Fraction Calculator With Steps

Steps

1Write every number as a fraction
$\left(\frac{1}{2} + \frac{1}{3}\right) \times \frac{3}{5} - 1\tfrac{1}{2}$
$\left(\frac{1}{2} + \frac{1}{3}\right) \times \frac{3}{5} - \frac{3}{2}$
1 1/2 = (1 × 2 + 1)/2 = 3/2.
2Add
$\frac{1}{2} + \frac{1}{3}$
$\frac{1}{2}+\frac{1}{3}=\frac{1\cdot 3}{2\cdot 3}+\frac{1\cdot 2}{3\cdot 2}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$
The least common denominator of 2 and 3 is 6. The expression is now 5/6 × 3/5 − 3/2.
3Multiply
$\frac{5}{6} \times \frac{3}{5}$
$\frac{5}{6}\times \frac{3}{5}=\frac{5\cdot 3}{6\cdot 5}=\frac{15}{30}=\frac{1}{2}$
Multiply the numerators and the denominators. The expression is now 1/2 − 3/2.
4Subtract
$\frac{1}{2} - \frac{3}{2}$
$\frac{1}{2}-\frac{3}{2}=\frac{1}{2}-\frac{3}{2}=\frac{-2}{2}=-1$
The denominators match, so only the numerators combine.

About Fraction Calculator

This fraction calculator is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded. It does exact arithmetic on fractions, mixed numbers, negatives and decimals, and it writes out the steps so you can see where the answer came from.

Type fractions the way you would on paper: 3/4, -2/5, 1 1/2 for a mixed number, 0.75 for a decimal, or 0.(3) and 0.1(6) for a repeating decimal. Expressions can have three or more terms and brackets, such as (1/2 + 1/3) × 3/5 − 1 1/2, and the working is typeset as stacked fractions. The result is shown as a reduced fraction, a mixed number, a decimal and a percent. A decimal that never ends is shown with a bar over its repeating block, so 1/3 reads 0.3 with a bar over the 3 rather than a rounded 0.333333.

Because the numbers are stored as exact whole-number ratios, there is no rounding error in the working. That matters for long chains of operations, where a calculator that uses floating point can drift. Here 1/3 + 1/3 + 1/3 is exactly 1.

How to use Fraction Calculator

Choose a mode: Calculate, Simplify, Compare, Decimal to fraction, Fraction to decimal, Improper to mixed or Fraction to percent.
In Calculate mode type one expression with +, −, × and ÷ and as many brackets as you need. Mixed numbers are written with a space, such as 2 1/2, and repeating decimals as 0.(3).
Read the result as a reduced fraction, a mixed number, a decimal and a percent.
The tool opens on a worked example. Read the steps to see each operation done in the order brackets and precedence require.
For an improper result, a second panel shows how to convert it to a mixed number.

Features

Exact rational arithmetic with no floating-point error, using whole-number numerators and denominators of any size.
Expressions with any number of terms, brackets, mixed numbers, negative fractions, decimals and repeating decimals such as 0.(3) and 0.1(6).
Results shown as a fraction, a mixed number, a decimal and a percent together.
Repeating decimals shown exactly with a bar over the repeating block, for example 1/7 = 0.142857 repeating, and accepted as input.
Step-by-step working in typeset math: converting each number to a fraction, then each operation in order with its least common denominator or reciprocal and the simplification.
Compare mode that shows both fractions over a common denominator and as decimals.
Decimal to fraction, fraction to decimal, improper to mixed number and fraction to percent conversions.
Clear messages for a zero denominator or division by zero.

How each operation works

Adding and subtracting need a common denominator, and the calculator uses the least common multiple of the two denominators so the numbers stay small. Multiplying works straight across. Dividing multiplies by the reciprocal of the second fraction. After each operation the result is divided through by the greatest common divisor, which puts it in lowest terms.

a/b + c/d = (a×d + c×b) / (b×d), over the LCD
a/b × c/d = (a×c) / (b×d)
a/b ÷ c/d = (a×d) / (b×c)
simplify: divide top and bottom by gcd(top, bottom)

Worked examples

1/2 + 1/3 gives 5/6
The LCD of 2 and 3 is 6. Rewrite as 3/6 + 2/6 = 5/6. The GCD of 5 and 6 is 1, so it is already simplified.
3/4 ÷ 2/5 gives 15/8 = 1 7/8 = 1.875
Multiply by the reciprocal: 3/4 × 5/2 = 15/8. 15 ÷ 8 is 1 remainder 7, so the mixed number is 1 7/8.
5/6 as a decimal gives 0.8(3)
Dividing 5 by 6 gives 0.8333 with the 3 repeating forever, written 0.8(3).

Common fractions as decimals and percents

Fraction	Decimal	Percent
1/2	0.5	50%
1/3	0.(3)	33.(3)%
2/3	0.(6)	66.(6)%
1/4	0.25	25%
3/4	0.75	75%
1/5	0.2	20%
1/6	0.1(6)	16.(6)%
1/8	0.125	12.5%
3/8	0.375	37.5%
7/8	0.875	87.5%
1/7	0.(142857)	14.(285714)%

Good to know

Why some fractions repeat

A fraction in lowest terms ends as a decimal only if its denominator has no prime factors other than 2 and 5. So 3/8 (8 = 2 × 2 × 2) ends at 0.375, while 1/3, 1/6 and 1/7 repeat. The length of the repeating block is at most one less than the denominator, which is why 1/7 repeats six digits and 3/11 only two, as 0.(27).

