Fraction Calculator With Step-by-Step Working

Enter two fractions or mixed numbers and pick an operation to get the answer in lowest terms, as a mixed number and as a decimal, with the working shown.

Runs in your browserFree, no sign-upLast reviewed October 13, 2026

1 1/2 + 2/3

Simplified fraction: 13/6; improper fraction, lowest terms
Mixed number: 2 1/6; whole number and fraction
Decimal: 2.1(6); digits in brackets repeat forever
Percent: 216.(6)%; digits in brackets repeat
Before simplifying: 13/6; already in lowest terms

Working, step by step

Step	What to do	Working
1	Write the first number as a fraction	1 1/2 = (1 x 2 + 1)/2 = 3/2
2	Find the least common denominator	LCD of 2 and 3 = 2 x 3 ÷ GCD(2, 3) = 6 ÷ 1 = 6
3	Rewrite both fractions over the common denominator	3/2 = (3 x 3)/(2 x 3) = 9/6, and 2/3 = (2 x 2)/(3 x 2) = 4/6
4	Add the numerators	9/6 + 4/6 = (9 + 4)/6 = 13/6
5	Simplify	GCD(13, 6) = 1, so 13/6 is already in lowest terms
6	Convert to a mixed number	13 ÷ 6 = 2 remainder 1, so 13/6 = 2 1/6

Answer

1 1/2 + 2/3 = 13/6 = 2 1/6 = 2.1(6)

Quick answers

How do you add fractions with different denominators?: Find the least common denominator, rewrite both fractions over it, add the numerators and simplify. For 1/2 + 1/3 the common denominator is 6, so the sum is 3/6 + 2/6 = 5/6.
How do you subtract fractions?: Use the same common-denominator method as addition, then subtract the numerators. For 3/4 - 5/6 the common denominator is 12, giving 9/12 - 10/12 = -1/12. A negative result simply means the second fraction was larger.
How do you multiply fractions?: Multiply the numerators together and the denominators together, then simplify. 2/3 x 3/4 = 6/12, and dividing top and bottom by their greatest common divisor, 6, gives 1/2. No common denominator is needed.
How do you divide fractions?: Flip the second fraction and multiply. 1/2 ÷ 1/4 becomes 1/2 x 4/1 = 4/2 = 2. Dividing by a fraction smaller than 1 always gives an answer larger than the number you started with.
What is 1/2 plus 1/4?: 3/4, or 0.75. Rewrite 1/2 as 2/4 so both fractions share the denominator 4, then add the numerators: 2/4 + 1/4 = 3/4.
How do you add mixed numbers?: Turn each mixed number into an improper fraction, then add as usual. 1 3/4 + 2 5/8 becomes 7/4 + 21/8 = 14/8 + 21/8 = 35/8, which is 4 3/8 as a mixed number.

How Fraction Calculator works

This fraction calculator adds, subtracts, multiplies or divides two fractions and shows how the answer was reached. Type each value as a fraction (3/4), a mixed number with a space (1 1/2), a whole number or a decimal. The result appears as a simplified fraction, a mixed number, a decimal and a percent, followed by a numbered table of steps: the least common denominator, the rewritten fractions, the greatest common divisor used to simplify, and the conversion to a mixed number. With the starting values, 1 1/2 + 2/3 = 13/6 = 2 1/6. All arithmetic is done on whole numbers, so the fraction is exact rather than rounded.

The rule for each operation

a/b + c/d = (a x d + c x b)/(b x d). a/b - c/d = (a x d - c x b)/(b x d). a/b x c/d = (a x c)/(b x d). a/b ÷ c/d = (a x d)/(b x c).

The addition and subtraction rules always work, but they can produce large numbers that then need reducing. The calculator uses the least common denominator instead: LCD = b x d ÷ GCD(b, d). For 3/4 and 5/6 that is 4 x 6 ÷ 2 = 12 rather than 24. After the operation it divides the numerator and denominator by their greatest common divisor to reach lowest terms. A mixed number w n/d is first rewritten as (w x d + n)/d, so 3 3/4 becomes 15/4.

Worked examples with the full steps

Each result below is the calculator's own output for the inputs shown.

Adding a mixed number and a fraction

First fraction 1 1/2; Operation + Add; Second fraction 2/3

13/6 = 2 1/6 = 2.1(6). Steps: 1 1/2 = 3/2; LCD of 2 and 3 = 6; 3/2 = 9/6 and 2/3 = 4/6; 9/6 + 4/6 = 13/6; GCD(13, 6) = 1; 13 ÷ 6 = 2 remainder 1.

Subtracting mixed numbers

First fraction 3 3/4; Operation - Subtract; Second fraction 1 7/8

15/8 = 1 7/8 = 1.875. Steps: 15/4 - 15/8, LCD 8, 30/8 - 15/8 = 15/8.

Multiplying mixed numbers

First fraction 2 1/2; Operation x Multiply; Second fraction 1 1/3

10/3 = 3 1/3 = 3.(3). Steps: 5/2 x 4/3 = 20/6; GCD(20, 6) = 2, so 20/6 = 10/3.

Dividing a whole number by a negative fraction

First fraction 5; Operation ÷ Divide; Second fraction -2/3

-15/2 = -7 1/2 = -7.5. Steps: 5 = 5/1; -2/3 flips to -3/2; 5/1 x (-3/2) = -15/2.

