Fraction Calculator

Type a fraction expression, click Calculate. This fraction calculator returns the exact answer as a simplified fraction - never a rounded decimal.

• Fraction expression - the only box. Use / for the fraction bar and + - * / between fractions. The page loads with 1/2 + 1/3.
• Example chips - tap one to load it instead of typing: 3/4 - 1/6, 2/3 * 4/5, or 7/8 + 3/4.

Click Calculate on the preloaded 1/2 + 1/3 and the result line reads 5/6 - not 0.833, not 0.83, but the exact fraction in lowest terms. That is the point of a fraction calculator: decimals like $0.8333\ldots$ never terminate, so exact work stays in fractions, and the answer comes back simplified automatically.

Sum, difference, product, or quotient - the fraction calculator reads the operation you typed and applies the matching rule, then reduces whatever comes out.

This page is more than a static fraction calculator - it is also an AI tutor you can ask questions:

• Ask in plain words. “What is 3/4 minus 1/6?” The AI solves it step by step.
• Take a photo of your homework. No typing: the AI reads the fractions and shows the common denominator it chose.
• Ask about the ideas, not just the number. “Why do I need a common denominator to add?” gets a real explanation - check every number against the fraction calculator above.
• Work backwards. Give the answer and one input, and ask what the other fraction must be.
• Keep asking follow-ups. Each answer opens the next question, and the fraction calculator page keeps teaching.

A fraction is built from three parts: a numerator on top, a fraction bar in the middle, and a denominator below. In $\frac{3}{4}$, the denominator 4 says the whole is cut into 4 equal pieces; the numerator 3 says how many of those pieces you take. Read it as “3 of the 4 pieces” - or as a division, because the bar is a division sign in disguise: $\frac{3}{4} = 3 \div 4$.

Two conventions name the family:

• Proper fraction - numerator smaller than denominator, like $\frac{3}{4}$: less than one whole.
• Improper fraction - numerator larger than or equal to the denominator, like $\frac{3}{2}$: one whole or more. It converts to a mixed number, but for arithmetic the improper form is the one to keep.

One more fact does most of the work on this page: multiplying the numerator and the denominator by the same number leaves the fraction's value unchanged. That is why $\frac{1}{2}$ and $\frac{3}{6}$ are the same number wearing different sizes - and it is the move the fraction calculator uses whenever a common denominator is needed.

Fractions only add when their denominators match - you can only count pieces of the same size. So the first move is always: rewrite both fractions over a common denominator.

$\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}$

The formula builds that common denominator $bd$ in one step: scale each fraction to the new size ($\frac{a}{b}$ becomes $\frac{ad}{bd}$, and $\frac{c}{d}$ becomes $\frac{bc}{bd}$), then add the scaled numerators.

Subtraction is the same rule with the sign flipped:

$\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}$

Watch it on the form's default, $\frac{1}{2}+\frac{1}{3}$:

1. Common denominator: $2 \times 3 = 6$.
2. Scale: $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$.
3. Add the tops: $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$.

And on the chip $\frac{3}{4}-\frac{1}{6}$: over 12, that is $\frac{9}{12} - \frac{2}{12} = \frac{7}{12}$.

One caution: $bd$ always works but is not always the least denominator - after combining, simplify the result. The fraction calculator picks the denominator and reduces the answer for you.

Adding and subtracting are two of the four operations on fractions. Multiplication and division are the other two - and they follow a different, easier rule.

Multiplication needs no common denominator. Multiply straight across, top times top and bottom times bottom:

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

On the chip $\frac{2}{3} \times \frac{4}{5}$: tops give $2 \times 4 = 8$, bottoms give $3 \times 5 = 15$, so the product is $\frac{8}{15}$ - already in lowest terms.

Division flips the second fraction and multiplies - “keep, change, flip”:

$\dfrac{a}{b}\div\dfrac{c}{d}=\dfrac{a}{b}\times\dfrac{d}{c}$

Why flip? Dividing by $\frac{c}{d}$ asks “how many $\frac{c}{d}$'s fit in this?” - and the reciprocal $\frac{d}{c}$ is exactly the factor that undoes $\frac{c}{d}$, since $\frac{c}{d} \times \frac{d}{c} = 1$.

The contrast with the last block is worth saying out loud: addition demands equal denominators; multiplication ignores them. The fraction calculator applies the right rule to whatever you type - knowing which is which is the skill being tested.

Add $\frac{1}{2}+\frac{1}{3}$ - the expression the fraction calculator preloads.

1. Find a common denominator. The denominators are 2 and 3; neither divides the other, so use $2 \times 3 = 6$.
2. Scale both fractions. $\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}$, and $\frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6}$. Same numbers, now in pieces of the same size.
3. Add the numerators. $\frac{3}{6} + \frac{2}{6} = \frac{5}{6}$. The denominator stays 6 - it names the piece size, which did not change.
4. Simplify. Nothing but 1 divides both 5 and 6, so $\frac{5}{6}$ is already in lowest terms.

The exact answer is $\frac{5}{6}$. As a decimal it runs $0.8333\ldots$, which never terminates - exactly why the fraction calculator keeps the answer in fraction form. Type the expression into the box above and the result line reads 5/6; ask the AI tutor to show the steps and every number matches.

Two more chips from the form, one for each remaining rule.

Multiply $\frac{2}{3} \times \frac{4}{5}$:

1. Multiply the numerators: $2 \times 4 = 8$.
2. Multiply the denominators: $3 \times 5 = 15$.
3. Read off the product: $\frac{8}{15}$. No common denominator needed, and no simplification left to do.

Subtract $\frac{3}{4} - \frac{1}{6}$:

1. Common denominator: 4 and 6 share the multiple 12.
2. Scale: $\frac{3}{4} = \frac{9}{12}$ and $\frac{1}{6} = \frac{2}{12}$.
3. Subtract the tops: $\frac{9}{12} - \frac{2}{12} = \frac{7}{12}$ - lowest terms already.

Notice what each rule demanded: the multiplication never looked at the other fraction's denominator, while the subtraction was impossible until both shared one. Run all three of this page's computations - $\frac{1}{2}+\frac{1}{3}$, $\frac{2}{3} \times \frac{4}{5}$, $\frac{3}{4}-\frac{1}{6}$ - through the fraction calculator above and watch 5/6, 8/15, and 7/12 come back simplified every time.

1. Adding tops and bottoms separately. The classic: $\frac{1}{2}+\frac{1}{3}$ read as $\frac{2}{5}$. It feels natural - add the 1s, add the 2 and 3 - but it adds halves to thirds as if they were the same piece size. The true answer is $\frac{5}{6}$, and the fraction calculator will never bless $\frac{2}{5}$: type both expressions and compare.
2. Stopping before simplifying. An answer with a common factor still in it is unfinished - reduce by dividing top and bottom by their greatest common factor. The fraction calculator simplifies every result automatically, which makes it a good checker for hand work: if your hand answer differs from the result line, simplify yours first, then compare again.
3. Typing mixed numbers straight in. A whole number sitting next to a fraction, like 1 1/2, will not be read the way you mean it - convert to the improper fraction $\frac{3}{2}$ first, then type. One and a half is three halves; the fraction calculator speaks fractions fluently but reads exactly what you type.

All three are setup mistakes - the arithmetic after them is usually fine. Check the setup, click Calculate, and let the fraction calculator catch the rest.