Mixed numbers and improper fractions

A mixed number such as 2 1/2 is a whole number plus a proper fraction, equal to the improper fraction 5/2. The calculator converts mixed input to an improper fraction before doing any arithmetic, then shows the result as a mixed number as well. For a negative mixed number, the minus sign applies to the whole value: −3 2/3 is −11/3.

Privacy: how it works

The fractions you enter are processed by code running in your browser tab. Nothing is sent to Ulkaa or anyone else, and there is nothing to sign in to.

Tips

Write a mixed number with a single space between the whole part and the fraction, as in 1 3/4.
A decimal such as 0.75 is accepted as an input anywhere a fraction is.
If you want a rounded decimal for a calculation by hand, read it from the repeating form and cut it where you need.
To check an answer, the Compare mode shows two fractions over one denominator, which is the same test teachers use.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your fractions are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your fractions are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

How do I add fractions with different denominators?

Find a common denominator, rewrite both fractions over it, add the numerators, keep the denominator and simplify. For 1/2 + 1/3 the common denominator is 6, so 3/6 + 2/6 = 5/6.

How do I simplify a fraction?

Find the greatest common divisor of the numerator and the denominator and divide both by it. For 12/18 the GCD is 6, so it simplifies to 2/3.

How do I convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient is the whole part and the remainder goes over the denominator. 17/5 is 3 remainder 2, so 3 2/5.

How do I turn a decimal into a fraction?

Write the decimal over a power of ten with as many zeros as it has decimal places, then simplify. 0.75 is 75/100, which is 3/4.

How do I divide fractions?

Flip the second fraction and multiply. 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8.

What do the brackets in a decimal mean?

The digits in parentheses repeat forever. 0.8(3) is 0.8333 and so on, and 0.(142857) is 0.142857142857 and so on.

Can it handle very large numerators or denominators?

Yes. Numerators and denominators are stored as exact whole numbers, so they are not limited to the size of an ordinary calculator display.

Steps

1Write every number as a fraction
$\left(\frac{1}{2} + \frac{1}{3}\right) \times \frac{3}{5} - 1\tfrac{1}{2}$
$\left(\frac{1}{2} + \frac{1}{3}\right) \times \frac{3}{5} - \frac{3}{2}$
1 1/2 = (1 × 2 + 1)/2 = 3/2.
2Add
$\frac{1}{2} + \frac{1}{3}$
$\frac{1}{2}+\frac{1}{3}=\frac{1\cdot 3}{2\cdot 3}+\frac{1\cdot 2}{3\cdot 2}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$
The least common denominator of 2 and 3 is 6. The expression is now 5/6 × 3/5 − 3/2.
3Multiply
$\frac{5}{6} \times \frac{3}{5}$
$\frac{5}{6}\times \frac{3}{5}=\frac{5\cdot 3}{6\cdot 5}=\frac{15}{30}=\frac{1}{2}$
Multiply the numerators and the denominators. The expression is now 1/2 − 3/2.
4Subtract
$\frac{1}{2} - \frac{3}{2}$
$\frac{1}{2}-\frac{3}{2}=\frac{1}{2}-\frac{3}{2}=\frac{-2}{2}=-1$
The denominators match, so only the numerators combine.

About Fraction Calculator

Fraction

Decimal

Percent

1/2

0.5

50%

1/3

0.(3)

33.(3)%

2/3

0.(6)

66.(6)%

1/4

0.25

25%

3/4

0.75

75%

1/5

0.2

20%

1/6

0.1(6)

16.(6)%

1/8

0.125

12.5%

3/8

0.375

37.5%

7/8

0.875

87.5%

1/7

0.(142857)

14.(285714)%

Fraction Calculator

Result

Steps

About Fraction Calculator

How to use Fraction Calculator

Features

How each operation works

Worked examples

Common fractions as decimals and percents

Good to know

Why some fractions repeat

Mixed numbers and improper fractions

Privacy: how it works

Tips

Frequently asked questions

Is it really free?

Do I need an account?

Does it run in my browser?

Is my data uploaded?

How do I add fractions with different denominators?

How do I simplify a fraction?

How do I convert an improper fraction to a mixed number?

How do I turn a decimal into a fraction?

How do I divide fractions?

What do the brackets in a decimal mean?

Can it handle very large numerators or denominators?

Popular Fraction Calculator pages

Fraction Calculator

Result

Steps

About Fraction Calculator

How to use Fraction Calculator

Features

How each operation works

Worked examples

Common fractions as decimals and percents

Good to know

Why some fractions repeat

Mixed numbers and improper fractions

Privacy: how it works

Tips

Frequently asked questions

Is it really free?

Do I need an account?

Does it run in my browser?

Is my data uploaded?

How do I add fractions with different denominators?

How do I simplify a fraction?

How do I convert an improper fraction to a mixed number?

How do I turn a decimal into a fraction?

How do I divide fractions?

What do the brackets in a decimal mean?

Can it handle very large numerators or denominators?

Popular Fraction Calculator pages