How do you add fractions with different denominators?

First find a common denominator, the least common multiple of the two bottom numbers, and rewrite each fraction over it. Then add the numerators and keep the denominator. For 1/2 + 1/3 the common denominator is 6, so 3/6 + 2/6 = 5/6. For mixed numbers such as 2 3/8 + 1 5/16 the denominators 8 and 16 have the common denominator 16: 38/16 + 21/16 = 59/16, which is 3 11/16.

How do you subtract mixed numbers?

Turn each into an improper fraction, subtract over a common denominator and convert back. For 5 1/4 − 2 7/8: 21/4 − 23/8 = 42/8 − 23/8 = 19/8 = 2 3/8. Working with improper fractions means you never have to borrow.

How do you multiply fractions and mixed numbers?

Write mixed numbers as improper fractions, multiply the numerators and multiply the denominators, then simplify. 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 3 1/3. You do not need a common denominator to multiply.

How do you divide fractions?

Multiply by the reciprocal of the second fraction, which is that fraction turned upside down. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2. A whole number divides the same way, as a fraction over 1: 5 ÷ 2/3 = 5/1 × 3/2 = 15/2 = 7 1/2. Dividing by zero is not possible, and the calculator says so.

How do you simplify a fraction?

Divide the numerator and the denominator by their greatest common divisor (GCD). The GCD of 18 and 24 is 6, so 18/24 = 3/4, in lowest terms. Euclid’s algorithm finds the GCD by repeated division, and the calculator writes it out: 24 = 1 × 18 + 6, then 18 = 3 × 6 + 0, so the last non-zero remainder, 6, is the GCD.

How do you turn a fraction into a decimal?

Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. Some fractions never end: 1/3 = 0.(3) and 1/6 = 0.1(6), where the digits in parentheses repeat forever. A fraction in lowest terms ends exactly when its denominator has no prime factors except 2 and 5.

How do you turn a decimal into a fraction?

Write the digits after the point over a power of 10 with as many zeros, then simplify: 0.375 = 375/1000 = 3/8. For a repeating decimal, subtract it from a shifted copy of itself: with x = 0.(6), 10x − x = 6, so x = 6/9 = 2/3. Type 0.(3) with the repeating digits in parentheses and the calculator does this for you.

What do the brackets in 0.(3) mean?

The digits inside the parentheses repeat forever, so 0.(3) is 0.3333… and 1/6 = 0.1(6) is 0.1666…. A bar over the repeating digits means the same thing; parentheses are easier to type. The calculator also shows the value rounded to 4 places, marked ≈, for the times you need a plain number.

How do I type a mixed number?

Put a space between the whole number and the fraction: 2 3/8. A hyphen (2-3/8) and the fraction characters ½ ¼ ¾ also work, as do improper fractions such as 19/8 and decimals such as 2.375. A minus sign in front applies to the whole mixed number, so −2 3/8 is −19/8.

Can I use it for tape-measure fractions like 5/16 inch?

Yes. The marks on a tape are fractions with denominators 2, 4, 8, 16 and 32, so 2 3/8 + 1 5/16 = 3 11/16 works the same whether the numbers are inches or not. For lengths in feet, inches and metric, with the answer rounded to the nearest 1/16 inch, use the feet and inches calculator.

Are the answers exact, or rounded?

They are exact. Every number is kept as a fraction of two whole numbers of any size, so nothing is ever rounded, and 0.1 + 0.2 is exactly 3/10. The only rounded figure is the one labelled “Rounded to 4 places”. A decimal that repeats for longer than 48 digits is cut off with an ellipsis.

Fraction Calculator

To add fractions, give them a common denominator and add the numerators: 2 3/8 + 1 5/16 = 3 11/16 (59/16 as an improper fraction, 3.6875 as a decimal). Subtract the same way, multiply straight across, and divide by multiplying by the reciprocal: 3/4 ÷ 1/2 = 1 1/2. Simplify by dividing the top and bottom by their greatest common divisor: 18/24 = 3/4. A fraction as a decimal either ends, 3/8 = 0.375, or repeats, 1/3 = 0.(3), with the repeating digits in parentheses. Type mixed numbers as 2 3/8, fractions as 3/4 or decimals as 0.75; the calculator is exact and shows every step.

