Statistics How To

Integer: Simple Definition and Examples

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An integer includes whole numbers and negative whole numbers. Integers can be positive, negative, or zero. For example, 1, -1, 0, 101 and -101 are all whole numbers.

The set of integers is often given the symbol Z, and Z is defined as

{…, -3, -2,-1, 0, 1, 2, 3,…}

There are an infinite number of integers. Integers can be ordered by being placed on a number line; the integer to the right is always greater than the one to the left.

integer

A number line showing the distance between -1 and 1.


Absolute Value of an Integer

The absolute value of an integer is the distance from that integer to the origin (0). Since both 3 and -3 are 3 units (steps) away from the origin, the absolute value of both numbers is 3.

The absolute value of -3 is 3, because it’s three spaces from zero on the number line.


The Sign of an Integer

The sign (-) for all integers to the left of the origin (0) is (-) and for all integers to the right (+). Negative integers are those with a (-) sign and positive integers are those with a (-) sign. Positive integers may be written without their sign.

Adding and Subtracting Integers

To add two integers with the same sign, add the absolute values and give the sum the same sign as both integers.
For example: (-4) + (-7) = -(4 + 7)= – 11.

To add two integers with different signs, find the difference in absolute values and give the difference the same sign as the number with the largest absolute value.
For example: (-5) + (3)

  1. Find the absolute values (5 and 3).
  2. Find the difference between 5 and 3 (5 – 3 = 2).
  3. Find the sign of the largest absolute value. -5 has a negative sign.
  4. Add the sign from Step 3 to the difference you found in Step 2. The result is -2.

Subtracting an integer means adding its opposite.
For example:
Subtracting -2 from 10, we get:
10 – – 2 = 10 + 2 (2 is the opposite of -2) = 12.
Subtracting 2 from 10 we get:
10 + (-2) = 8.

When an integer is added to or subtracted by another integer the result is always an integer.

Multiplying Integers

To multiply an integer, multiply the absolute value. If the two integers being multiplied have the same sign, the result is positive. If the two integers have different signs, the result is negative.

When one integer is multiplied by another the result is always an integer. But when one is divided by another the result may or may not be an integer. For example, while 3/3 = 1 and 8/4 = 2 and are integers, 3/4 and 8/5 are not an integers.

Sources:
Positive and Negative Integers
Adding and Subtracting Integers

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Integer: Simple Definition and Examples was last modified: October 12th, 2017 by Stephanie Glen