Fraction Calculator Negative and Positive Numbers

How to Use This Calculator

Using our fraction calculator is simple. Follow these steps:

1. Enter the first fraction in the first input field.
2. Select the operation you want to perform (addition, subtraction, multiplication, or division).
3. Enter the second fraction in the second input field.
4. Click the "Calculate" button to see the result.
5. Review the detailed solution and any notes provided.

The calculator will display the result in its simplest form and provide a step-by-step explanation of how the calculation was performed.

Input Format

Fractions should be entered in the format "a/b" where "a" is the numerator and "b" is the denominator. For example, to enter 3/4, simply type "3/4".

Operations Supported

• Addition (+)
• Subtraction (-)
• Multiplication (×)
• Division (÷)

Basic Fraction Operations

Fractions are numbers that represent parts of a whole. They consist of a numerator (top number) and a denominator (bottom number). Here's how to perform basic operations with fractions:

Addition of Fractions

To add two fractions, follow these steps:

1. Find a common denominator for both fractions.
2. Convert each fraction to have the common denominator.
3. Add the numerators together.
4. Simplify the resulting fraction if possible.

Subtraction of Fractions

To subtract two fractions, follow these steps:

1. Find a common denominator for both fractions.
2. Convert each fraction to have the common denominator.
3. Subtract the numerators.
4. Simplify the resulting fraction if possible.

Multiplication of Fractions

To multiply two fractions, follow these steps:

1. Multiply the numerators together.
2. Multiply the denominators together.
3. Simplify the resulting fraction if possible.

Division of Fractions

To divide two fractions, follow these steps:

1. Multiply the first fraction by the reciprocal of the second fraction.
2. Simplify the resulting fraction if possible.

Working with Negative Fractions

Negative fractions are fractions with a negative sign. They can be added, subtracted, multiplied, and divided just like positive fractions, but there are some important rules to remember:

Adding and Subtracting Negative Fractions

When adding or subtracting negative fractions, the rules are similar to working with negative numbers:

• Adding a negative fraction is the same as subtracting its absolute value.
• Subtracting a negative fraction is the same as adding its absolute value.

Multiplying Negative Fractions

When multiplying negative fractions, the rules are the same as for negative numbers:

• A positive fraction multiplied by a negative fraction results in a negative fraction.
• A negative fraction multiplied by a negative fraction results in a positive fraction.

Dividing Negative Fractions

When dividing negative fractions, the rules are similar to multiplying:

• A positive fraction divided by a negative fraction results in a negative fraction.
• A negative fraction divided by a negative fraction results in a positive fraction.

Worked Examples

Here are some worked examples to help you understand how to perform fraction operations with negative and positive numbers:

Example 1: Adding Positive Fractions

Calculate 3/4 + 2/3.

1. Find a common denominator: 12
2. Convert fractions: 9/12 + 8/12
3. Add numerators: 17/12

Example 2: Subtracting Negative Fractions

Calculate 3/4 - (-2/3).

1. Convert to addition: 3/4 + 2/3
2. Find a common denominator: 12
3. Convert fractions: 9/12 + 8/12
4. Add numerators: 17/12

Example 3: Multiplying Negative Fractions

Calculate (-3/4) × (-2/3).

1. Multiply numerators: -3 × -2 = 6
2. Multiply denominators: 4 × 3 = 12
3. Simplify: 6/12 = 1/2

Example 4: Dividing Negative Fractions

Calculate (-3/4) ÷ (-2/3).

1. Multiply by reciprocal: (-3/4) × (3/2)
2. Multiply numerators: -3 × 3 = -9
3. Multiply denominators: 4 × 2 = 8
4. Simplify: -9/8