# Absolute Value of an Integer

Absolute value of an integer is its numerical value without taking the sign into consideration.

The absolute values of -9 = 9; the absolute value of 5 = 5 and so on.

The symbol used to denote the absolute value is, two vertical lines (| |), one on either side of an integer.

Therefore, if 'a' represents an integer, its absolute value is represented by |a| and is always non-negative.

Note:

(i) |a| = a; when 'a' is positive or zero.

(ii) |a| = -a; when 'a' is negative.

## Definition of Absolute Value of an Integer:

The numerical value of an integer regardless of its sign is known as its absolute value.

The two vertical bars | | represent the absolute value.

If x represents an integer, then

| x | = x if x is +ve or zero

| -x | = x if x is -ve.

The absolute value of 5, written as |5|, is 5 and the absolute value of -5, written as| -5|, is 5.

The absolute value of 15, written as | 15 |, is 15 and the absolute value of -15, written as | -15 |, is 15.

The absolute value of 0, written as | 0 |, is 0.

Find the absolute value of the following:

(i) -76

(ii) +50

(iii) -100

Solution:

(i) -76 = |76|

(ii) +50 = |50|

(iii) -100 = |100|

Examples on absolute value of an integer:

(i) Absolute value of - 7 is written as |- 7| = 7 [here mod of - 7 = 7]

(ii) Absolute value of + 2 is written as |+ 2| = 2 [here mod of + 2 = 2]

(iii) Absolute value of - 15 is written as |- 15| = 15 [here mod of - 15 = 15]

(iv) Absolute value of + 17 is written as |+ 17| = 17 [here mod of + 17 = 17]

On a number line the number indicates the distance from 0 and the sign before the number tells us whether the distance is to the right or left of 0. For example +5 is 5 units away to the right of 0 where as -5 is 5 units away to the left of 0 on the number line. The numerical value of the unit regardless of the sign is called absolute value of an integer. The absolute value of an integer is always positive. Thus, the absolute value of 5 and -5 is 5. It is written as |5|

So, |5| = 5 and |-5| = 5

Find the mod of:

(i) |14 - 6| = |8| = 8

(ii) - |- 10| = - 10

(iii) 15 - |- 6| = 15 - 6 = 9

(iv) 7 + |- 7| = 7 + 7 = 14

Note: (i) A positive number with a sign in front of its numerical value means increase or gain.

(ii) A negative number with a sign in front of its numerical value means decrease or loss.

Different Types of Solved Examples on Absolute Value of an Integer:

1. Write the opposites of the following statements:

(i) 28 m to the right

(ii) running 75 km towards East

(iii) loss of $250 (iv) 780 m above sea level (v) increase in population Solution: (i) 28 m to the left (ii) running 75 km towards West (iii) gain of$ 250

(iv) 780 m below sea level

(v) decrease in population

2. Represent the following numbers as integers with appropriate signs.

(i) 7°C above normal temperature

(ii) A deposit of $5690 (iii) 23°C below 0°C Solution: (i) +7°C (ii) +$5690

(iii) -23°C

3. Compare -2 and -6 using number line

Solution:

Since -2 is to the right of -6, therefore -2 > -6 or -6 < -2.

4. Find the absolute value of each of the following:

(i) -12

(ii) 30

(iii) 0

Solution:

(i) The absolute value of -12 = | -12 | = 12

(ii) The absolute value of 30 = | 30 | = 30

(ii) The absolute value of 0 = | 0 | = 0

[Since integer 0 is neither positive nor negative, the absolute value of zero is zero i.e., | 0 | = 0.

5. Find the value of 24 + | -14 |.

Solution:

24 + | -14 |.

= 24 + 14, since | -14 | = 14.

6. Write all the integers between

(i) -1 and 3

(ii) -3 and 4

Solution:

(i) The integers between -1 and 3 are 0, 1, 2.

(ii) The integers between -3 and 4 are -2, -1, 0, 1, 2, 3.

7. Which of the following pairs of integers is greater?

(i) 6, -6

(ii) 0, -9

(iii) 0, 8

(iv) -8, -3

(v) 4, -9

Solution:

(i) 6 > -6; since, every positive integer is greater than every negative integer.

(ii) 0 > -9; since, 0 is greater than every negative integer.

(iii) 0 < 8; Since, 0 is less than every positive integer.

(iv) -8 < -3; Since, If x = 8 and b = 3 then x > y, therefore, -x < -y.

(v) 4 > -9; Since, every positive integer is greater than every negative integer.

## You might like these

• ### Ordering Integers | Integers from Greater to Lesser, Lesser to Greater

In ordering integers we will learn how to order the integers on a number line. An integer on a number line is always greater than every integer on its left. Thus, 3 is greater than

• ### Representation of Integers on a Number Line | Integers on Number Line

Representation of integers on a number line is explained here step by step. In the number line the positive numbers are to the right side and the negative numbers are to the left side.

Numbers - Integers

Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### 2nd Grade Place Value | Definition | Explanation | Examples |Worksheet

Sep 14, 24 04:31 PM

The value of a digit in a given number depends on its place or position in the number. This value is called its place value.

2. ### Three Digit Numbers | What is Spike Abacus? | Abacus for Kids|3 Digits

Sep 14, 24 03:39 PM

Three digit numbers are from 100 to 999. We know that there are nine one-digit numbers, i.e., 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are 90 two digit numbers i.e., from 10 to 99. One digit numbers are ma

3. ### Worksheet on Three-digit Numbers | Write the Missing Numbers | Pattern

Sep 14, 24 02:12 PM

Practice the questions given in worksheet on three-digit numbers. The questions are based on writing the missing number in the correct order, patterns, 3-digit number in words, number names in figures…

4. ### Comparison of Three-digit Numbers | Arrange 3-digit Numbers |Questions

Sep 13, 24 02:48 AM

What are the rules for the comparison of three-digit numbers? (i) The numbers having less than three digits are always smaller than the numbers having three digits as: