Fraction Calculator

Add, subtract, multiply, divide or simplify fractions, mixed numbers and whole numbers. The answer arrives in lowest terms, as a mixed number, a decimal and a percentage, with every step worked out.

First value

Type a fraction like 3/4, a mixed number like 2 1/3, or a whole number like 7.

Second value

The minus sign goes in front of the whole number: -2 3/4 is minus two and three quarters.

Answer, in lowest terms

37/12

3/4 + 2 1/3 =

As a mixed number

3 1/12

37 ÷ 12 = 3 remainder 1

As a decimal

3.083333

Rounded: this decimal repeats forever.

As a percentage

308.33%

3.083333 × 100 — the decimal moved two places.

How this answer is worked out

Read the values: 3/4 stays 3/4 and 2 1/3 means (2 × 3 + 1)/3 = 7/3.
Common denominator: LCM(4, 3) = 12, so 3/4 = 9/12 and 7/3 = 28/12.
Add the numerators: 9 + 28 = 37, over 12 → 37/12.
Divide both by the GCF: GCF(37, 12) = 1, so 37/12 is already in lowest terms.
37 ÷ 12 = 3 remainder 1, which is 3 1/12.
37 ÷ 12 = 3.083333, rounded — this decimal repeats forever.

Common fractions as decimals and percentages

Fraction	Decimal	Percentage
	0.5	50%
	0.333333 repeats	33.33%
	0.666667 repeats	66.67%
	0.25	25%
	0.75	75%
	0.2	20%
	0.4	40%
	0.6	60%
	0.8	80%
	0.166667 repeats	16.67%
	0.833333 repeats	83.33%
	0.125	12.5%
	0.375	37.5%
	0.625	62.5%
	0.875	87.5%
	0.1	10%
	0.3	30%
	0.7	70%
	0.9	90%
	0.0625	6.25%
	0.1875	18.75%
	0.3125	31.25%
	0.4375	43.75%
	0.5625	56.25%
	0.6875	68.75%
	0.8125	81.25%
	0.9375	93.75%

Press a fraction to load it into the first value. The rows tagged as repeating never stop, however many decimals you write.

Updated: September 11, 2026

Fraction calculator. Simplify, add, subtract, multiply and divide fractions and mixed numbers.

A fraction calculator adds, subtracts, multiplies, divides or simplifies fractions and returns the answer in lowest terms. Both boxes accept a fraction, a mixed number or a whole number, and the numbered steps below the cards name the common denominator and the GCF used to get there.

What Is a Fraction Calculator?

A fraction calculator handles the arithmetic that fractions make awkward: finding a common denominator, combining the numerators, and reducing whatever comes out. Enter 3/4 and 2 1/3 with the plus sign selected and the answer is 37/12, which is the same number written 3 1/12 as a mixed number, 3.083333 as a decimal and 308.33% as a percentage. All four forms appear at once, so you can take whichever one the homework, the recipe or the tape measure asks for.

Three words carry most of the vocabulary here. A fraction is in lowest terms when the only whole number dividing both the top and the bottom is 1, which is why 37/12 stays as it is: 37 and 12 share no factor. A fraction whose top is at least as big as its bottom, like 37/12, is improper, and rewriting it as a whole number plus a leftover gives the mixed number 3 1/12. Improper describes the shape of the fraction and says nothing about whether the answer is right — 37/12 and 3 1/12 are the same quantity, and US classrooms accept either unless the question names a form.

Many fraction calculators hand you a numerator box and a denominator box, so a mixed number needs a third box for the whole part and a negative mixed number leaves you guessing where the minus goes. Both boxes here take one string instead: 3/4, 2 1/3 or 7, with a single leading minus owning the whole value, so -2 3/4 reads as minus two and three quarters rather than minus two plus three quarters. There is no Calculate button either. The page arrives with an answer already in it and recomputes on every keystroke.

The limits are short. It works on two values at a time, and it wants fractions rather than decimals — typing 0.125 puts a note under that box pointing you at 1/8, because turning a decimal back into a fraction is a different question with its own rounding decisions. For three or more fractions, the chip labeled "Use the answer" loads each result into the first box so you can keep going in pairs. And when the question is about proportions rather than fraction arithmetic, the percentage calculator works from the other end: what percent one number is of another.

How to Use the Fraction Calculator

The form is three rows deep: the operation pills, the two value boxes side by side, and a pair of chips underneath. On a narrow phone the two boxes stack instead of sitting side by side.

1. Pick the operation. The pills read +, −, × and ÷, plus one worded option, Simplify. Choosing Simplify hides the second box and gives the first one the whole row, because reducing a fraction needs only one value.

2. Type the first value. A fraction (3/4), a mixed number (2 1/3, with a space between the whole part and the fraction) or a whole number (7) all parse. One leading minus covers everything after it, so -2 3/4 is a single negative quantity.

3. Type the second value the same way. The hint under this box carries the rule that catches people out: the minus goes in front of the whole number, so -2 3/4 rather than 2 -3/4.

4. Read the four cards, which are already filled in. They show the answer in lowest terms, the same value as a mixed number, as a decimal and as a percentage, each with one line underneath explaining where it came from. The line under the first card echoes your own problem back with the operator between the two values, which is how you confirm that 2 1/3 was read as two and a third and not as 21/3. Every card has a copy button.

5. Work down the numbered steps, which are open when the page loads rather than folded away. For 3/4 + 2 1/3 there are six: read the values, find the common denominator, add the numerators, divide by the GCF, convert to a mixed number, and divide out the decimal. Multiplication, division and Simplify skip the common-denominator line, so they show one fewer. The mixed-number line only appears when the answer has a whole part, which is why 3/4 × 1/6 = 1/8 lists four.

Below the steps sits a table of common fractions with their decimals and percentages, from halves and thirds through to all eight sixteenths. Each fraction in it is a button: pressing 5/8 loads 5/8 into the first box, which beats typing it. Four rows carry a small repeats tag on the decimal — 1/3, 2/3, 1/6 and 5/6 — and that tag means what it says. Those decimals never stop, however many places you write out.

Fraction Formulas

\frac{a}{b} + \frac{c}{d} = \frac{ad + cb}{bd}

$a$ = Numerator of the first fraction, the number on top
$b$ = Denominator of the first fraction, the number underneath
$c$ = Numerator of the second fraction
$d$ = Denominator of the second fraction

The formula above is the safe general rule for addition: multiplying the two denominators always produces a common denominator, since bd is a multiple of both. It is not always the smallest one. The least common denominator of two fractions is the least common multiple of their denominators, and that is the number the second step names, so 3/4 and 7/3 go over LCM(4, 3) = 12 rather than over any larger multiple. When both values already share a denominator the step says so and skips the rewrite: 5/8 and 1/8 stay put instead of being pushed over 64.

Subtraction is the same formula with the plus swapped for a minus. Multiplication needs no common denominator at all:

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Division flips the second value and multiplies by it, which is why the step for ÷ talks about a reciprocal:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}

A mixed number is converted before any of this happens. Multiply the whole part by the denominator, add the numerator, keep the denominator:

w\,\frac{n}{d} = \frac{wd + n}{d}

So 2 1/3 becomes (2 × 3 + 1)/3 = 7/3, which is the first line the calculator prints. A leading minus applies to the result of that conversion, not to the fraction part alone, so -2 3/4 is -11/4.

Whatever the operation produces then gets divided by the greatest common factor of its numerator and denominator:

\frac{n}{d} = \frac{n \div \text{GCF}}{d \div \text{GCF}}

One division is enough because the GCF is the largest common factor there is. 3/4 × 1/6 gives 3/24, whose GCF is 3, so the card reads 1/8. 21/98 has a GCF of 7 and lands on 3/14 in a single move rather than through repeated halving. When the GCF turns out to be 1, as with 37 and 12, the step says the fraction is already in lowest terms and nothing changes. The greatest common factor of two whole numbers up to 100 and the least common multiple of two whole numbers up to 12 are both grade-6 content in the Common Core standards (6.NS.B.4), which is why the steps name them rather than hiding the reduction.

What Each Mode Does

Mode	What the calculator does	Worked example
Add (+)	Rewrite both values over the LCM of the denominators, add the numerators, divide by the GCF	3/4 + 2 1/3 = 37/12 = 3 1/12
Subtract (−)	Same common denominator, subtract the numerators, then reduce	3/4 − 1/6 = 7/12
Multiply (×)	Multiply the tops, multiply the bottoms, then reduce	3/4 × 1/6 = 3/24 = 1/8
Divide (÷)	Flip the second value into its reciprocal and multiply	3/4 ÷ 1/6 = 18/4 = 9/2 = 4 1/2
Simplify	Divide top and bottom by their GCF; the second box disappears	21/98 = 3/14, with a GCF of 7
Whole values, any mode	A whole number sits over 1 and joins the same arithmetic	7 × 2/3 = 14/3 = 4 2/3

Worked Fraction Examples

Adding a fraction to a mixed number: 3/4 plus 2 1/3

This is the problem the page opens with, so the answer is on screen before you touch anything. The first step converts the mixed number: 3/4 stays 3/4, while 2 1/3 means (2 × 3 + 1)/3 = 7/3. Quarters and thirds have no denominator in common, so the second step finds LCM(4, 3) = 12 and rewrites both as 9/12 and 28/12. Adding the numerators gives 9 + 28 = 37 over 12, and since GCF(37, 12) = 1 there is nothing to divide out — 37/12 is already in lowest terms.

The remaining two steps convert that answer into the other forms the cards show. 37 ÷ 12 = 3 remainder 1, so the mixed number is 3 1/12. As a decimal, 37 ÷ 12 = 3.083333, rounded, because 12 carries a factor of 3 and that division repeats forever. The percentage card reads 308.33%, which reads oddly for a moment until you notice that three whole units on their own come to 300%.

Subtracting sixths from quarters: 3/4 minus 1/6

Select the − pill and the common-denominator step returns LCM(4, 6) = 12 again, this time turning 3/4 into 9/12 and 1/6 into 2/12. Subtracting the numerators gives 9 − 2 = 7 over 12, and 7 and 12 share no factor, so the answer stays 7/12.

The mixed-number card has nothing to add here: 7/12 is a proper fraction, its top is smaller than its bottom, and the card says so rather than inventing a whole part of 0. The decimal is 0.583333, flagged as rounded for the same reason as before, and the percentage is 58.33%. Order matters for subtraction, so if you meant 1/6 − 3/4 the swap chip flips the two values without any retyping.

How many 1/6-cup scoops fit in 3/4 cup

Dividing by a fraction is what you need when the question is how many small measures fit inside a larger one. Pick ÷, put 3/4 in the first box and 1/6 in the second, and the step explains the move rather than asserting it: 1/6 flips to 6/1, so 3/4 × 6/1 = 18/4. The GCF of 18 and 4 is 2, which turns 18/4 into 9/2.

That improper fraction is the mixed number 4 1/2, or 4.5 as a decimal — four full scoops and half of a fifth one. Nothing repeats in this answer, because 2 is one of the two primes that make decimals stop, so the decimal card says the value is exact rather than rounded. The percentage, 450%, is the same figure read as a share: three quarters is four and a half times a sixth.

Simplifying 21/98 to lowest terms

Choose Simplify and the second box disappears, since reducing a fraction involves only one value. Type 21/98. The steps shorten to four, because there is nothing to combine and no common denominator to find: read the value, note that it only has to be written in lowest terms, divide both parts by GCF(21, 98) = 7, and divide out the decimal.

The answer is 3/14. Finding the GCF in one go is the point of the method — halving would not work here, since 21 is odd and cannot be halved at all, and dividing by 7 once does the whole job. The decimal is 0.214286, rounded: 14 factors into 2 and 7, and that 7 is enough to make the division repeat. The percentage card reads 21.43%.

Scaling a recipe: 7 cups times 2/3

A batch calls for 7 cups of flour and you want two thirds of it. Put 7 in the first box, pick ×, and put 2/3 in the second. The whole number joins the arithmetic as 7/1, the multiply step goes straight across — 7 × 2 = 14 on top, 1 × 3 = 3 underneath — and 14/3 has a GCF of 1, so it stands.

14 ÷ 3 = 4 remainder 2, so you need 4 2/3 cups. The decimal is 4.666667, rounded, which is the figure to use with a kitchen scale, and 466.67% is the same scaling read as a percentage of one cup. A measuring cup cannot show you 4.666667, which is exactly why the mixed number gets its own card: four cups plus a two-thirds cup is something you can pour.

A negative mixed number: -2 3/4 plus 3

Many fraction tools ask you to put the minus into the numerator box, which leaves a negative mixed number ambiguous. Here you type -2 3/4 into the first box as one value, and the reading step confirms what it did with the sign: -2 3/4 means -(2 × 4 + 3)/4 = -11/4, a single quantity two and three quarters below zero.

Add 3 to that. The whole number becomes 3/1, both values go over 4, and the numerators add as -11 + 12 = 1, giving 1/4. The GCF is 1, so 1/4 is the answer; the mixed-number card reports that there is no whole part; the decimal is 0.25, exact, because 4 is a power of 2; and the percentage is 25%. If you type the sign inside instead, as 2 -3/4, a note appears under that box telling you to move the minus in front of the whole number.

Fraction Mistakes That Cost Points

Adding the bottom numbers as well as the top ones. 1/8 + 3/8 is 4/8, and 4/8 reduces to 1/2. Adding the denominators too would give 4/16, a quarter, which is half of the right answer. The denominator names the size of the pieces, so eighths plus eighths give you more eighths, never smaller ones.
Stopping one step before lowest terms. 5/8 + 1/8 comes to 6/8, and 6 and 8 still share a factor of 2, so the answer a teacher wants is 3/4. This is the step that costs the point on an otherwise right answer, and it is the step the calculator labels with the GCF it divided by.
Reaching for the GCF when the LCM is what you need. Combining two fractions needs the least common multiple of the denominators; reducing the result needs the greatest common factor of that result. The worked steps name each one where it belongs, LCM in the common-denominator line and GCF in the line after the arithmetic.
Flipping the wrong fraction in a division. 3/4 ÷ 1/6 flips the second value only: 3/4 × 6/1 = 18/4, which reduces to 9/2 or 4 1/2. Flipping the first one instead answers a different question and gives a much smaller number.
Reducing across two fractions before the denominators match. Canceling a common factor inside one fraction is fine at any point, but the numerators of two different fractions cannot be added or subtracted until both sit over the same denominator. The order of the steps is deliberate: common denominator first, GCF last.
Putting the minus inside the mixed number. 2 -3/4 is ambiguous and the calculator asks you to move the sign. Write -2 3/4, which is one negative quantity worth -11/4. A minus on a denominator, as in 3/-4, is accepted and rewritten as -3/4, since the value is the same either way.
Treating the decimal card as the exact answer. 37/12 prints as 3.083333 and that decimal repeats forever, which the card says outright. Rounding at the start of a longer calculation is how small errors grow, so carry 37/12 and convert on the last line.

Getting More Out of the Calculator

Chain instead of retyping. Add 1/8 + 3/8 to get 1/2, press the chip labeled "Use the answer", and 1/2 is sitting in the first box ready for the next operation. Retyping a result like 37/12 by hand is an easy place to drop a digit, and chaining is also how you handle three or more fractions in a row.
Load a common fraction with one press. Every fraction in the reference table is a button, so pressing 5/8 puts 5/8 into the first box. It is faster than typing and it rules out a slip like 5/85.
Check the mixed number against the decimal. 3 1/12 and 3.083333 should agree on the whole number 3, and the fraction left over should look about the right size. When the whole parts disagree, one of the boxes holds a value you did not intend.
Read the line under the first card before you trust the answer. It repeats both values with the operator between them, so a mixed number typed without its space shows up at once: 213 comes back as the whole number 213, not as 2 1/3.
Swap before you subtract or divide. Both operations depend on which value comes first, and the swap chip exchanges the two boxes, so 3/4 − 1/6 = 7/12 becomes the reverse subtraction without retyping either value.
Keep every number under eight digits. The arithmetic runs on whole numbers with no rounding at all, and the ceiling that keeps each intermediate product exact is 9,999,999 per part. The limit is applied after a mixed number has been converted to an improper fraction, which is why 9999999 1/2 is refused even though each piece you typed is inside it.
Send the problem rather than a screenshot. Change a value and the address bar picks it up, so the link you copy reopens the same problem for whoever you send it to. A page loaded fresh at its default state carries no query string at all.

Fraction Terms Worth Knowing

Lowest terms

A fraction where the only whole number dividing both the top and the bottom is 1. 6/8 is not in lowest terms; 3/4 is the same value fully reduced. Also called simplest form.

Proper fraction

A fraction whose numerator is smaller than its denominator, so its value sits between 0 and 1. 3/4 and 7/12 are proper, which is why neither of them has a mixed-number form.

Improper fraction

A fraction whose numerator is at least as large as its denominator, so the value is 1 or more. 37/12 is improper and correct; it is the form the first card shows.

Mixed number

A whole number written beside a proper fraction, meaning the two added together. 3 1/12 is three plus one twelfth, the same quantity as 37/12.

Greatest common factor (GCF)

The largest whole number that divides two numbers exactly. Dividing a numerator and denominator by their GCF reduces a fraction in one move: 21/98 has a GCF of 7 and becomes 3/14.

Least common denominator (LCD)

The smallest denominator two fractions can share, which is the least common multiple of their denominators. For quarters and thirds it is 12, so 3/4 becomes 9/12 and 7/3 becomes 28/12.

Reciprocal

A fraction with its numerator and denominator exchanged. Dividing by a fraction is the same as multiplying by its reciprocal, so 3/4 ÷ 1/6 becomes 3/4 × 6/1.

