A Fraction Calculator adds, subtracts, multiplies, or divides two fractions and simplifies the answer to lowest terms.

Fractions are useful when an exact ratio matters. Unlike a rounded decimal, a fraction such as:

1/3

keeps the exact relationship between numerator and denominator instead of approximating it as:

0.3333…

This makes fraction arithmetic useful for measurements, recipes, ratios, algebra, classroom exercises, and everyday calculations.

Enter the numerator and denominator of each fraction, choose the operation, and review the simplified result.

Understand the two parts of a fraction

A fraction such as:

3/5

contains:

3 — numerator

and:

5 — denominator

The numerator tells you how many parts are being considered.

The denominator tells you how many equal parts make one whole.

So:

3/5

means three out of five equal parts.

The denominator can never be zero.

How to use the Fraction Calculator

1. Enter the numerator of the first fraction.
2. Enter its denominator.
3. Choose addition, subtraction, multiplication, or division.
4. Enter the numerator and denominator of the second fraction.
5. Calculate the result.
6. Review the simplified fraction.
7. Convert an improper fraction to a mixed number when useful.

Keep negative signs clear and never enter zero as a denominator.

The four fraction operations

Operation	General rule
Addition	a/b + c/d = (ad + bc)/bd
Subtraction	a/b − c/d = (ad − bc)/bd
Multiplication	a/b × c/d = ac/bd
Division	a/b ÷ c/d = ad/bc

Addition and subtraction require compatible denominators.

Multiplication works directly across the numerators and denominators.

Division works by multiplying by the reciprocal of the second fraction.

The final result should then be simplified when possible.

Adding fractions

Fractions need a common denominator before their numerators can be added.

Consider:

2/3 + 1/4

The denominators are:

3 and 4

A common denominator is:

12

Convert each fraction:

2/3 = 8/12

and:

1/4 = 3/12

Now add:

8/12 + 3/12 = 11/12

So:

2/3 + 1/4 = 11/12

Why the addition formula works

For:

a/b + c/d

a common denominator can be created by multiplying the denominators:

bd

Convert the first fraction:

a/b × d/d = ad/bd

Convert the second:

c/d × b/b = bc/bd

Because:

d/d = 1

and:

b/b = 1

the values of the original fractions have not changed.

Now the denominators match:

ad/bd + bc/bd

So:

a/b + c/d = (ad + bc)/bd

The calculator performs this process automatically.

Using the least common denominator

Multiplying the denominators always creates a common denominator, but it may not be the smallest one.

Consider:

1/6 + 1/8

Multiplying:

6 × 8 = 48

would work.

But the least common denominator is:

24

So:

1/6 = 4/24

and:

1/8 = 3/24

Then:

4/24 + 3/24 = 7/24

Using the least common denominator often keeps intermediate numbers easier to work with.

Do not add the denominators

A common mistake is:

1/3 + 1/4 = 2/7

That is incorrect.

Thirds and fourths represent differently sized pieces.

First convert them into equal-sized parts:

1/3 = 4/12

1/4 = 3/12

Then:

4/12 + 3/12 = 7/12

So:

1/3 + 1/4 = 7/12

Subtracting fractions

Subtraction follows the same common-denominator principle.

Consider:

5/6 − 1/4

A common denominator is:

12

Convert:

5/6 = 10/12

and:

1/4 = 3/12

Now subtract:

10/12 − 3/12 = 7/12

Therefore:

5/6 − 1/4 = 7/12

Once the denominators match, subtract only the numerators.

Multiplying fractions

Fraction multiplication is more direct.

Use:

a/b × c/d = ac/bd

For example:

2/3 × 5/7

Multiply the numerators:

2 × 5 = 10

Multiply the denominators:

3 × 7 = 21

So:

2/3 × 5/7 = 10/21

No common denominator is required.

Reduce before multiplying when possible

Cross-cancellation can make multiplication easier.

