Calculator Positive and Negative Numbers

Working with positive and negative numbers is a fundamental math skill that applies to many real-world situations. This guide explains the basics of addition, subtraction, multiplication, and division with positive and negative numbers, along with practical examples and a built-in calculator.

Introduction

Positive and negative numbers are essential in mathematics and everyday life. Positive numbers represent quantities that are greater than zero, while negative numbers represent quantities that are less than zero. Understanding how to work with both types of numbers is crucial for solving problems in finance, science, engineering, and more.

In this guide, you'll learn the basic rules for adding, subtracting, multiplying, and dividing positive and negative numbers. We'll also provide a working calculator to help you practice these operations and see the results immediately.

Basic Operations

Addition and Subtraction

When adding or subtracting numbers with the same sign, simply add or subtract their absolute values and keep the same sign.

Addition Rules

Positive + Positive = Positive

Negative + Negative = Negative

Positive - Positive = Positive or Negative (depending on which is larger)

Negative - Negative = Positive or Negative (depending on which is larger)

Multiplication and Division

When multiplying or dividing numbers with different signs, the result is negative. When both numbers have the same sign, the result is positive.

Multiplication Rules

Positive × Positive = Positive

Negative × Negative = Positive

Positive × Negative = Negative

Negative × Positive = Negative

Division Rules

Positive ÷ Positive = Positive

Negative ÷ Negative = Positive

Positive ÷ Negative = Negative

Negative ÷ Positive = Negative

Combining Operations

When combining operations, follow the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Example

Calculate: 5 + (-3) × 2

Solution: First multiply -3 × 2 = -6, then add 5 + (-6) = -1

Real-World Examples

Understanding positive and negative numbers helps in many practical situations:

Banking: Credits are positive, debits are negative
Temperature: Above freezing is positive, below is negative
Elevation: Above sea level is positive, below is negative
Sports: Points scored are positive, points allowed are negative

Example 1: Banking Transactions

If you have $100 in your account and you spend $50, your new balance is $50 (100 + (-50) = 50). If you then deposit $30, your balance becomes $80 (50 + 30 = 80).

Example 2: Temperature Changes

If the temperature is 10°C and it drops by 5°C, the new temperature is 5°C (10 + (-5) = 5). If it then rises by 3°C, the temperature becomes 8°C (5 + 3 = 8).

Common Mistakes

When working with positive and negative numbers, it's easy to make some common mistakes:

Forgetting to change the sign when subtracting a negative number (e.g., 5 - (-3) = 5 + 3 = 8)
Confusing the rules for multiplication and division of negative numbers
Not following the correct order of operations

Tip

To avoid mistakes, double-check your work and use the calculator provided to verify your results.

FAQ

What is the difference between positive and negative numbers?

Positive numbers are greater than zero and represent quantities that are more than nothing. Negative numbers are less than zero and represent quantities that are less than nothing.

How do you add two negative numbers?

When adding two negative numbers, you add their absolute values and keep the negative sign. For example, -3 + (-2) = -5.

What happens when you multiply two negative numbers?

When you multiply two negative numbers, the result is positive. For example, -3 × -2 = 6.

How do you subtract a negative number?

Subtracting a negative number is the same as adding its positive counterpart. For example, 5 - (-3) = 5 + 3 = 8.

What is the order of operations when working with positive and negative numbers?

The order of operations is Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).