Repeating decimal

A decimal whose digits fall into a pattern that never ends. It happens whenever a reduced denominator has a prime factor other than 2 or 5, so 1/3 shows as 0.333333 with a repeats tag and 5/6 as 0.833333.

Frequently Asked Questions About Fractions

How do I add fractions with different denominators?

Rewrite both over a common denominator, add the numerators, then reduce. For 3/4 + 2 1/3 the calculator converts 2 1/3 to 7/3, uses LCM(4, 3) = 12 to get 9/12 and 28/12, and adds them to 37/12.

How do I simplify fractions?

Find the biggest number that goes into both the top and the bottom, then divide each by it. That number is the GCF. Chipping away one factor at a time also works: 24/36 halves twice to 6/9, and dividing by 3 lands on 2/3 — three moves, where GCF(24, 36) = 12 gets there in one. After an addition or a multiplication there is nothing left to reduce, since every answer here arrives in lowest terms, so Simplify is the mode for a fraction that came off a worksheet or a tape measure.

What is 3/4 as a mixed number?

It has no mixed form. A mixed number needs a whole part, and 3/4 is a proper fraction whose top is smaller than its bottom, so the value is under 1. The mixed-number card reports that instead of inventing 0 3/4.

How do I enter a mixed number like 2 1/3?

Type it into one box exactly as you write it, with a space between the whole part and the fraction: 2 1/3. There is no separate whole-number field to fill in. The line under the first card repeats your problem back as 3/4 + 2 1/3 =, so you can see the space was read as a mixed number; the first worked step then spells the conversion out, 2 1/3 means (2 × 3 + 1)/3 = 7/3, rather than 21/3.

Can I add three or more fractions at once?

The form holds two values, so three fractions take two passes. Combine the first two, press the chip labeled "Use the answer" to move that result into the first box, then type the third value into the second box. Chaining that way also saves you from copying an answer like 37/12 across by hand.

Why does the decimal for 1/3 never end?

A fraction's decimal stops only when its reduced denominator is built from 2s and 5s, the prime factors of 10. The 3 in 1/3 is neither, so the division repeats forever: the card shows 0.333333 and marks it as rounded. Wolfram MathWorld states the same condition.

Do I need the LCM or the GCF?

Both, at different moments. The LCM of the two denominators gives the common denominator you add over, which is what least common denominator means. The GCF of the answer's numerator and denominator is what you divide by to reach lowest terms. The steps name each one: LCM(4, 3) = 12 in the second line, GCF(37, 12) = 1 in the fourth.

How do I turn a fraction into a percentage?

Divide the top by the bottom, then multiply by 100. 3/8 is 0.375, which is 37.5%. The percentage card does it for the answer and its subtitle names the move, the decimal times 100 with the point shifted two places. Working the other way around, from a part and a whole to a rate, is what the percentage calculator is for.

How do I type a negative fraction or a negative mixed number?

One minus in front of the whole value. -2 3/4 means minus two and three quarters, or -11/4 as an improper fraction. Writing 2 -3/4 puts a note under that box asking you to move the sign, while a minus on the denominator such as 3/-4 is accepted and rewritten as -3/4.

Why will the calculator not take 0.125?

It reads fractions, not decimals, and the hint under the field says so with the fraction you probably wanted: write 1/8 rather than 0.125. Turning a decimal back into a fraction is a separate job with its own rounding decisions, so it is not folded in here.

What is 11/16 as a decimal?

0.6875, or 68.75%. Sixteenths turn up on rulers and tape measures, so all eight of them sit in the reference table under the steps, alongside 1/16 at 0.0625 and 15/16 at 0.9375.

Is there an app to install, or a button to press?

There is nothing to install and no button to press. The served page already contains the answer for 3/4 + 2 1/3, and changing either box recalculates in place with no reload and nothing to submit. It runs in any browser on a phone, tablet or laptop, costs nothing, and needs no account or sign-in.

The answer is 37/12, which is bigger than 1. Should I convert it?

Only if the question asks. 37/12 and 3 1/12 are the same number, and an improper fraction is a legitimate final answer. Word problems about quantities usually want the mixed number, because 3 1/12 cups is something you can measure, while algebra tends to prefer the improper form, which multiplies and divides more cleanly.

How accurate is the result, and which form should I hand in?

The fraction card is exact: the arithmetic runs on whole numerators and denominators with no rounding anywhere in the chain. The decimal card is the only rounded figure, and it tells you whether the decimal stops or repeats. For homework, copy the form the question named — lowest terms unless it says otherwise, the mixed number when the wording is about how many and how much is left over, and the percentage when the question is about a share of something.

Sources & References

Content verified by the Smart Calculators Team