Sum of Fractions Calculator

Enter two fractions to calculate their sum.

Calculate the Sum of Two Fractions

First Fraction
Second Fraction
Result

How to Calculate the Sum of Two Fractions?

When adding fractions, whether they are mixed fractions (e.g., \( 2\frac{3}{4} \)) or simple fractions (e.g., \( \frac{3}{4} \)), you can follow these steps:

  1. Separate the mixed fraction into its whole and fractional parts: For a mixed fraction like \( 2\frac{3}{4} \), break it into the whole number part (2) and the fractional part (\( \frac{3}{4} \)). If both fractions are simple, like \( \frac{3}{4} \) and \( \frac{5}{6} \), no splitting is needed.
  2. Find a common denominator: For both simple fractions and the fractional parts, find the least common denominator (LCD), and rewrite the fractions with the same denominator.
  3. Add the fractional and whole parts: After adding the fractional parts, if the numerator exceeds the denominator, convert the result into a mixed fraction. If there is a whole number part, add it to the total.
  4. Simplify the result: If there are common factors between the numerator and denominator, simplify the fraction.

Examples

Example 1: Calculate the sum of the mixed fractions \( 2\frac{3}{4} \) and \( 1\frac{5}{6} \)

Solution:

1. Separate the fractions:

\( 2\frac{3}{4} = 2 + \frac{3}{4} \)

\( 1\frac{5}{6} = 1 + \frac{5}{6} \)

2. Find a common denominator:

The least common denominator of 4 and 6 is 12.

Convert \( \frac{3}{4} \) to \( \frac{9}{12} \), and \( \frac{5}{6} \) to \( \frac{10}{12} \).

3. Add the fractional and whole parts:

\( \text{Fractional part sum:} \quad \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12} \)

\( \text{Whole part sum:} \quad 2 + 1 = 3 \)

4. Combine the results:

\( 3 + 1\frac{7}{12} = 4\frac{7}{12} \)

Result: \( 2\frac{3}{4} + 1\frac{5}{6} = 4\frac{7}{12} \)

Example 2: Calculate the sum of the simple fractions \( \frac{3}{4} \) and \( \frac{5}{6} \)

Solution:

1. Find a common denominator:

The least common denominator of 4 and 6 is 12.

Convert \( \frac{3}{4} \) to \( \frac{9}{12} \), and \( \frac{5}{6} \) to \( \frac{10}{12} \).

2. Add the fractions:

\( \frac{9}{12} + \frac{10}{12} = \frac{19}{12} = 1\frac{7}{12} \)

Result: \(\frac{3}{4} + \frac{5}{6} = 1\frac{7}{12}\)

Example 3: Calculate the sum of the mixed fraction \( 3\frac{1}{2} \) and the simple fraction \( \frac{2}{3} \)

Solution:

1. Separate the fractions:

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

2. Find a common denominator:

The least common denominator of 2 and 3 is 6.

Convert \( \frac{1}{2} \) to \( \frac{3}{6} \), and \( \frac{2}{3} \) to \( \frac{4}{6} \).

3. Add the fractional and whole parts:

\( \text{Fractional part sum:} \quad \frac{3}{6} + \frac{4}{6} = \frac{7}{6} = 1\frac{1}{6} \)

\( \text{Whole part sum:} \quad 3 + 0 = 3 \)

4. Combine the results:

\( 3 + 1\frac{1}{6} = 4\frac{1}{6} \)

Result: \( 3\frac{1}{2} + \frac{2}{3} = 4\frac{1}{6} \)