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Purcell Math

Math Methods Grades 4-8

Understanding Simple Operations with Integers

Introduction

Mastering integer operations is foundational to building math skills. Let’s dive into the rules for basic operations involving integers—addition, subtraction, multiplication, and division—using examples to make things crystal clear.

Multiplying and Dividing with Positive and Negative Integers

The results of multiplying or dividing integers depend on the signs of the numbers involved:

Negative × Positive = Negative
Examples:
-2 multiplied by 3 equals -6
−2 × 3 = −6
-8 divided by 2 equals -4
−8 ÷ 2 = −4

Negative × Negative = Positive
Examples:
-3 multiplied by -4 equals 12
−3 ×−4 = 12
-6 divided by -2 equals 3
−6 ÷ −2 = 3

Multiplying or Dividing by One and Zero

Certain unique rules apply when integers are multiplied or divided by 1 or 0:

Multiplying or Dividing by One: Any integer multiplied or divided by 1 results in that integer itself.
Examples:
3 multiplied by 1 equals 3
3 × 1 = 3
6 divided by 1 equals 6
6 ÷ 1 = 6

Multiplying by Zero: Any number multiplied by 0 results in 0.
Example:
4 multiplied by 0 equals 0
4 × 0 = 0

Dividing by Zero: Not Defined. Division by zero does not have a meaningful result in mathematics.
Example:
4 divided by 0
4 ÷ 0 is undefined.

Why These Rules Matter

Understanding these operations and why they work is critical for solving more complex algebraic expressions. Familiarity with integer rules makes it easier to work with variables, balance equations, and solve problems that involve both positive and negative numbers.

Conclusion

Mastering simple operations with integers creates a solid foundation for future math concepts, and these rules will become second nature with practice!

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