How do you simplify a fraction?

Divide the numerator and the denominator by their greatest common divisor. For 24/36 that divisor is 12, and dividing both gives 2/3. Dividing by any smaller common divisor, such as 6, gives 4/6 — a step in the right direction that still needs reducing again.

How do I know when a fraction is in lowest terms?

When the only number that divides both parts is 1. The panel says this directly: a divisor of 1 means nothing could be cancelled, so the reduced fraction is printed exactly as the input was. 7/4 and 1/2 are both of that kind, which is why the divisor line exists rather than the answer line alone.

Can the answer be an improper fraction?

Yes. 100/75 reduces to 4/3, which is greater than one, and the page prints it as 4/3 rather than as a mixed number. Reducing does not make a fraction proper or improper, and turning 4/3 into a whole number beside a fraction is a different notation handled by the mixed number page.

What does the decimal line add?

The same number in the form most tools and spreadsheets want. It is shown to six places, so for a fraction such as 2/3, whose decimal never terminates, those places are rounded — 0.666667 rather than the true repeating value. Whether a fraction terminates at all is answered on the fraction to decimal page.

Can I simplify a ratio such as 6 : 4 here?

No. A ratio is reduced with the same divisor but it is a different notation with a different answer shape — 3 : 2 rather than 3/2 — and ratios can carry units where fractions cannot. Enter it on the ratio page instead; this page takes one fraction.

What happens with a negative or zero numerator?

A negative numerator keeps its sign: -18/24 reduces to -3/4, with the divisor reported as 6 rather than -6, since the greatest common divisor is taken between the two magnitudes. A numerator of zero reduces to a bare 0, and the divisor is then the denominator — 50 for 0/50, because 50 is what both parts were divided by.

Simplify Fractions Calculator

Result

2/3

Fraction in lowest terms

Greatest common divisor: 12
As a decimal: 0.666667

A simplify fractions calculator reduces a fraction to lowest terms and, unlike almost every other one, tells you which number it divided by to get there. 24/36 becomes 2/3, and the divisor behind that is 12 — the largest number that divides both 24 and 36. That second reading is the whole point of the page, because the reduced fraction alone cannot tell you whether anything happened: 7/4 and 1/2 are already in lowest terms, and their main reading is identical to the input, so a panel that showed only the answer would look the same whether it had done the work or not. Here the divisor line gives it away, printing 1 for a fraction that was already as simple as it gets. A third reading gives the same number as a decimal, six places deep, which is the form a fraction usually has to become before it can be used in a spreadsheet or compared against a measurement — and for fractions that do not divide evenly those six places are rounded, not exact. The page simplifies and does nothing else: it does not add, subtract, multiply or divide fractions, it does not turn a decimal back into a fraction, and it does not reduce a ratio such as 6 : 4, which is a different notation with a different answer shape.

Eight fractions reduced, with the divisor used

Fraction	Divisor	Lowest terms	Decimal
24/36	12	2/3	0.666667
100/75	25	4/3	1.333333
7/4	1	7/4	1.75
1/2	1	1/2	0.5
0/50	50	0	0
18/24	6	3/4	0.75
9/12	3	3/4	0.75
100000/100000	100000	1	1

Each row is one reduction, and the columns are the input, the greatest common divisor that was divided out, the answer in lowest terms, and the same number as a decimal. The first column always shows the fraction as it was entered, never the reduced form — printing the reduced form there would make the column useless, since rows six and seven would then be identical to each other, and rows three and four would look as though nothing had happened. That is the pair worth looking at first: 18/24 and 9/12 both reduce to 3/4, and the divisors behind them are 6 and 3, so the two rows are identical in the third and fourth columns and different in the second. Those two rows are the argument for printing the divisor at all. Row one is the default case, which reduces a long way. Row two stays improper, at 4/3. Rows three and four cannot be reduced at all and report a divisor of 1, one of them greater than one and one of them less, since being in lowest terms has nothing to do with size. Row five has a zero numerator and reports the denominator as the divisor. Row eight is a fraction of a hundred thousand over itself, which reduces to a bare 1 with a divisor at the top of the field's range, and it is the one row where the decimal column and the answer agree on being exactly 1.

