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How Do You Use Negative Numbers on A Calculator

Reviewed by Calculator Editorial Team

Negative numbers are a fundamental concept in mathematics that represent values less than zero. They're used in various fields like finance, physics, and engineering. This guide will explain how to work with negative numbers on a calculator, including basic operations and practical examples.

The Basics of Negative Numbers

Negative numbers are numbers that are less than zero. They're represented by a minus sign (-) before the number. For example, -5, -3.14, and -0.001 are all negative numbers.

The number line is a useful tool for visualizing negative numbers. Positive numbers extend to the right of zero, while negative numbers extend to the left. The distance between two numbers on the number line is called the absolute value.

Absolute value of a number x is written as |x| and represents the distance of x from zero on the number line.

Negative numbers have several important properties:

  • Adding a negative number is the same as subtracting its absolute value
  • Subtracting a negative number is the same as adding its absolute value
  • Multiplying two negative numbers gives a positive result
  • Dividing two negative numbers gives a positive result

Common Operations with Negatives

Addition and Subtraction

When adding or subtracting negative numbers, follow these rules:

  • Positive + Negative = Positive - Negative
  • Negative + Positive = Negative - Positive
  • Negative + Negative = Negative + Negative (add the absolute values)
  • Positive - Negative = Positive + Positive
  • Negative - Positive = Negative + Positive
  • Negative - Negative = Negative - Negative (subtract the absolute values)
Remember that subtracting a negative number is the same as adding its absolute value. This is known as the "double negative" rule.

Multiplication and Division

When multiplying or dividing negative numbers:

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

The key rule is that the product or quotient of two negative numbers is positive, while the product or quotient of one negative and one positive number is negative.

Using Negatives on a Calculator

Most calculators have a dedicated negative/positive button (often marked with a ± symbol) that toggles the sign of the current number. Here's how to use it:

  1. Enter the number you want to make negative
  2. Press the ± button to change its sign
  3. Continue with your calculation as needed

If your calculator doesn't have a ± button, you can still enter negative numbers by typing the minus sign before the number.

To enter -5 on a calculator: Press the minus sign (-) followed by 5.

When performing operations with negative numbers, remember to:

  • Use the ± button to change signs as needed
  • Follow the order of operations (PEMDAS/BODMAS)
  • Pay attention to parentheses when they're used

Practical Examples

Example 1: Simple Addition

Calculate 5 + (-3):

  1. Enter 5
  2. Press +
  3. Press ± to make it -3
  4. Press = to get the result: 2

Example 2: Subtraction

Calculate (-4) - (-2):

  1. Press ± to make it -4
  2. Press -
  3. Press ± to make it -2
  4. Press = to get the result: -2

Example 3: Multiplication

Calculate (-3) × (-5):

  1. Press ± to make it -3
  2. Press ×
  3. Press ± to make it -5
  4. Press = to get the result: 15

Example 4: Division

Calculate (-10) ÷ 2:

  1. Press ± to make it -10
  2. Press ÷
  3. Enter 2
  4. Press = to get the result: -5

FAQ

Can I enter negative numbers directly on a calculator?
Yes, most calculators allow you to enter negative numbers by typing the minus sign (-) before the number. For example, to enter -5, press the minus sign followed by 5.
What happens when I divide a negative number by a positive number?
The result will be negative. For example, (-6) ÷ 2 = -3. This follows the rule that a negative divided by a positive is negative.
How do I change a positive number to negative on a calculator?
Most calculators have a ± (negative/positive) button that toggles the sign of the current number. Press this button to change the sign of the displayed number.
What's the difference between subtracting a negative and adding a positive?
Subtracting a negative is the same as adding its absolute value. For example, 5 - (-3) is the same as 5 + 3, which equals 8.
Can I use parentheses with negative numbers?
Yes, you can use parentheses to group negative numbers and ensure they're treated as a single unit in calculations. For example, (-3) × (-2) = 6.