Updated 2026-09-29Runs in your browser: nothing you enter is uploadedHow this tool works

2 3/8 + 1 5/16 = 3 11/16

3 11/16

As an improper fraction 59/16, decimal 3.6875.

Fraction: 59/16
Mixed number: 3 11/16
Decimal: 3.6875
Percent: 368.75%
Reciprocal: 16/59

The working, step by step

Write each number as a fraction: 2 3/8 = (2 × 8 + 3)/8 = 19/8; 1 5/16 = (1 × 16 + 5)/16 = 21/16.
Find a common denominator: LCM(8, 16) = 8 × 16 ÷ 8 = 16.
19/8 = (19 × 2)/16 = 38/16.
21/16 already has the denominator 16.
Add the numerators and keep the denominator: 38 + 21 = 59, so 59/16.
Simplify: GCD(59, 16) = 1 (Euclid: 59 = 3 × 16 + 11, 16 = 1 × 11 + 5, 11 = 2 × 5 + 1, 5 = 5 × 1 + 0), so 59/16 is already in lowest terms.
As a mixed number: 59 ÷ 16 = 3 remainder 11, so 3 11/16.
As a decimal: 59/16 = 3.6875.

Worked examples

Each answer is in lowest terms, worked out by the calculator above; type any of these sums to see the steps.
Problem	Answer	Improper fraction	Decimal
1/2 + 1/3	5/6	5/6	0.8(3)
3/4 + 5/8	1 3/8	11/8	1.375
2 3/8 + 1 5/16	3 11/16	59/16	3.6875
3/4 − 1/6	7/12	7/12	0.58(3)
5 1/4 − 2 7/8	2 3/8	19/8	2.375
2/3 × 3/4	1/2	1/2	0.5
2 1/2 × 1 1/3	3 1/3	10/3	3.(3)
3/4 ÷ 1/2	1 1/2	3/2	1.5
5 ÷ 2/3	7 1/2	15/2	7.5
1 1/2 ÷ 3/8	4	4	4

Common fractions as decimals and percents

Divide the top by the bottom to get the decimal, and multiply by 100 for the percent. The digits in parentheses repeat forever.
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%
2/5	0.4	40%
3/5	0.6	60%
4/5	0.8	80%
1/6	0.1(6)	16.(6)%
5/6	0.8(3)	83.(3)%
1/7	0.(142857)	14.(285714)%
1/8	0.125	12.5%
3/8	0.375	37.5%
5/8	0.625	62.5%
7/8	0.875	87.5%
1/9	0.(1)	11.(1)%
1/10	0.1	10%
1/12	0.08(3)	8.(3)%
1/16	0.0625	6.25%
1/20	0.05	5%
1/32	0.03125	3.125%

Repeating decimals and their blocks

A fraction in lowest terms repeats when its denominator has a prime factor other than 2 and 5. The repeating block is never longer than the denominator minus one.
Fraction	Decimal	Repeating block	Block length
1/3	0.(3)	3	1
2/3	0.(6)	6	1
1/6	0.1(6)	6	1
5/6	0.8(3)	3	1
1/7	0.(142857)	142857	6
1/9	0.(1)	1	1
1/11	0.(09)	09	2
1/12	0.08(3)	3	1
1/13	0.(076923)	076923	6
1/15	0.0(6)	6	1

How to add, subtract, multiply and divide fractions by hand

Turn mixed numbers into improper fractions. Multiply the whole number by the denominator and add the numerator: 2 3/8 = (2 × 8 + 3)/8 = 19/8.
To add or subtract, find a common denominator. Use the least common multiple of the denominators and rewrite each fraction over it: 1/2 + 1/3 = 3/6 + 2/6. Then add or subtract the numerators and keep the denominator: 5/6.
To multiply, multiply straight across. Multiply the numerators, then the denominators: 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 3 1/3.
To divide, multiply by the reciprocal. Flip the second fraction and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2.
Simplify with the GCD. Divide the numerator and denominator by their greatest common divisor: the GCD of 18 and 24 is 6, so 18/24 = 3/4.
Convert between fractions and decimals. Divide the top by the bottom for the decimal: 3/8 = 0.375. To go back, write the decimal over a power of 10 and simplify: 0.375 = 3/8.