Formula

d = gcd(n, D) n/D = (n ÷ d) / (D ÷ d) decimal = n ÷ D, rounded to six places

Numerator: The top of the fraction: 24 in 24/36. It may be negative or zero. A negative numerator keeps its sign through the division — -18/24 comes out as -3/4 — because the fraction carries its sign on top and never on the bottom.
Denominator: The bottom of the fraction: 36 in 24/36. It must be positive and it cannot be zero, since the fraction would not exist. It is capped at 100000, which is a limit on how large the two numbers may be rather than a rule about fractions.
Divisor (d): The greatest common divisor of the two numbers: 12 for 24 and 36, 6 for 18 and 24, and 1 for a fraction that cannot be reduced at all. This is the reading this page adds to the ones every other fraction tool gives, and it answers two questions at once — how much was cancelled, and whether anything was cancelable in the first place. When the numerator is zero the divisor is the denominator, which is what was actually divided out to turn 0/50 into 0.
Simplified fraction: The result of dividing both numbers by the divisor: 2/3 for 24/36. It is printed in lowest terms by construction, and it can be an improper fraction — 100/75 reduces to 4/3 and stays as 4/3 rather than becoming a mixed number, because that is a different notation handled on a different page.
Decimal: The same number written in decimal: 0.666667 for 2/3. It is rounded to six places, so it is an approximation whenever the division does not come out evenly; 2/3 differs from the true value by about 3.3 × 10⁻⁷. The page shows the six places because the decimal is a useful second reading of the same quantity, not because it is claiming precision — a fraction whose decimal repeats for ever is what the fraction to decimal page explains.

The first use is the exercise: simplifying is taught as soon as factors are, and the divisor is the step that gets marked, which is why this page prints it rather than hiding it. The second is checking a reduction done by hand — if your divisor is not the one on the panel, one of the two fractions is not the other. The third is a fraction already in lowest terms, where the panel says so with a divisor of 1 instead of leaving you to compare the answer against the input. The fourth is a fraction whose reduced form is an improper fraction, such as 100/75, where the answer stays as 4/3 and the decimal above 1 makes it obvious nothing was lost. The fifth is a decimal you already have, where reading the third line tells you what the fraction is worth without doing the long division yourself.

Worked examples

24/36
1. Find the greatest common divisor of 24 and 36: both divide by 2, 3, 4, 6 and 12, and the largest is 12
2. Divide the numerator: 24 ÷ 12 = 2
3. Divide the denominator: 36 ÷ 12 = 3
4. The reduced fraction is 2/3, and 2 and 3 share no factor other than 1
5. As a decimal: 2 ÷ 3 = 0.666666…, which is 0.666667 to six places
The default case: a fraction that reduces a long way and lands on a genuinely simpler pair. The divisor is 12, and it is worth noticing that 6 would have got part of the way — 24/36 to 4/6 — without finishing, which is why the greatest common divisor is the one the page reports rather than any common divisor. The decimal is rounded: 2/3 is 0.666666… and never terminates, so the six places shown differ from the true value in the seventh. That is a display decision, and the page that explains when a fraction terminates is a different one.
100/75
1. Find the greatest common divisor of 100 and 75: both divide by 25
2. Divide the numerator: 100 ÷ 25 = 4
3. Divide the denominator: 75 ÷ 25 = 3
4. The reduced fraction is 4/3, which is greater than 1
An improper fraction, which this page prints as it is: 4/3, not 1 1/3. Reducing does not change whether a fraction is improper, and turning it into a whole number beside a fraction is the mixed number page's job — doing it here would mean one panel with two different notations on it. Note that the decimal reading is the quickest way to see the size of the answer: 1.333333 says the quantity is a third above one, which 4/3 also says and rather less immediately.
7/4
1. Find the greatest common divisor of 7 and 4: 7 is prime and is not a factor of 4, so the only common divisor is 1
2. Dividing by 1 leaves both numbers as they were
3. The reduced fraction is 7/4, identical to the input
4. As a decimal: 7 ÷ 4 = 1.75 exactly
Already in lowest terms, and the case that shows why the divisor is on the panel at all. The main reading is the input written back — 7/4 becomes 7/4 — so the answer alone cannot tell you whether the page did anything. The divisor line says 1, which is the page reporting that it looked and found nothing to do. A reading of 1 is information here rather than a failure; a reading of 0 would be a bug, since dividing by zero is not a reduction.
0/50
1. Find the greatest common divisor of 0 and 50: every number divides 0, so the greatest common divisor is 50, the other number
2. Divide both: 0 ÷ 50 = 0 and 50 ÷ 50 = 1
3. The reduced fraction is 0/1, which is written as a bare 0 because a denominator of 1 is not written
4. As a decimal: 0
A zero numerator reduces all the way to nothing, and the divisor is 50 rather than 1 — because 50 is what both numbers were actually divided by to get there. That is the same definition as everywhere else on the page: the divisor is what was cancelled, not what could have been. The main reading prints as a bare 0 with no denominator, the same convention the fraction notation uses for any whole number.
-18/24
1. Find the greatest common divisor of 18 and 24: both divide by 6
2. Divide both numbers by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, so the fraction is -3/4
3. The sign stays on the numerator and the denominator stays positive
4. As a decimal: -3 ÷ 4 = -0.75
The case that pins down where the sign lives. The divisor is 6 and not -6: the greatest common divisor is taken between the two magnitudes, so it is always positive, and the minus sign is not part of it. The reduced fraction carries the sign on the numerator only, so -18/24 is -3/4 and never 3/-4. The decimal reading keeps the sign too, which is a cheap way to confirm that the reduction did not drop it.

