Online Calculator That Does Negative Numbers

How This Calculator Works

This calculator performs basic arithmetic operations that include negative numbers. It handles addition, subtraction, multiplication, and division with negative values correctly, following standard mathematical rules.

Basic Operations

The calculator performs the following operations when negative numbers are involved:

• Addition: When adding a negative number to a positive number, subtract the absolute value of the negative number from the positive number.
• Subtraction: When subtracting a negative number, it's equivalent to adding its absolute value.
• Multiplication: The product of two negative numbers is positive, while the product of a positive and negative number is negative.
• Division: The quotient of two negative numbers is positive, while the quotient of a positive and negative number is negative.

The Formula

The calculator uses standard arithmetic formulas for operations with negative numbers:

The calculator applies these formulas automatically when you enter negative numbers in the input fields.

Worked Examples

Let's look at some practical examples of how this calculator handles negative numbers:

Example 1: Addition with Negative Numbers

Calculate 5 + (-3):

1. Enter 5 in the first field
2. Select "+" as the operation
3. Enter -3 in the second field
4. Click Calculate

The result will be 2, because 5 + (-3) = 5 - 3 = 2.

Example 2: Subtraction with Negative Numbers

Calculate 10 - (-4):

1. Enter 10 in the first field
2. Select "-" as the operation
3. Enter -4 in the second field
4. Click Calculate

The result will be 14, because 10 - (-4) = 10 + 4 = 14.

Example 3: Multiplication with Negative Numbers

Calculate -6 × 3:

1. Enter -6 in the first field
2. Select "×" as the operation
3. Enter 3 in the second field
4. Click Calculate

The result will be -18, because a negative times a positive is negative.

Example 4: Division with Negative Numbers

Calculate -20 ÷ 5:

1. Enter -20 in the first field
2. Select "÷" as the operation
3. Enter 5 in the second field
4. Click Calculate

The result will be -4, because a negative divided by a positive is negative.

Common Mistakes

When working with negative numbers, there are several common errors to avoid:

1. Sign Errors in Operations

Remember that subtracting a negative is the same as adding a positive, and adding a negative is the same as subtracting a positive. For example:

• 5 - (-3) = 5 + 3 = 8 (not 2)
• 10 + (-4) = 10 - 4 = 6 (not 14)

2. Incorrect Multiplication Rules

Remember that multiplying two negative numbers gives a positive result, while multiplying a positive and negative number gives a negative result. For example:

• -3 × -2 = 6 (positive)
• 4 × -5 = -20 (negative)

3. Division Sign Errors

When dividing negative numbers, the result is positive only if both numbers are negative. Otherwise, the result is negative. For example:

• -12 ÷ -3 = 4 (positive)
• 15 ÷ -5 = -3 (negative)

4. Forgetting Absolute Values

When dealing with temperature differences or other measurements, remember that the absolute value represents the magnitude without regard to direction. For example:

• The temperature difference between 5°C and -3°C is |5 - (-3)| = 8°C
• The absolute value of -7 is 7