What does a fraction of a fraction mean?

It means multiply. Two thirds of five eighths is 2/3 × 5/8, and the word "of" and the multiplication sign do exactly the same job on this page. Multiply the top numbers together and the bottom numbers together: (2 × 5) over (3 × 8) is 10/24, which reduces by 2 to 5/12, or 0.41(6) as a decimal. The bracketed 6 repeats for ever. The tool prints those three lines as the working, so the answer can be checked rather than trusted.

How do I enter a mixed number?

Write the whole part, a space, then the fraction: 1 3/4. The tool converts it to 7/4 and says so as the first line of the working, because that is the step every mixed number calculation starts with. A minus sign applies to the whole quantity, so -1 3/4 is -7/4 rather than -1 plus three quarters. If you paste a fraction glyph from a document, 1½ is read the same as 1 1/2. Answers come back as an improper fraction and as a mixed number together, so 7/2 and 3 1/2 are both on screen.

Why does the decimal repeat?

Because of what the denominator is made of. Once a fraction is in its lowest terms its decimal stops only if the denominator is built from twos and fives, the two numbers that divide ten. So 1/8 is 0.125 and stops, while 1/3 is 0.(3), 1/6 is 0.1(6) and 1/7 is 0.(142857), each repeating for ever. The digits inside the brackets are the part that repeats, and the tool finds them by long division rather than assuming them: it watches for a remainder it has seen before, which is the moment the pattern starts over.

Does this calculator round?

The fraction arithmetic never rounds. Decimal and percentage previews are worked out to 240 fractional digits, with parentheses around a cycle found within that span. If a terminating expansion or repeating cycle runs longer, the preview is cut short and marked with an ellipsis. The exact simplified fraction remains on screen. Each typed numeric entry is limited to 200 characters; longer drafts remain visible with an error.

How do I convert a decimal to a fraction?

Select Add, enter the decimal in the first box and zero in the second. 0.375 = 375/1000 = 3/8; 4.5 = 45/10 = 9/2 = 4 1/2. A repeating decimal must name its period: 0.(3) = 1/3 and 0.41(6) = 5/12. A finite 0.3333 is 3333/10000. Use the existing Fraction to Decimal page for a conversion preset.

Can it multiply a fraction by a whole number?

Yes. Put the whole number in either box on its own: 5/8 × 24 gives (5 × 24) over (8 × 1), which is 120/8 and reduces to 15. Written as "of" it reads the way the question usually does, five eighths of 24, and gives the same answer. When the result does not land on a whole number you get both forms, so 2/3 × 5 is 10/3 and 3 1/3.

How do I calculate with three fractions or mixed numbers?

Choose the operation, then Add a third number. For 1 1/2 + 2 3/4 + 3 1/4, enter those three numbers and choose Add: the result is 15/2, or 7 1/2. The same selected operation applies to both steps from left to right. For 8 ÷ 2 ÷ 2, the result is (8 ÷ 2) ÷ 2 = 2. Different operations, nested expressions or general order-of-operations problems are not parsed.

Which fraction is larger, and how do I order fractions?

Switch to Compare & order and enter values separated by commas, semicolons or new lines. For 3/4, 2/3, 0.7, ascending order is 2/3 < 0.7 < 3/4. Fractions are compared by exact cross-products, so close values are not tied because a decimal rounded them together. Negative fractions, mixed numbers, repeating decimals and percentages work; equal values retain their original relative order.

How do I convert between percentages, decimals and fractions?

A percent means division by 100: 25% is 25/100 = 1/4 = 0.25. Enter 25% in the first box, choose Add and leave the second at zero. A fraction’s percent is its value multiplied by 100, so 3/8 = 0.375 = 37.5%. The percent row keeps repeating digits in parentheses and marks a longer cut preview.

How do I simplify a numeric complex fraction?

Treat its numerator and denominator as the two numbers. For (3/4)/(5/6), enter 3/4 in the first box, 5/6 in the second and choose Divide. Multiplying by the reciprocal gives 3/4 × 6/5 = 18/20 = 9/10. The boxes take single numeric values; sums within the numerator or denominator must be calculated first. Variables, partial fractions and nested expression strings are not supported.

Can this convert inches, millimetres or feet?