Limitations

The denominator must be positive and cannot be zero — a fraction with a zero denominator does not exist, and the page refuses it rather than returning something. The numerator may be negative, and may be zero: 0/50 reduces to a bare 0. Both numbers must be whole numbers, and the denominator is capped at 100000; the numerator has no cap beyond the point where the arithmetic stops being exact, and a decimal numerator is rejected. The divisor the page reports is the greatest common divisor, which is the reduction that finishes the job, and not the first common divisor that comes to mind — for 24/36 that is 12, and 6 would leave 4/6 still reducible. The six decimal places are a display width, not a promise: for a fraction whose decimal repeats they are rounded, and this page does not say whether they are or not, or how long the repeating part is. If that matters, the fraction to decimal page is where the question is answered. The page simplifies one fraction and does nothing else: it does not add, subtract, multiply or divide fractions, it does not convert a decimal into a fraction, and it does not reduce a ratio such as 6 : 4. That last one looks like the same operation and is not: the same divisor is used, but the answer is written as a ratio and ratios can carry units, whereas a fraction cannot. The reduced fraction is not converted into a mixed number either, so a result greater than one stays improper.

Frequently asked questions

How do you simplify a fraction?: Divide the numerator and the denominator by their greatest common divisor. For 24/36 that divisor is 12, and dividing both gives 2/3. Dividing by any smaller common divisor, such as 6, gives 4/6 — a step in the right direction that still needs reducing again.
How do I know when a fraction is in lowest terms?: When the only number that divides both parts is 1. The panel says this directly: a divisor of 1 means nothing could be cancelled, so the reduced fraction is printed exactly as the input was. 7/4 and 1/2 are both of that kind, which is why the divisor line exists rather than the answer line alone.
Can the answer be an improper fraction?: Yes. 100/75 reduces to 4/3, which is greater than one, and the page prints it as 4/3 rather than as a mixed number. Reducing does not make a fraction proper or improper, and turning 4/3 into a whole number beside a fraction is a different notation handled by the mixed number page.
What does the decimal line add?: The same number in the form most tools and spreadsheets want. It is shown to six places, so for a fraction such as 2/3, whose decimal never terminates, those places are rounded — 0.666667 rather than the true repeating value. Whether a fraction terminates at all is answered on the fraction to decimal page.
Can I simplify a ratio such as 6 : 4 here?: No. A ratio is reduced with the same divisor but it is a different notation with a different answer shape — 3 : 2 rather than 3/2 — and ratios can carry units where fractions cannot. Enter it on the ratio page instead; this page takes one fraction.
What happens with a negative or zero numerator?: A negative numerator keeps its sign: -18/24 reduces to -3/4, with the divisor reported as 6 rather than -6, since the greatest common divisor is taken between the two magnitudes. A numerator of zero reduces to a bare 0, and the divisor is then the denominator — 50 for 0/50, because 50 is what both parts were divided by.

References

Reduced Fraction — the lowest terms of a fraction, which is the form this page returns and the form it checks the input against — Wolfram MathWorld (United States)
Greatest Common Divisor — the largest integer dividing two given integers, reported on this page as the divisor that was used — Wolfram MathWorld (United States)
Fraction — the quotient of two integers written with a numerator and a denominator, and the reading of the same number as a decimal — Wolfram MathWorld (United States)
Improper Fraction — a fraction whose numerator is at least its denominator, which a reduced fraction can be and which this page prints without converting — Wolfram MathWorld (United States)
Relatively Prime — two integers with no common factor greater than one, the condition under which the divisor is 1 and nothing can be reduced — Wolfram MathWorld (United States)

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