Fraction Calculator

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

This fraction calculator is used to perform fraction operations such as addition, subtraction, multiplication, and division. It offers two modes, including:

✔️ Simple: It provides a basic input field to perform operations like addition, subtraction, multiplication, and division.

✔️ Advance: It provides mixed number pattern input to get detailed fraction calculation using the same basic operations.

Our tool works with both proper and improper fractions. You can also get the long division steps with a single click when needed. It makes fraction calculations easy and fast for everyone, whether you're solving simple fractions or working with mixed numbers.

What Are Fractions?

“A fraction represents a part of a whole number, object, or quantity using two numbers.”

Numerator (Top number): It shows how many parts are being considered
Denominator (Bottom number): It shows the total number of equal parts

For Example, $ \frac{1}{6} $ means 1 out of 6 equal parts. Imagine a pizza cut into 6 slices, if you have 1 slice, that is $ \frac{1}{6} $ of the pizza. Fractions like this help us show parts of a whole in everyday life.

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

1️⃣ Select the Option: Choose the option from the given dropdown, whether it is 'Simple' or 'Advance'

2️⃣ Enter your Values: Input the numerators and denominators in the designated fields

3️⃣ Select the Operation: Choose addition ( ➕ ), subtraction ( ➖ ), multiplication ( ✖️ ), or division ( ➗ )

4️⃣ Click Calculate: Press the “CALCULATE”, and this fractions calculator will display the result instantly

Addition of Fractions:

There are three scenarios to be considered when adding fractions:

1. Adding Fractions with the Same Denominator

When both fractions have the same bottom number, addition becomes very simple. You only add the numerators, while the denominator stays the same.

→ Example

$ \frac{3}{8} + \frac{2}{8} = \frac{3+2}{8} = \frac{5}{8} $

2. Adding Fractions with Different Denominators

When a fraction has unlike denominators, start by finding the least common denominator (LCD). To find it, you can use LCD Calculator. After that, convert each fraction and add them.

→ 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} $

Now Add:

$ \frac{3}{12} + \frac{2}{12} = \frac{5}{12} $

3. Adding Mixed Fractions

A mixed number includes a whole part and a fractional part, so you should add them accurately.

→ Example

$ 2\frac{1}{3} + 1\frac{1}{6} $

Multiply the whole number by the denominator: 3 x 2 = 6
Add the result to your numerator: 6 + 1 = 7
As the new numerator is written as: $ 2\frac{1}{3} = \frac{7}{3}$ and $1\frac{1}{6} = \frac{7}{6}$

$\frac{7}{3} + \frac{7}{6}$ = $\frac{42}{18} + \frac{21}{18}$ = $\frac{63}{18}$ = $\frac{7}{2}$

Final Answer

$\frac{7}{2}$ OR $ 3\frac{1}{2}$

Subtraction of Fractions:

Subtracting fractions follows the same idea as adding them. The steps you follow depends on whether the fractions have the same denominator or different. You can also refer to the fraction addition above for help.

→ Example

$ \frac{5}{8} - \frac{2}{5} = \frac{5×5}{8×5} - \frac{2×8}{5×8} = \frac{25}{40} - \frac{16}{40} = \frac{9}{40} $

Multiplication of Fractions:

Multiplying fractions is simpler than adding and subtracting fractions because you don't need to have a common denominator. Just multiply the numerator together and the denominator together to get the solution.

→ Example

$ \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} $

$ \frac{5}{7} \times \frac{2}{3} = \frac{10}{21} $

Division of Fractions:

For dividing fractions, start by flipping the second fraction to get its reciprocal and then multiply the first fraction by this reciprocal. Now, simplify the result if possible. Generally, this method, often called “flip and multiply,” makes fraction division quick.

→ Example

$ \frac{2}{5} \div \frac{3}{7} $

Step 1: Flip the second fraction (find its reciprocal)

$ \frac{3}{7} \to \frac{7}{3} $

Step 2: Multiply the first fraction by the reciprocal

$ \frac{2}{5} \times \frac{7}{3}$

Step 3: Simplify the fraction

$ \frac{14}{15} $

Fractions with Negative Numbers

Handling negative fractions is no different. You can enter negative values and the fraction calculator works out the results. It shows them in improper fractions or simplified forms.

Handling Powers of 10 in Fractions

When working with decimals, understanding the powers of 10 is important. This concept simplifies converting fractions to decimals. It also helps convert decimals back to fractions.

For example, to convert the decimal 0.75 to a fraction:

Write the decimal as a fraction: 0.75 = $ \frac{75}{100}$

Simplify the fraction: Dividing the numerator and the denominator by their greatest common factor. In this case, the greatest common factor is 25. So, you have:

Simplify by dividing numerator and denominator by 25: 75 ÷ 25 / 100 ÷ 25 = 3/4

FAQs:

How to calculate fractions?

Use this fractions calculator to add, subtract, multiply, or divide fractions. It finds the least common denominator and simplifies the results for you.

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 the fraction to decimal calculator to convert decimals like 0.75 to fractions like

What is 1/4 × 1/4?

1/4 multiplied by 1/4 equals 1/16.

Limitations:

Fractions with very large numerators or denominators might be difficult to add, so the calculator does not support such bigger inputs
The calculator does not function if any input field is left blank
Entering ‘0’ in the denominator will make your fractions infinite, thus making the tool unable to calculate results

References:

Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107, 525–545.
Kalra, P. B., Hubbard, E. M., & Matthews, P. G. (2020). Taking the Relational Structure of Fractions Seriously: Relational Reasoning Predicts Fraction Knowledge in Elementary School 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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EN	ES	PL
DE	ID	JA
KO	CS	PT
FR	IT	RU
FI	ZH-TW	TR
AR