Operating with Integers: Arithmetic with Positive and Negative Integers

Introduction

In this lesson, we will explore how to perform arithmetic operations such as addition, subtraction, multiplication, and division with positive and negative integers.

Key Concepts

1. Addition of Integers

   • When adding two integers with the same sign, add their absolute values and keep the common sign.
   • When adding two integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the integer with the larger absolute value.

2. Subtraction of Integers

   • To subtract an integer, add its opposite. For example, to compute $a - b$, use $a + (-b)$.

3. Multiplication of Integers

   • The product of two integers with the same sign is positive. The product of two integers with different signs is negative.

4. Division of Integers

   • Similar to multiplication, the quotient of two integers with the same sign is positive, while the quotient of two integers with different signs is negative.

Example Calculation

Let's calculate: $-5 + 3$.

1. Since the numbers have different signs, subtract the absolute values: $|-5| - |3| = 5 - 3 = 2$.
2. The larger absolute value is from $-5$, so the result is negative:
   $-5 + 3 = -2$

Now, let’s compute: $-6 - 4$.

1. Change it to addition: $-6 + (-4)$.
2. Add the absolute values: $6 + 4 = 10$.
3. Since both numbers are negative, the result is negative:
   $-6 - 4 = -10$

Key Questions

• What happens when you add a positive integer to a negative integer?
• How do you convert subtraction of integers into addition?
• What sign do you get when multiplying two negative integers?

Summary

Understanding how to operate with positive and negative integers is crucial in mathematics. Practice these rules to become proficient in handling arithmetic with integers.