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Doing Negative Numbers on A Calculator

Reviewed by Calculator Editorial Team

Working with negative numbers on a calculator can seem intimidating, but with the right approach, it becomes straightforward. This guide explains how to enter and perform calculations with negative numbers, covering addition, subtraction, multiplication, and division.

How to Enter Negative Numbers

Most modern calculators have a dedicated negative sign button (often marked with a ± symbol). Here's how to use it:

  1. Press the number you want to make negative.
  2. Press the ± button to toggle the sign.
  3. If you need to enter a negative number directly, look for a negative sign button or use the subtraction key with a leading zero.

Tip: If your calculator doesn't have a ± button, you can enter a negative number by pressing the subtraction key followed by the number (e.g., -5).

Basic Operations with Negative Numbers

Addition and Subtraction

When adding or subtracting negative numbers, follow these rules:

  • Adding two negative numbers: -a + (-b) = -(a + b)
  • Subtracting a negative number: a - (-b) = a + b
  • Subtracting a positive number: a - b = a + (-b)

Example: (-3) + (-5) = -8

Multiplication and Division

When multiplying or dividing negative numbers:

  • Negative × Negative = Positive
  • Negative × Positive = Negative
  • Negative ÷ Negative = Positive
  • Negative ÷ Positive = Negative

Example: (-4) × (-2) = 8

Order of Operations

When working with negative numbers in complex expressions, remember PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction):

Example: 10 - 3 × (-2) + 4 = 10 - (-6) + 4 = 10 + 6 + 4 = 20

Common Mistakes to Avoid

When working with negative numbers, these common errors can lead to incorrect results:

  1. Forgetting to change the sign when multiplying or dividing: (-a) × (-b) = ab, not -ab.
  2. Ignoring the order of operations: Always calculate multiplication and division before addition and subtraction.
  3. Misplacing the negative sign: -a² is not the same as (-a)².

Pro Tip: Double-check your calculations, especially when dealing with multiple negative numbers and operations.

Real-World Examples

Negative numbers are used in many practical situations. Here are a few examples:

Banking

When you withdraw money from your account, the transaction is recorded as a negative number. For example, if you have $100 and withdraw $30, your new balance is $70.

Temperature

Negative temperatures are common in many parts of the world. For example, -5°C is colder than 5°C.

Elevation

Negative elevation indicates depth below sea level. For example, Death Valley is at -86 meters elevation.

Negative Number Scenarios
Scenario Example Calculation
Bank Balance Starting with $100, withdraw $30 100 - 30 = $70
Temperature Change Temperature drops from 5°C to -3°C 5 - (-3) = +8°C change
Elevation Difference From sea level (-0) to Death Valley (-86m) 0 - (-86) = +86m change

FAQ

Can I use a calculator to solve equations with negative numbers?
Yes, calculators can help solve equations with negative numbers. Just follow the order of operations (PEMDAS) and use the calculator's functions carefully.
What happens if I divide by a negative number?
Dividing by a negative number gives a negative result if the numerator is positive, and a positive result if both numbers are negative.
How do I square a negative number?
Squaring a negative number always results in a positive number. For example, (-3)² = 9.