```Question 20091
The integer number system is a basic system of numbers.
Integers are the whole numbers, negative whole numbers, and zero.
For example, 4698785, 26, 2, 0, -26, and -3232 are integers, but numbers like 1/2, 4.00022, 1.5, Pi, and -9.29 are not. We can say that an integer is in the set: {...3,-2,-1,0,1,2,3,...}

1) When adding integers of the same sign, we add their absolute values, and give the result the same sign.

Examples:

2 + 5 = 7
(-7) + (-2) = -(7 + 2) = -9

2) When adding integers of the opposite signs, we take their absolute values, subtract the smaller from the larger, and give the result the sign of the integer with the larger absolute value.Example:

8 + (-17) = ?
The absolute values of 8 and -17 are 8 and 17.
Subtracting the smaller from the larger gives 17 - 8 = 9, and since the larger absolute value was 17, we give the result the same sign as -17, so 8 + (-17) = -9.

::Subtracting Integers
Subtracting an integer is the same as adding its opposite.

Examples:

In the following examples, we convert the subtracted integer to its opposite, and add the two integers.
7 - 4 = 7 + (-4) = 3

::Multiplying Integers
To multiply a pair of integers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opposite signs, their product is the opposite of the product of their absolute values (their product is negative). If one or both of the integers is 0, the product is 0.

Example:

In the product below, both numbers are positive, so we just take their product.
4 × 3 = 12

::Dividing Integers
To divide a pair of integers if both integers have the same sign, divide the absolute value of the first integer by the absolute value of the second integer.
To divide a pair of integers if both integers have different signs, divide the absolute value of the first integer by the absolute value of the second integer, and give this result a negative sign.

Examples:

In the division below, both numbers are positive, so we just divide as usual.
4 ÷ 2 = 2.

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