Wanna learn all the basics of Integers concepts? Then start with the absolute value of an integer. Integer Absolute Value is an important and basic concept to learn other concepts of Integers. Refer to all the rules, definitions, solved examples, types, etc to understand the concept more clearly. Follow the below sections to get more idea on how to find the Absolute Value of an Integer in detail and Solved Problems for finding the Integer Absolute Value using different approaches.

## Absolute Value of an Integer – Introduction

Integers Absolute Value is the distance of that integer value from zero irrespective of (positive or negative) direction. While considering the absolute value, its numerical value is taken without taking the sign into consideration.

An integer is any positive or negative whole number. Therefore, the positive integer has a negative sign and vice versa.

A positive number is a number that is greater than zero. It is represented by a “+” symbol and can be written with or without a symbol in front of it. The gain in some value or something is written with a positive number. A negative number is a number that is less than zero. It is represented by a “-” symbol and can be written with a “-” symbol in front of it. The loss in some value or something is written with a negative number.

A number line is a kind of diagram on which the numbers are marked at intervals. These are used to illustrate simple and easy numerical operations. Using the number line allows seeing a number is in relationship to other numbers and from zero. Zero, is present in the middle and separates positive and negative numbers. On the right side of zero, we can find numbers that are greater than zero (positive numbers) and on the left side, we can find numbers that are less than zero (negative numbers). The absolute value of the integer is the same as the distance from zero to a specific number.

### Representation of Absolute Value of an Integer

Integer Absolute Value is represented with two vertical lines. i.e., | |, one on either side of the integer.

|a| = a, when a is the positive integer

|a| = -a, when a is the negative integer

**Examples:**

- Absolute integer value of -15 is written as |-15| = 15 {here mod of -15 = 15}
- Absolute integer value of 8 is written as |8| = 8 {here mod of 8 = 8}

### Adding and Subtracting Absolute Value of Integers

To add 2 integers with the same (positive or negative) sign, add absolute values and assign the sum with the same sign as same both values.

**Example:**

(-7) + (-4) = -(7 + 4)= – 11.

To add 2 integers with different signs, find the difference in absolute integer values and give that product the same sign of the largest absolute value.

**Example:**

(-7)+(2)= -5

**How to find the absolute value?**

- First of all, find the absolute values of (7 and 2)
- Find the difference of numbers between 7 and 2 (7-2=5)
- Find the sign of the largest absolute value i.e., negative, as 7 is of (-)sign
- Add the sign to the difference we got in Step 2.
- Hence the final solution is -5

When an integer is subtracted or added by another integer, the result will be an integer.

### Multiplication of Absolute Value of Integers

To multiply the integer values, we have to multiply the absolute values. If the integers that are to be multiplied have the same sign, then the result will be positive. If both the integers have different signs, then the result will be negative.

When an integer is multiplied by another integer, then the result will be an integer itself.

### Absolute Value of Integers Examples

**Question 1:**

Write the absolute value of each of the following?

(i) 15

(ii) -24

(iii) -375

(iv) 0

(v) +7

(vi) +123

**Solution: **

(i) 15

(ii) 24

(iii) 375

(iv) 0

(v) 7

(vi) 123

**Question 2: **

Evaluate the following integers

(i) |-7| + |+5| + |0|

(ii) |10| – |-15| + |+12|

(iii) – |+3| – |-3| + |-6|

(iv) |-8| – |17| + |-12|

**Solution: **

(i) 12

(ii) 7

(iii) 0

(iv) 3

**Question 3:**

State whether the statements are true or false?

(i) The absolute value of -3 is 3.

(ii) The absolute value of an integer is always greater than the integer.

(iii) |+5| = +5

(iv) |-5| = -5

(v) – |+5| = 5

(vi) – |-5| = -5

**Solution:**

(i) True

(ii) False

(iii) True

(iv) False

(v) False

(vi) True

### Methods to Compute the Absolute Value of Integer

There are 3 approaches to find the Integers Absolute value. These approaches are helpful while solving problems. Finding the absolute value is the first step in solving the problems.

**Method 1: **

As the absolute value of the integer is always positive. For the positive integer, the absolute number is the number itself. For the negative number, the absolute number is multiplied by other negative numbers.

**Method 2:**

Negative numbers are saved in 2’s complement form. To get the absolute number, toggle bits of the number, then 1 to the result.

**Method 3:**

The built-in function library finds the absolute value of an integer.

To solve most of the problems, knowing the absolute value of the integer is important. This method is used in the real world and it has all sorts of math clues. Absolute values are often used in distance problems and also sometimes used for inequalities. Integers Absolute values are really helpful to get clarity on many things.

We have mentioned the important concept of Integers Absolute Value in the above article. Hope you got a clear idea of definitions, rules, and how to solve the problems. If you have any doubts, you can contact us from the below comment box. You can also directly ping us to know other information. Stay tuned to our page to get the latest and important information about all mathematical concepts.