Frequently asked questions

How do you add fractions with different denominators?: First find a common denominator, the least common multiple of the two bottom numbers, and rewrite each fraction over it. Then add the numerators and keep the denominator. For 1/2 + 1/3 the common denominator is 6, so 3/6 + 2/6 = 5/6. For mixed numbers such as 2 3/8 + 1 5/16 the denominators 8 and 16 have the common denominator 16: 38/16 + 21/16 = 59/16, which is 3 11/16.
How do you subtract mixed numbers?: Turn each into an improper fraction, subtract over a common denominator and convert back. For 5 1/4 − 2 7/8: 21/4 − 23/8 = 42/8 − 23/8 = 19/8 = 2 3/8. Working with improper fractions means you never have to borrow.
How do you multiply fractions and mixed numbers?: Write mixed numbers as improper fractions, multiply the numerators and multiply the denominators, then simplify. 2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 3 1/3. You do not need a common denominator to multiply.
How do you divide fractions?: Multiply by the reciprocal of the second fraction, which is that fraction turned upside down. 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 1 1/2. A whole number divides the same way, as a fraction over 1: 5 ÷ 2/3 = 5/1 × 3/2 = 15/2 = 7 1/2. Dividing by zero is not possible, and the calculator says so.
How do you simplify a fraction?: Divide the numerator and the denominator by their greatest common divisor (GCD). The GCD of 18 and 24 is 6, so 18/24 = 3/4, in lowest terms. Euclid’s algorithm finds the GCD by repeated division, and the calculator writes it out: 24 = 1 × 18 + 6, then 18 = 3 × 6 + 0, so the last non-zero remainder, 6, is the GCD.
How do you turn a fraction into a decimal?: Divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375. Some fractions never end: 1/3 = 0.(3) and 1/6 = 0.1(6), where the digits in parentheses repeat forever. A fraction in lowest terms ends exactly when its denominator has no prime factors except 2 and 5.
How do you turn a decimal into a fraction?: Write the digits after the point over a power of 10 with as many zeros, then simplify: 0.375 = 375/1000 = 3/8. For a repeating decimal, subtract it from a shifted copy of itself: with x = 0.(6), 10x − x = 6, so x = 6/9 = 2/3. Type 0.(3) with the repeating digits in parentheses and the calculator does this for you.
What do the brackets in 0.(3) mean?: The digits inside the parentheses repeat forever, so 0.(3) is 0.3333… and 1/6 = 0.1(6) is 0.1666…. A bar over the repeating digits means the same thing; parentheses are easier to type. The calculator also shows the value rounded to 4 places, marked ≈, for the times you need a plain number.
How do I type a mixed number?: Put a space between the whole number and the fraction: 2 3/8. A hyphen (2-3/8) and the fraction characters ½ ¼ ¾ also work, as do improper fractions such as 19/8 and decimals such as 2.375. A minus sign in front applies to the whole mixed number, so −2 3/8 is −19/8.
Can I use it for tape-measure fractions like 5/16 inch?: Yes. The marks on a tape are fractions with denominators 2, 4, 8, 16 and 32, so 2 3/8 + 1 5/16 = 3 11/16 works the same whether the numbers are inches or not. For lengths in feet, inches and metric, with the answer rounded to the nearest 1/16 inch, use the feet and inches calculator.
Are the answers exact, or rounded?: They are exact. Every number is kept as a fraction of two whole numbers of any size, so nothing is ever rounded, and 0.1 + 0.2 is exactly 3/10. The only rounded figure is the one labelled “Rounded to 4 places”. A decimal that repeats for longer than 48 digits is cut off with an ellipsis.

How it works

Every number you type is read as an exact fraction of two whole numbers (up to 30 digits each): a mixed number a b/c is (a × c + b)/c, a decimal is its digits over a power of 10, and a repeating decimal such as 0.1(6) is worked out by subtracting a shifted copy of itself. Addition and subtraction rewrite both fractions over the least common multiple of the denominators, LCM(a, b) = a × b ÷ GCD(a, b), and combine the numerators; multiplication multiplies numerators and denominators; division multiplies by the reciprocal. Results are reduced by the greatest common divisor found with Euclid’s algorithm, and shown as an improper fraction, a mixed number, a decimal and a percent. A decimal is found by long division: when the remainder reaches 0 the decimal ends, and when a remainder comes back the digits since then repeat, written in parentheses. The working shown starts from the fractions as typed, so 6/8 keeps its denominator until the simplify step. Everything runs in your browser and nothing you type is sent anywhere.

Sources

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