This page calculates numeric fractions in whatever matching units you supply; it does not convert between units or round a length to a ruler increment. Use Feet and Inches Calculator for feet/inch arithmetic and an explicitly chosen fraction of an inch. Decimal-to-fraction conversion here gives the exact fraction, such as 0.875 = 7/8, rather than assuming a nearest sixteenth.

Can I use a ratio as a fraction?

A comparison ratio a:b corresponds to a/b, so 3:4 becomes 3/4. Use Ratio Calculator to simplify ratios with fractional terms or distinguish comparison ratios from part-to-whole shares. The share of the first part in 3:4 is 3/(3+4) = 3/7, a different fraction.

Fraction Calculator

Q: How do I convert between percentages, decimals and fractions?

A percent means division by 100: 25% is 25/100 = 1/4 = 0.25. Enter 25% in the first box, choose Add and leave the second at zero. A fraction’s percent is its value multiplied by 100, so 3/8 = 0.375 = 37.5%. The percent row keeps repeating digits in parentheses and marks a longer cut preview.

Q: How do I simplify a numeric complex fraction?

Treat its numerator and denominator as the two numbers. For (3/4)/(5/6), enter 3/4 in the first box, 5/6 in the second and choose Divide. Multiplying by the reciprocal gives 3/4 × 6/5 = 18/20 = 9/10. The boxes take single numeric values; sums within the numerator or denominator must be calculated first. Variables, partial fractions and nested expression strings are not supported.

Calculate with two or three fractions, mixed numbers, decimals or percentages, with exact working and simplified, mixed, decimal and percentage answers together. Choose Add a third number for three terms using the same operation from left to right. Switch to Compare & order for an exact list ranking: 2/3 < 0.7 < 3/4. For one-number conversions, add zero: 0.375 becomes 3/8 and 25% becomes 1/4. Repeating decimals use parentheses, so 0.(3) means exactly 1/3; 0.3333 means exactly 3333/10000.

2/3 of 5/85/1210/24 before simplifying · 0.41(6), where the digits in brackets repeat for ever · 41.(6)%

Operation

First

Second

Show

Each box takes a fraction like 3/4, a mixed number like 1 3/4, a whole number like 7 or a decimal like 0.75 or a percentage like 25%, and the answer comes back in every form at once. First box: a fraction, like 2/3. Second box: a fraction, like 5/8.

Simplifiedreduced from 10/24
5/12
As a mixed numbersmaller than one, so there is no whole part
5/12
As a decimalthe digits in brackets repeat, 1 of them, for ever
0.41(6)
As a percentagethe same value out of a hundred
41.(6)%

The working

The same steps you would write on paper, and only the ones these two numbers actually needed.

2/3 of 5/8 means 2/3 × 5/8.
Multiply across: (2 × 5) over (3 × 8) = 10/24.
Divide both by 2: 10/24 = 5/12.

Worked cases

Each one is computed by the same code that answers your own numbers, every time this page loads.

Decimal in0.375 as a fraction
3/8 · 0.375 as a decimal
Mixed numbers2 1/4 by 1 1/3
3 · 36/12 before simplifying, 3 as a decimal
Whole number5/8 of 24
15 · 120/8 before simplifying, 15 as a decimal

Exact rational arithmetic, then the conversions. Exact fraction arithmetic and comparisons. Decimal previews show a repeating cycle when it is found within 240 displayed digits; longer expansions are cut short and marked. Each numeric entry is limited to 200 characters. The exact fraction remains available. The numerator and the denominator stay whole numbers from start to finish, the answer is reduced once by the greatest common divisor, and where a decimal is too long for the page it is cut short rather than rounded, so every digit on screen is a real digit of the value at that place.

