Calculator for Negative Numbers and Fractions

This calculator helps you perform mathematical operations with negative numbers and fractions. Whether you need to add, subtract, multiply, or divide fractions, this tool provides accurate results and explains the process step-by-step.

How to Use This Calculator

Using this calculator is straightforward. Follow these steps:

Select the operation you want to perform (addition, subtraction, multiplication, or division).
Enter the first fraction or decimal number in the first input field.
Enter the second fraction or decimal number in the second input field.
Click the "Calculate" button to see the result.
Review the detailed explanation of the calculation.

The calculator will display the result in both fraction and decimal forms, making it easy to understand the outcome.

Basic Operations with Fractions

Working with fractions involves specific rules for each operation. Here's a quick overview:

Addition and Subtraction

To add or subtract fractions, you need a common denominator. The formula is:

a/b ± c/d = (a×d ± c×b)/(b×d)

For example, 1/2 + 1/3 = (1×3 + 1×2)/(2×3) = 5/6.

Multiplication

Multiplying fractions is simpler. Multiply the numerators together and the denominators together:

(a/b) × (c/d) = (a×c)/(b×d)

For example, 1/2 × 3/4 = (1×3)/(2×4) = 3/8.

Division

To divide fractions, multiply by the reciprocal of the second fraction:

(a/b) ÷ (c/d) = (a×d)/(b×c)

For example, 1/2 ÷ 3/4 = (1×4)/(2×3) = 4/6 = 2/3.

Converting Between Fractions and Decimals

Converting between fractions and decimals is essential for understanding numbers. Here's how to do it:

Fraction to Decimal

Divide the numerator by the denominator:

a/b = a ÷ b

For example, 3/4 = 3 ÷ 4 = 0.75.

Decimal to Fraction

Express the decimal as a fraction with a denominator of 1, then simplify:

0.a = a/10, 0.ab = ab/100, etc.

For example, 0.75 = 75/100 = 3/4.

Worked Examples

Let's look at some practical examples to see how the calculator works.

Example 1: Adding Fractions

Calculate 1/2 + 1/3:

Find a common denominator: 6.
Convert the fractions: 3/6 + 2/6.
Add the numerators: 5/6.

The result is 5/6 or 0.833...

Example 2: Multiplying Fractions

Calculate 2/3 × 4/5:

Multiply the numerators: 2×4 = 8.
Multiply the denominators: 3×5 = 15.
Simplify the fraction: 8/15.

The result is 8/15 or 0.533...

FAQ

Can I use negative numbers with this calculator?: Yes, the calculator accepts negative numbers for all operations. Just enter a negative sign before the number.
How do I simplify fractions?: The calculator automatically simplifies results to their lowest terms. For example, 4/6 becomes 2/3.
What if I enter an invalid fraction?: The calculator will display an error message if you enter an invalid fraction (like 0/0 or a/b where b is 0).
Can I use mixed numbers?: Yes, you can enter mixed numbers in the format "a b/c" (e.g., 1 1/2). The calculator will convert them to improper fractions for calculations.
How accurate are the results?: The calculator uses precise arithmetic operations to ensure accurate results. Decimal results are rounded to 4 decimal places.