Integer Operations: Addition, Subtraction, Multiplication, Division Rules

Study Notes

Operations with Integers

Integers are a subset of the number system that includes all positive numbers, negative numbers, and 0. They can represent quantities such as temperature, distance, and money. This article focuses on the operations performed on integers, including addition, subtraction, multiplication, division, and their rules. For more information about integers, visit, which discusses properties such as closure, commutativity, associativity, distributivity, identity, and rational numbers.

Addition Rules for Integers

When adding two integers, follow these rules:

If both signs are positive (+ + = +), the sign of the sum will be positive.
If one sign is negative (- + = -) and the other is positive, change the smaller number's sign to positive before adding them. Then, if the signs are different (- + = -), change the larger number's sign to negative. The sign of the sum will be negative.
If both signs are negative, add the absolute values and assign the same sign as one of the original numbers.

Example: 2 + 3 = 5 (both signs are positive) -1 - 3 = -4 (signs are negative) -5 + 2 = -3 (signs are negative)

Subtraction Rules for Integers

Subtract two integers following these rules:

If either integer is zero, the operation results in the other integer.
To subtract a smaller value from a larger value, change the operator from subtraction to addition and switch the sign of the second integer.
When removing a larger value from a smaller value, change both quantities' signs to opposite ones and then follow rule #2.

Example: 3 - 2 = 1 (subtract a smaller positive from a larger one) -2 -- 3 = -5 (change operators and signs)

Multiplication and Division Rules for Integers

For multiplication:

Multiply two negative numbers or multiply a negative number by a positive number to get a negative answer.
Otherwise, multiply two positive numbers or multiply a negative number by a negative number, resulting in a positive product.

Division also follows similar rules, representing the quotient as a fraction with the dividend over the divisor.

Example: (2)(-3) = -6 (negative times negative equals positive) (-4)(3) = -12 (positive times negative equals negative)

In summary, when performing operations with integers, consider their signs and apply the appropriate rules for each operation. These rules help ensure consistency and accuracy when working with integers.

Description

Learn about the rules for performing operations on integers, including addition, subtraction, multiplication, division, and their specific rules like changing signs and dealing with positive and negative integers. This article provides examples to help understand how to work with integers effectively.