maths > integers

Sign and Absolute Value of Integers

what you'll learn...

overview

The two numbers received:5=5$\textrm{\left(r e c e i v e d\right\rangle} 5 = 5$ and given:5=5$\textrm{\left(g i v e n\right\rangle} 5 = - 5$ have same amount and different directions.

The amount of an integer is given by absolute value of the integer.

The direction of an integer is given by the sign of the integer. The sign of an integer is either positive or negative.

direction and quantity

The two numbers received:5=5$\textrm{\left(r e c e i v e d\right\rangle} 5 = 5$ and given:5=5$\textrm{\left(g i v e n\right\rangle} 5 = - 5$ are considered. It is noted that the amount in the two quantities are equal, only the directions are different.

Considering received:5=5$\textrm{\left(r e c e i v e d\right\rangle} 5 = 5$ and given:5=5$\textrm{\left(g i v e n\right\rangle} 5 = - 5$

The amount in the two quantities are equal.
The amount given by an integer is the absolute value of the integer.
eg: Absolute value of $- 4$ is $4$. Absolute value of $6$ is $6$.

The direction of the two quantities are different.
The direction information of an integer is the sign of the integer.
eg: Sign of $- 4$ is negative or $-$ve. Sign of $6$ is positive or $+$ve.

The word "absolute" means: viewed or taken without relation to other things. In numbers the direction information, positive or negative, provides the relative measure. Absolute value removes that and provides only the amount.

The word "sign" means a symbol used to denote some information. The sign of integers is the symbol used to show the direction, that is positive and negative.

Absolute Value of an Integer : The count or measure without the direction information is the absolute value of an integer.

Sign of an Integer: Integers are directed whole numbers. The directed information of integers is called sign and is either positive or negative:

eg: $21$ ($21$ received) has "positive" sign

eg: $- 16$ ($16$ given) has "negative" sign

examples

What is the absolute value of $- 3$?
The answer is "$3$"

What is the absolute value of $44$?
The answer is "$44$"

absolute symbol

Addition, subtraction, multiplication, and division are represented with symbols $+$, $-$, $\times$, $\div$ respectively.

In line of representing mathematical operations with symbols, the absolute value of a number is represented as follows.
absolute value of $- 3$
$= | - 3 |$
$= 3$

The expression $| - 4 |$ is read as, absolute value of negative 4.

examples

What is $| - 12 |$?
The answer is "$12$"

What is the sign of $- 7$

Absolute Value of an Integer - Simplified procedure : Remove any negative sign in the given integer.

What is $| 27 |$?
The answer is "$27$"

What is the sign of $27$?

What is $| - 93 |$?
The answer is "whole number $93$"

What is the sign of $- 93$?

summary

Absolute Value of an Integer : The count or measure without the direction information is the absolute value of an integer.

Sign of an Integer: The directed information of integers is called sign and is either positive or negative.

•  $| 4 | =$ absolute value of $4$ = 4

•  $\textrm{s i g n} 4 =$ positive

•  $| - 4 | =$ absolute value of $- 4$ = 4

•  $\textrm{s i g n} - 4 =$ negative

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