Common questions

What does a fraction of a fraction mean?: It means multiply. Two thirds of five eighths is 2/3 × 5/8, and the word "of" and the multiplication sign do exactly the same job on this page. Multiply the top numbers together and the bottom numbers together: (2 × 5) over (3 × 8) is 10/24, which reduces by 2 to 5/12, or 0.41(6) as a decimal. The bracketed 6 repeats for ever. The tool prints those three lines as the working, so the answer can be checked rather than trusted.
How do I enter a mixed number?: Write the whole part, a space, then the fraction: 1 3/4. The tool converts it to 7/4 and says so as the first line of the working, because that is the step every mixed number calculation starts with. A minus sign applies to the whole quantity, so -1 3/4 is -7/4 rather than -1 plus three quarters. If you paste a fraction glyph from a document, 1½ is read the same as 1 1/2. Answers come back as an improper fraction and as a mixed number together, so 7/2 and 3 1/2 are both on screen.
Why does the decimal repeat?: Because of what the denominator is made of. Once a fraction is in its lowest terms its decimal stops only if the denominator is built from twos and fives, the two numbers that divide ten. So 1/8 is 0.125 and stops, while 1/3 is 0.(3), 1/6 is 0.1(6) and 1/7 is 0.(142857), each repeating for ever. The digits inside the brackets are the part that repeats, and the tool finds them by long division rather than assuming them: it watches for a remainder it has seen before, which is the moment the pattern starts over.
Does this calculator round?: The fraction arithmetic never rounds. Decimal and percentage previews are worked out to 240 fractional digits, with parentheses around a cycle found within that span. If a terminating expansion or repeating cycle runs longer, the preview is cut short and marked with an ellipsis. The exact simplified fraction remains on screen. Each typed numeric entry is limited to 200 characters; longer drafts remain visible with an error.
How do I convert a decimal to a fraction?: Select Add, enter the decimal in the first box and zero in the second. 0.375 = 375/1000 = 3/8; 4.5 = 45/10 = 9/2 = 4 1/2. A repeating decimal must name its period: 0.(3) = 1/3 and 0.41(6) = 5/12. A finite 0.3333 is 3333/10000. Use the existing Fraction to Decimal page for a conversion preset.
Can it multiply a fraction by a whole number?: Yes. Put the whole number in either box on its own: 5/8 × 24 gives (5 × 24) over (8 × 1), which is 120/8 and reduces to 15. Written as "of" it reads the way the question usually does, five eighths of 24, and gives the same answer. When the result does not land on a whole number you get both forms, so 2/3 × 5 is 10/3 and 3 1/3.
How do I calculate with three fractions or mixed numbers?: Choose the operation, then Add a third number. For 1 1/2 + 2 3/4 + 3 1/4, enter those three numbers and choose Add: the result is 15/2, or 7 1/2. The same selected operation applies to both steps from left to right. For 8 ÷ 2 ÷ 2, the result is (8 ÷ 2) ÷ 2 = 2. Different operations, nested expressions or general order-of-operations problems are not parsed.
Which fraction is larger, and how do I order fractions?: Switch to Compare & order and enter values separated by commas, semicolons or new lines. For 3/4, 2/3, 0.7, ascending order is 2/3 < 0.7 < 3/4. Fractions are compared by exact cross-products, so close values are not tied because a decimal rounded them together. Negative fractions, mixed numbers, repeating decimals and percentages work; equal values retain their original relative order.
How do I convert between percentages, decimals and fractions?: A percent means division by 100: 25% is 25/100 = 1/4 = 0.25. Enter 25% in the first box, choose Add and leave the second at zero. A fraction’s percent is its value multiplied by 100, so 3/8 = 0.375 = 37.5%. The percent row keeps repeating digits in parentheses and marks a longer cut preview.
How do I simplify a numeric complex fraction?: Treat its numerator and denominator as the two numbers. For (3/4)/(5/6), enter 3/4 in the first box, 5/6 in the second and choose Divide. Multiplying by the reciprocal gives 3/4 × 6/5 = 18/20 = 9/10. The boxes take single numeric values; sums within the numerator or denominator must be calculated first. Variables, partial fractions and nested expression strings are not supported.
Can this convert inches, millimetres or feet?: This page calculates numeric fractions in whatever matching units you supply; it does not convert between units or round a length to a ruler increment. Use Feet and Inches Calculator for feet/inch arithmetic and an explicitly chosen fraction of an inch. Decimal-to-fraction conversion here gives the exact fraction, such as 0.875 = 7/8, rather than assuming a nearest sixteenth.
Can I use a ratio as a fraction?: A comparison ratio a:b corresponds to a/b, so 3:4 becomes 3/4. Use Ratio Calculator to simplify ratios with fractional terms or distinguish comparison ratios from part-to-whole shares. The share of the first part in 3:4 is 3/(3+4) = 3/7, a different fraction.

Exact fraction arithmetic and comparisons. Decimal previews show a repeating cycle when it is found within 240 displayed digits; longer expansions are cut short and marked. Each numeric entry is limited to 200 characters. The exact fraction remains available.