Consider:

14/15 × 25/28

Before multiplying, simplify common factors between numerators and denominators.

Reduce:

14 and 28

by 14:

14 ÷ 14 = 1

28 ÷ 14 = 2

Then reduce:

25 and 15

by 5:

25 ÷ 5 = 5

15 ÷ 5 = 3

The multiplication becomes:

1/3 × 5/2

Now:

1 × 5 = 5

and:

3 × 2 = 6

So:

14/15 × 25/28 = 5/6

This gives the same answer as multiplying first and simplifying afterward, but the intermediate numbers stay smaller.

Cancellation does not work across addition

Cancellation is valid between factors in multiplication.

It is not valid across terms separated by addition or subtraction.

For example:

2/3 + 3/5

you cannot cancel the two 3s.

Instead:

2/3 = 10/15

and:

3/5 = 9/15

Then:

10/15 + 9/15 = 19/15

Dividing fractions

To divide fractions, multiply by the reciprocal of the second fraction.

For example:

2/3 ÷ 4/5

The reciprocal of:

4/5

is:

5/4

So:

2/3 × 5/4

Multiply:

10/12

Simplify:

10/12 = 5/6

Therefore:

2/3 ÷ 4/5 = 5/6

A useful way to remember the process is:

Keep the first fraction, change division to multiplication, and invert the second fraction.

Do not invert the first fraction

For:

3/4 ÷ 2/5

the fraction being divided by is:

2/5

Its reciprocal is:

5/2

So:

3/4 × 5/2 = 15/8

Do not invert the first fraction or both fractions.

Check fraction division by multiplying back

Suppose:

2/3 ÷ 4/5 = 5/6

To check the result:

5/6 × 4/5

gives:

20/30

Reduce:

20/30 = 2/3

The original dividend is recovered.

That is a useful way to verify a division result.

Simplify fractions to lowest terms

A fraction is simplified when the numerator and denominator no longer share a factor greater than 1.

Consider:

18/24

The greatest common factor is:

6

Divide both values:

18 ÷ 6 = 3

24 ÷ 6 = 4

Therefore:

18/24 = 3/4

The numerical value stays the same.

Only the representation changes.

Using the greatest common factor

Consider:

42/56

The greatest common factor is:

14

Divide:

42 ÷ 14 = 3

56 ÷ 14 = 4

So:

42/56 = 3/4

The Fraction Calculator can perform this simplification automatically.

Improper fractions are valid

A fraction does not need to have a smaller numerator than denominator.

For example:

7/4

is a valid fraction.

It can also be written as:

1 3/4

Both forms represent the same value.

The improper form is often easier for calculations.

The mixed-number form may be easier to read in measurements, recipes, and everyday quantities.

Convert mixed numbers before calculating

Suppose you need:

2 1/3 + 1 3/4

Convert:

2 1/3

to an improper fraction:

2 × 3 + 1 = 7

So:

2 1/3 = 7/3

Then:

1 3/4 = 7/4

Now:

7/3 + 7/4

Use denominator 12:

28/12 + 21/12 = 49/12

Convert back if needed:

49/12 = 4 1/12

For calculations entered directly as mixed numbers, use the Mixed Number Calculator.

Whole numbers can be written as fractions

Any whole number can be written over:

1

For example:

5 = 5/1

Suppose you need:

5 + 2/3

Write:

5/1 + 2/3

Convert:

5/1 = 15/3

Then:

15/3 + 2/3 = 17/3

which can also be written:

5 2/3

Negative fractions

A negative fraction needs only one negative sign.

These expressions represent the same value:

−3/4

(−3)/4

and:

3/(−4)

But:

(−3)/(−4)

is positive:

3/4

For readability, the cleanest form is usually:

−3/4

Adding a negative fraction

Consider:

2/3 + (−1/4)

This is equivalent to:

2/3 − 1/4

Use denominator 12:

8/12 − 3/12 = 5/12

So:

2/3 + (−1/4) = 5/12

Subtracting a negative fraction

Consider:

3/5 − (−1/2)

Subtracting a negative becomes addition:

3/5 + 1/2

Use denominator 10:

6/10 + 5/10 = 11/10

or:

1 1/10

Parentheses make negative-fraction expressions easier to read.

