Mastering Integer Operations: Rules and Examples for Addition, Subtraction, Multiplication, and Division

Integers

Integers are a set of positive and negative whole numbers, including zero

Integers are a set of positive and negative whole numbers, including zero. They do not include fractions or decimals. The set of integers can be written as {…,-3, -2, -1, 0, 1, 2, 3,…}.

Integers are used to represent quantities such as counting numbers, negative values, and positions on a number line. They are often used in various mathematical operations, such as addition, subtraction, multiplication, and division.

When adding and subtracting integers, there are a few rules to keep in mind:

1. Adding integers with the same sign: When adding two integers with the same sign (both positive or both negative), you simply add their absolute values and keep the same sign. For example, (-5) + (-3) = -8.

2. Adding integers with different signs: When adding two integers with different signs, you subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. For example, (-5) + 3 = -2.

3. Subtracting integers: Subtracting an integer is the same as adding its opposite. For example, 4 – 2 is equivalent to 4 + (-2).

4. Multiplying integers: When multiplying integers, the rules are as follows:
– If the signs of the integers are the same (both positive or both negative), the product is positive. For example, (-2) * (-3) = 6.
– If the signs of the integers are different, the product is negative. For example, (-2) * 3 = -6.

5. Dividing integers: When dividing integers, the rules are similar to multiplication:
– If the signs of the integers are the same, the quotient is positive. For example, (-12) / (-3) = 4.
– If the signs of the integers are different, the quotient is negative. For example, (-12) / 3 = -4.

Understanding integers is crucial in many areas of mathematics, such as algebra, number theory, and calculus. They provide a foundation for working with more complex numbers and equations. Practicing and becoming comfortable with operations involving integers will greatly benefit your mathematical skills.

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