Add and Subtract Fractions Calculator

The denominator names the size of the piece; the numerator counts how many you have. Three eighths plus one eighth is four eighths for the same reason three apples plus one apple is four apples — the thing being counted does not change:

$\frac{3}{8} + \frac{1}{8} = \frac{3+1}{8} = \frac{4}{8} = \frac{1}{2}$

So when the denominators already match, add or subtract the numerators and leave the denominator alone. Then reduce: divide top and bottom by their greatest common factor.

This is exactly why $\frac{1}{2} + \frac{1}{3}$ is not $\frac{2}{5}$. Halves and thirds are different-sized pieces, so there is nothing to count yet. Making the denominators match is not a formality — it is the whole job.

A quick way to check any fraction answer is to convert to decimals: $\frac{3}{8} + \frac{1}{8} = 0.375 + 0.125 = 0.5$, which is exactly $\frac{1}{2}$.

1. Find the least common denominator (LCD) — the smallest number both denominators divide into. For 4 and 6 it is 12; for 6 and 8 it is 24.
2. Rewrite each fraction by multiplying its top and bottom by the same factor, so its value is unchanged: $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$.
3. Add or subtract the numerators over that shared denominator.
4. Simplify the result, and convert to a mixed number if the numerator is larger than the denominator.

If you cannot see the LCD, multiplying the two denominators always gives a common denominator — $\frac{1}{6} + \frac{1}{8}$ over 48 works fine. The answer is the same; you just have more reducing to do at the end.

Mixed numbers. Either convert to improper fractions first ($3\frac{1}{4} = \frac{13}{4}$), or keep the whole numbers separate and deal with the fraction parts. Whole numbers count as a denominator of 1: $2 = \frac{2}{1}$.

• Never add the denominators. $\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1$, not $\frac{2}{4}$.
• Multiply the numerator too. Turning $\frac{5}{6}$ into twenty-fourths means $\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$ — changing only the bottom changes the value.
• Borrowing across a mixed number. In $3\frac{3}{12} - 1\frac{10}{12}$ the top fraction is too small. Borrow one whole from the 3: it becomes $2\frac{15}{12}$, because $1 = \frac{12}{12}$ and $\frac{12}{12} + \frac{3}{12} = \frac{15}{12}$. Now subtract normally.
• Subtraction order matters. $\frac{1}{3} - \frac{1}{2} = -\frac{1}{6}$; a negative answer is a real answer, not a mistake.
• Finish the reduction. $\frac{6}{8}$ is correct but not simplified; the expected answer is $\frac{3}{4}$.