30 | = 30
Hence absolute value of -30 is 30

(02) Find the absolute value of following expressions;

Solution

(i) | – 7 / 2 |

The absolute value ignores the sign of the number.

| – 7 / 2 | ⟹ 7 / 2

(ii) – | – 3 |

we know that;
| – 3 | ⟹ 3

– | – 3 | ⟹ -3

(iii) | 3 – 4 |

lets first solve the expression inside the mod bracket.

3 – 4 = -1

So now the expression can be written as;
| 3 – 4 | = | – 1 |

Removing the mod bracket, we get;
| – 1 | = 1

Hence, number 1 is the solution.

(iv) – | 2(2) – 1 |

First solve the expression inside the mod bracket.

⟹ 2(2) – 1
⟹ 4 – 1
⟹ 3

The expression can be written as;
– | 2(2) – 1 | = – | 3 |

– | 3 | = – 3

Hence, number -3 is the solution.