A denominator cannot be zero

Fractions such as:

5/0

do not have an ordinary mathematical value.

Division by zero is undefined.

Likewise:

0/0

should not be treated as an ordinary fraction equal to zero.

The calculator should reject zero when it is entered as a denominator.

A zero numerator is allowed

A fraction such as:

0/7

is valid.

Its value is:

0

as long as the denominator is not zero.

Therefore:

0/7 = 0

Zero cannot be used as a fraction divisor

Consider:

3/4 ÷ 0/5

Because:

0/5 = 0

this becomes division by zero.

The operation is therefore undefined.

A fraction with a zero numerator is valid by itself, but it cannot be used as the divisor in fraction division.

Fractions preserve exact ratios

Consider:

1/7

Its decimal form is approximately:

0.142857142857…

The digits continue.

If you round it to:

0.143

some information is lost.

Keeping:

1/7

preserves the exact ratio.

That can be especially useful in:

• algebra;
• measurements;
• multi-step calculations;
• ratios; and
• probability.

An exact fraction does not make an approximate measurement exact

Suppose a measurement was recorded as:

12.3 inches

Writing it as:

123/10 inches

represents 12.3 exactly.

But the original measurement may still have been rounded.

Converting an approximate decimal to a fraction does not restore precision that was never measured.

This distinction matters in construction, manufacturing, science, and other measurement-based work.

Decimal estimates are useful for checking the answer

You can use decimals to check whether a fraction result has a reasonable size.

For example:

5/8 = 0.625

and:

3/4 = 0.75

So:

5/8 + 3/4

should be approximately:

0.625 + 0.75 = 1.375

The exact calculation is:

5/8 + 6/8 = 11/8

and:

11/8 = 1.375

The decimal check supports the exact result.

Estimate before trusting an unexpected fraction

Suppose:

1/2 + 1/3

Both fractions are positive.

The answer must be:

greater than 1/2

but:

less than 1

The result:

5/6 ≈ 0.8333

fits that expectation.

A result such as:

2/5 = 0.4

would immediately look too small.

Simple estimation can catch many entry and arithmetic errors.

Fractions in measurements

Fractional inches are common in construction and measurement work.

Consider:

2 3/8 in + 1 5/16 in

Convert:

3/8 = 6/16

Now:

2 6/16 + 1 5/16

Add:

3 11/16 in

The fraction arithmetic is exact, although real-world measuring tools and tolerances can still limit practical precision.

Convert measurement units before adding

Do not directly add:

1/2 ft + 3/4 in

because the units differ.

Convert:

1/2 ft = 6 in

Then:

6 in + 3/4 in = 6 3/4 in

The arithmetic becomes meaningful only after the units use the same measurement basis.

Fractions in recipes

Suppose a recipe requires:

3/4 cup

and you want to make half the recipe.

Calculate:

3/4 × 1/2 = 3/8

So you need:

3/8 cup

If you double the recipe:

3/4 × 2 = 6/4

Simplify:

6/4 = 3/2 = 1 1/2

So you need:

1 1/2 cups

Equivalent fractions have the same value

Fractions can look different while representing the same quantity.

For example:

1/2

2/4

3/6

and:

4/8

are equivalent.

To create an equivalent fraction, multiply numerator and denominator by the same nonzero number.

For example:

1/2 × 4/4 = 4/8

Because:

4/4 = 1

the fraction’s value does not change.

Simplification reverses the process

Consider:

12/18

Both values can be divided by:

6

So:

12 ÷ 6 = 2

and:

18 ÷ 6 = 3

Therefore:

12/18 = 2/3

Simplification makes the fraction easier to read without changing its value.

