Fraction Calculator

In $\frac{3}{4}$ the bottom number, the denominator, says how many equal pieces one whole was cut into. The top number, the numerator, says how many of those pieces you have. A fraction is also just a division waiting to happen: $\frac{3}{4} = 3 \div 4 = 0.75$.

Two fractions are equivalent if one is the other with every piece cut smaller. Multiplying top and bottom by the same number is multiplying by $1$, so the value never moves:

$\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$

That single idea drives everything else on this page — simplifying runs it backwards, and finding a common denominator runs it forwards.

A fraction with a numerator smaller than its denominator is proper and worth less than one whole. When the numerator is larger, it is improper and can be written as a mixed number instead. Both forms are correct; improper fractions are what you calculate with, and mixed numbers are usually what you report.

Add or subtract — denominators must match first. Rewrite both fractions over a common denominator, then combine the numerators only and leave the denominator alone:

$\frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6}$

Multiply — no common denominator needed. Multiply straight across, tops together and bottoms together:

$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$

Divide — flip the second fraction and multiply:

$\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8}$

The single biggest source of wrong answers is borrowing the wrong rule: people find a common denominator before multiplying (harmless but wasteful), or add straight across (wrong). Ask which operation you are doing before you touch the numbers.

• Improper to mixed: divide and keep the remainder. $\frac{15}{8}$: $15 \div 8 = 1$ remainder $7$, so $1\frac{7}{8}$.
• Mixed to improper: whole $\times$ denominator $+$ numerator. $2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$. Always do this before multiplying or dividing.
• Fraction to decimal: divide top by bottom. $\frac{7}{8} = 0.875$.
• Decimal to percent: multiply by $100$. $0.875 = 87.5\%$.
• Simplify: divide top and bottom by their greatest common factor. $\frac{18}{24} \div \frac{6}{6} = \frac{3}{4}$.

To compare two fractions, put them over a common denominator or turn both into decimals — $\frac{5}{8} = 0.625$ beats $\frac{3}{5} = 0.6$. Never compare by numerator alone.

One habit prevents most fraction errors: estimate before you calculate. $\frac{2}{3}$ is a bit over a half and $\frac{1}{6}$ is small, so their sum should sit just under $1$ — and $\frac{5}{6}$ does. If your answer lands somewhere else entirely, you have almost certainly used the wrong rule rather than made an arithmetic slip.