Two Fractions Calculator

Enter two fractions, select the operation type, and calculate the result instantly.

Add, Subtract, Multiply, and Divide Two Fractions

First Fraction

Second Fraction

Result

What is a Fraction?

A fraction represents a part of a whole and is usually written in the form \( \frac{a}{b} \), where \( a \) is the numerator and \( b \) is the denominator. Fractions can either be regular fractions or mixed fractions. A mixed fraction consists of an integer part and a proper fraction part, like \( c\frac{d}{e} \).

How to Perform Operations with Fractions?

The steps for fraction operations vary depending on the operation. Below are the detailed steps for each operation:

1. Addition of Fractions

Same Denominator: Simply add the numerators and keep the denominator the same: \( \frac{a}{b} + \frac{c}{b} = \frac{a+c}{b} \)
Different Denominators: Find the least common multiple (LCM) of the denominators, adjust the fractions to have the same denominator, and then add them: \( \frac{a}{b} + \frac{c}{d} = \frac{a \cdot d + c \cdot b}{\text{lcm}(b,d)} \)

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

Solution:

1. The denominators are different, so we adjust them:

The LCM is 6

\( \frac{1}{2} = \frac{3}{6} \)

\( \frac{1}{3} = \frac{2}{6} \)

2. Same Denominator, add them together:

\( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \)

Result: \( \frac{1}{2} + \frac{1}{3} = \frac{5}{6} \)

2. Subtraction of Fractions

Same Denominator: Subtract the numerators and keep the denominator the same: \( \frac{a}{b} - \frac{c}{b} = \frac{a-c}{b} \)
Different Denominators: Find the LCM of the denominators, adjust the fractions to have the same denominator, and then subtract: \( \frac{a}{b} - \frac{c}{d} = \frac{a \cdot d - c \cdot b}{\text{lcm}(b,d)} \)

Example: Calculate \( \frac{5}{6} - \frac{1}{4} \).

Solution:

1. The denominators are different, so adjust them:

The LCM is 12:

\( \frac{5}{6} = \frac{10}{12} \)

\( \frac{1}{4} = \frac{3}{12} \)

2. Now the denominators are the same, direct subtraction:

\( \frac{10}{12} - \frac{3}{12} = \frac{7}{12} \)

Result: \( \frac{5}{6} - \frac{1}{4} = \frac{7}{12} \)

3. Multiplication of Fractions

Multiply the numerators and the denominators: \( \frac{a}{b} \times \frac{c}{d} = \frac{a \cdot c}{b \cdot d} \)
Simplify the fraction: If needed, simplify the fraction to its lowest terms.

Example: Calculate \( \frac{2}{3} \times \frac{3}{4} \).

Solution:

1. Multiply the numerators and the denominators:

\( \frac{2 \cdot 3}{3 \cdot 4} = \frac{6}{12} \)

2. Simplify the fraction:

\( \frac{6}{12} = \frac{1}{2} \)

Result: \( \frac{2}{3} \times \frac{3}{4} = \frac{1}{2} \)

4. Division of Fractions

Find the reciprocal of the second fraction: \( \frac{c}{d} = \frac{d}{c} \)
Multiply the first fraction by the reciprocal of the second fraction (multiply numerators and denominators): \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \cdot d}{b \cdot c} \)
Simplify the fraction: If needed, simplify the fraction to its lowest terms.

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

Solution:

1. Calculate the reciprocal of the second fraction:

\( \frac{2}{3} = \frac{3}{2} \)

2. Multiply with the reciprocal:

\( \frac{3}{5} \times \frac{3}{2} = \frac{9}{10} \)

Result: \( \frac{3}{5} \div \frac{2}{3} = \frac{9}{10} \)

Handling Mixed Fractions

Before performing any operations, mixed fractions should first be converted to improper fractions, then add, subtract, multiply and divide according to the above rules.

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

Solution:

1. Convert the mixed fraction to an improper fraction:

\( 2\frac{1}{2} = \frac{5}{2} \)

2. The denominators are different, adjust them:

The LCM is 6:

\( \frac{5}{2} = \frac{15}{6} \)

\( \frac{1}{3} = \frac{2}{6} \)

3. Perform the addition:

\( \frac{15}{6} + \frac{2}{6} = \frac{17}{6} \)

Result: \( 2\frac{1}{2} + \frac{1}{3} = \frac{17}{6} \)

Two Fractions Calculator

Add, Subtract, Multiply, and Divide Two Fractions

Result

What is a Fraction?

How to Perform Operations with Fractions?

1. Addition of Fractions

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

2. Subtraction of Fractions

Example: Calculate \( \frac{5}{6} - \frac{1}{4} \).

3. Multiplication of Fractions

Example: Calculate \( \frac{2}{3} \times \frac{3}{4} \).

4. Division of Fractions

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

Handling Mixed Fractions

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

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