Compare the four operations

Using:

2/3

and:

1/4

gives:

Operation	Calculation	Result
Addition	2/3 + 1/4	11/12
Subtraction	2/3 − 1/4	5/12
Multiplication	2/3 × 1/4	1/6
Division	2/3 ÷ 1/4	8/3 or 2 2/3

This makes the different rules easier to compare.

Common fraction calculation mistakes to avoid

Adding denominators

For addition and subtraction, first create a common denominator.

Forgetting to invert the divisor

Fraction division uses the reciprocal of the second fraction.

Inverting both fractions

Only the divisor is inverted.

Cancelling across addition

Cancellation works between factors in multiplication, not across addition or subtraction.

Leaving the fraction unreduced

Simplify when the numerator and denominator still share a common factor.

Using zero as a denominator

A zero denominator is undefined.

Mixing measurement units

Convert the units before adding or subtracting fractions.

Converting to decimals too early

Keeping fractions through intermediate steps can preserve exact values.

When to use another calculator

Use the Mixed Number Calculator for values such as:

2 3/4

or:

5 1/8

Use the Scientific Calculator when fractions appear inside calculations involving:

• powers;
• roots;
• logarithms;
• trigonometry; or
• scientific notation.

For ordinary decimal arithmetic and percentages, use the Basic Calculator.

FAQ

How do I add fractions with different denominators?

Find a common denominator, rewrite both fractions, then add the numerators.

For example:

2/3 + 1/4 = 8/12 + 3/12 = 11/12

Do I add the denominators?

No.

Once the denominators are the same, keep that denominator and add or subtract the numerators.

How do I subtract fractions?

Find a common denominator and subtract the numerators.

For example:

5/6 − 1/4 = 10/12 − 3/12 = 7/12

How do I multiply fractions?

Multiply numerator by numerator and denominator by denominator:

a/b × c/d = ac/bd

Then simplify the result.

How do I divide fractions?

Multiply the first fraction by the reciprocal of the second:

a/b ÷ c/d = a/b × d/c

What is a reciprocal?

The reciprocal of:

a/b

is:

b/a

For example, the reciprocal of:

3/5

is:

5/3

What does simplifying a fraction mean?

It means dividing the numerator and denominator by common factors until no factor greater than 1 remains.

Should the answer always be a proper fraction?

No.

Improper fractions are valid.

For example:

7/4

can also be written:

1 3/4

Can negative fractions be simplified?

Yes.

For example:

−12/18 = −2/3

Can zero be the numerator?

Yes.

For example:

0/5 = 0

Can zero be the denominator?

No.

A denominator of zero makes the fraction undefined.

Why does the denominator sometimes become larger during addition?

Creating a common denominator can make intermediate values larger.

The final fraction may reduce after the calculation.

Is a fraction more accurate than a decimal?

A fraction can preserve an exact mathematical ratio when the inputs are exact.

But converting a rounded measurement to a fraction does not recover lost measurement precision.

Can fractions be used with measurements?

Yes.

Make sure the units are the same before adding or subtracting them.

Why can I cancel before multiplication but not addition?

Cancellation removes common factors.

Terms separated by addition or subtraction are not common factors of the whole expression.

Mathematics reference

For additional explanations and worked examples involving fractions, mixed numbers, factors, and arithmetic, see:

OpenStax — Prealgebra 2e

Keep the ratio exact until another form is needed

A Fraction Calculator is useful because it preserves exact ratios that may become repeating or rounded when converted to decimals.

Addition and subtraction require common denominators.

Multiplication works directly across numerators and denominators.

Division uses the reciprocal of the divisor.

Simplification then reduces the final result to its lowest terms.

When fractions represent measurements, recipes, or other real quantities, keep the correct unit with the result and remember that exact arithmetic cannot make an approximate input more precise.