A negative mixed number

First fraction -2 1/3; Operation + Add; Second fraction 1/6

-13/6 = -2 1/6 = -2.1(6). Steps: -2 1/3 = -7/3 = -14/6; -14/6 + 1/6 = -13/6.

The minus sign applies to the whole mixed number: -2 1/3 means -(2 + 1/3).

Simplifying a single fraction

First fraction 12/16; Operation + Add; Second fraction 0

3/4 = 0.75. Adding 0 leaves the value unchanged, and the Simplify step divides top and bottom by GCD(12, 16) = 4.

Common fraction sums, differences, products and quotients

Answers people look up most often, each produced by the calculator.

Problem	Answer	Mixed number	Decimal
1/2 + 1/4	3/4	3/4	0.75
1/2 + 1/3	5/6	5/6	0.8(3)
1/3 + 1/4	7/12	7/12	0.58(3)
1/3 + 1/3	2/3	2/3	0.(6)
2/3 + 3/4	17/12	1 5/12	1.41(6)
1/8 + 3/16	5/16	5/16	0.3125
1 3/4 + 2 5/8	35/8	4 3/8	4.375
1/2 - 1/3	1/6	1/6	0.1(6)
7/8 - 1/4	5/8	5/8	0.625
5/6 - 1/3	1/2	1/2	0.5
1/2 x 1/2	1/4	1/4	0.25
2/3 x 3/4	1/2	1/2	0.5
3/5 x 5/9	1/3	1/3	0.(3)
2/3 x 6	4	4	4
3/4 ÷ 1/2	3/2	1 1/2	1.5
4 ÷ 2/3	6	6	6
9/10 ÷ 3/5	3/2	1 1/2	1.5

Digits in brackets repeat forever: 0.8(3) means 0.8333...

Ways to type a fraction

Both boxes accept the same formats.

A simple fraction with a slash: 3/4.
A mixed number with a space between the whole number and the fraction: 1 1/2. A hyphen also works: 1-1/2.
A negative value with a leading minus sign: -3/4 or -2 1/3.
A whole number: 5 is read as 5/1.
A terminating decimal: 0.75 is read as 75/100 and simplified with the rest of the working.
An unsimplified or improper fraction: 12/16 and 9/4 are accepted as they are.

Reading the decimal, the percent and the limits

The decimal is worked out by long division on the exact fraction. If it ends, every digit is shown: 15/8 is 1.875. If it repeats, the repeating block is put in brackets, so 13/6 is written 2.1(6) and 20/91 is written 0.(219780). When the repeating block is longer than 40 digits the decimal is rounded to 12 places and marked as rounded; 1/97 is shown as 0.010309278351. The fraction and mixed number are never rounded.

The Before simplifying figure is the raw result of the operation, such as 6/12 for 2/3 x 3/4, with a note saying what it was divided by.

The calculator works on two values at a time. For a longer sum such as 1/2 + 1/3 + 1/4, calculate the first pair, then type that answer (5/6) as the first fraction and add the third. It does not accept expressions with brackets, exponents or more than one operation in a box, and each number is limited to 30 digits. A denominator of 0, or dividing by a fraction equal to 0, gives an error because neither has a defined value.

How to use it

1
Type the First fraction, for example 3/4, 1 1/2 or -2/5.
2
Choose the Operation: + Add, - Subtract, x Multiply or ÷ Divide.
3
Type the Second fraction in the same way.
4
Read the Simplified fraction, Mixed number, Decimal and Percent in the result panel.
5
Follow the Working, step by step table to see the common denominator and the GCD used, then copy the Answer line if you need it.

Answers to common questions

How do I simplify a fraction to lowest terms?

Divide the numerator and the denominator by their greatest common divisor. For 12/16 the GCD is 4, so it reduces to 3/4. To do this here, enter the fraction, choose + Add and put 0 in the second box.

What is the difference between an improper fraction and a mixed number?

They are two ways to write the same value greater than 1. An improper fraction has a numerator larger than its denominator, such as 13/6. A mixed number splits it into a whole part and a remainder, 2 1/6. The calculator shows both.

Why do I need a common denominator to add but not to multiply?

Adding counts pieces, and pieces can only be counted together when they are the same size, which is what a shared denominator guarantees. Multiplying takes a fraction of a fraction, so the pieces are cut again and the denominators multiply instead.

What does GCD mean in the working?

Greatest common divisor: the largest whole number that divides both numbers exactly. It is also called the greatest common factor (GCF) or highest common factor (HCF). The calculator uses it twice, to find the least common denominator and to simplify the answer.

Can the answer be negative?

Yes. 3/4 - 5/6 gives -1/12, and the sign is carried through the mixed number and decimal as well. Two negative fractions multiplied or divided give a positive result, so -3/4 ÷ -1/2 = 3/2.

How do I turn the answer into a decimal by hand?

Divide the numerator by the denominator. 5/8 is 5 ÷ 8 = 0.625. If the denominator has prime factors other than 2 and 5, the decimal repeats instead of ending, which is why 5/6 becomes 0.8(3).

Does it work with three or more fractions?

Not in one go. Work through the fractions two at a time, carrying each answer into the first box. For 1/2 + 1/3 + 1/4, the first pair gives 5/6, and 5/6 + 1/4 gives 13/12, or 1 1/12.