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Fraction Calculator

Select the mode and enter the values and let this fraction calculator solve your fraction problem.

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Fraction Calculator: Add, Subtract, Multiply, and Divide Fractions

This free fraction calculator allows you to perform basic fraction operations such as addition, subtraction, multiplication, and division. It offers two modes:

Simple: Basic input fields for operations like addition, subtraction, multiplication, and division.
Advanced: Mixed number input format to handle more detailed fraction calculations.

The tool works with both proper and improper fractions. You can also view long division steps with a single click. This makes fraction calculations easy and fast for everyone, whether solving simple fractions or mixed numbers.

What Are Fractions?

A fraction represents a part of a whole number, object, or quantity using two numbers:

Numerator (top number): Shows how many parts are being considered.
Denominator (bottom number): Shows the total number of equal parts.

Example: \( \frac{1}{6} \) means 1 out of 6 equal parts. Imagine a pizza cut into 6 slices—having 1 slice is 1/6 of the pizza. Fractions help represent parts of a whole in everyday life.

How to Use This Fraction Calculator (Step-by-Step)

Select the Option: Choose 'Simple' or 'Advanced' mode.
Enter Your Values: Input numerators and denominators in the designated fields.
Select the Operation: Choose addition (➕), subtraction (➖), multiplication (✖️), or division (➗).
Click Calculate: Press “CALCULATE” to display the result instantly.

Addition of Fractions

There are three scenarios when adding fractions:

1. Fractions with the Same Denominator

Add numerators, keep the denominator the same.

Example: \( \frac{3}{8} + \frac{2}{8} = \frac{3+2}{8} = \frac{5}{8} \)

2. Fractions with Different Denominators

Find the least common denominator (LCD), convert fractions, then add.

Example: \( \frac{1}{4} + \frac{1}{6} \)

LCD of 4 and 6 is 12
Convert fractions: \( \frac{1}{4} = \frac{3}{12} \), \( \frac{1}{6} = \frac{2}{12} \)
Add: \( \frac{3}{12} + \frac{2}{12} = \frac{5}{12} \)

3. Adding Mixed Fractions

Convert mixed numbers to improper fractions, then add.

Example: \( 2\frac{1}{3} + 1\frac{1}{6} \)

Convert to improper fractions: \( 2\frac{1}{3} = \frac{7}{3} \), \( 1\frac{1}{6} = \frac{7}{6} \)
Find LCD (6) and add: \( \frac{14}{6} + \frac{7}{6} = \frac{21}{6} = 3\frac{1}{2} \)

Subtraction of Fractions

Subtraction follows the same idea as addition:

Example: \( \frac{5}{8} - \frac{2}{5} = \frac{25}{40} - \frac{16}{40} = \frac{9}{40} \)

Multiplication of Fractions

Multiply numerators together and denominators together.

Example: \( \frac{5}{7} \times \frac{2}{3} = \frac{10}{21} \)

Division of Fractions

Flip the second fraction (reciprocal) and multiply.

Example: \( \frac{2}{5} \div \frac{3}{7} \)

Flip the second fraction: \( \frac{3}{7} \to \frac{7}{3} \)
Multiply: \( \frac{2}{5} \times \frac{7}{3} = \frac{14}{15} \)

Fractions with Negative Numbers

Negative fractions work the same way. The calculator handles them and displays simplified results.

Converting Decimals to Fractions

Decimals can be converted to fractions using powers of 10.

Example: Convert 0.75 to a fraction:

Write as fraction: 0.75 = 75/100
Simplify by dividing numerator and denominator by 25: 75 ÷ 25 / 100 ÷ 25 = 3/4

FAQs

How to calculate fractions? Use this calculator to add, subtract, multiply, or divide fractions. It finds the LCD and simplifies the results.
What is 1/2 as a fraction? 1/2 is a proper fraction and equals 0.5 as a decimal.
How do I convert decimals to fractions? Use a decimal-to-fraction calculator. Example: 0.75 → 3/4.
What is 1/4 × 1/4? 1/4 × 1/4 = 1/16.

Limitations

Fractions with very large numerators or denominators may not work.
The calculator cannot function if any input field is blank.
Entering 0 in the denominator is invalid and prevents calculation.

References

Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations. Educational Studies in Mathematics, 107, 525–545.
Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Relational reasoning predicts fraction knowledge in children. Contemporary Educational Psychology, 62, 101896.

This calculator ensures privacy and does not use your input values for any third-party purposes. See our Privacy Policy for more details.

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