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Fraction Calculator

Add, subtract, multiply or divide two fractions or mixed numbers. Get the answer in simplest form, as a mixed number, a decimal and a percent.

Level: Grades 5–7

  • Common Core standard 5.NF.A.1Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.
  • Common Core standard 5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
  • Common Core standard 6.NS.A.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
  • Common Core standard 7.NS.A.1Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
  • Common Core standard 7.NS.A.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
Printable worksheet

Fraction Calculator

Inputs

Only for a mixed number, such as the 2 in 2 1/3. Leave it blank otherwise.

Can't be zero.

Only for a mixed number.

Can't be zero.

Result

Result (simplified)

19/12

3/4 + 5/6 = 19/12 (≈ 1.583333)

Mixed number
1 7/12
Decimal
1.583333
As a percent
158.333333%

See the step-by-step solution ↓

Step-by-step solution

  1. You can only add or subtract pieces of the same size. So find the smallest number that both 4 and 6 go into evenly (the LCD)

    LCD(4, 6)=12

  2. Rewrite both fractions with 12 on the bottom: multiply the top and bottom of 3/4 by 3, and multiply the top and bottom of 5/6 by 2. This changes how they look, not what they're worth

    34+56=3×34×3+5×26×2=912+1012

  3. Add the top numbers. The bottom stays the same, because the pieces are still the same size

    9+1012=1912

  4. No number except 1 divides both the top and the bottom, so the fraction can't get any simpler (as a mixed number, 1 7/12)

    1912

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

How to solve this on a calculator

The keys to press to get this page's worked-example answer on an ordinary calculator, with what the display should show after each step. A named-model tab follows that calculator's official guidebook.

3/4 + 5/6 with brackets

Problem
A recipe calls for 3/4 cup of milk and 5/6 cup of water. How much liquid is that in total?
Formula
a/b + c/d = (a ÷ b) + (c ÷ d)
Example values
a/b = 3/4 (the milk); c/d = 5/6 (the water). These are the fixed values from the worked example on this page, so the keys stay the same whatever you type into the calculator above.
Why a scientific calculator
Without a fraction key, brackets around each fraction keep its division together. You get the decimal, and can check it against the exact fraction. It also works on a basic calculator, fraction calculator (not on this site yet) or financial calculator.
The whole sequence
(3÷4)+(5÷6)=19÷12=

Step by step

  1. (3÷4)

    Type the first fraction as a division in brackets: (3 ÷ 4).

    Display: (3÷4)

  2. +(5÷6)

    Add the second fraction, also in brackets: + (5 ÷ 6).

    Display: (3÷4)+(5÷6)

  3. =

    Press =. The total is about 1.5833 cups; the 3s repeat forever, so the display is rounded.

    Display: 1.5833333333

  4. 19÷12=

    Check against the exact answer, 19/12: 19 ÷ 12 = gives the same decimal, so the sum is 19/12 = 1 7/12 cups.

    Display: 1.5833333333

If your answer looks wrong

  • Adding the tops and the bottoms, (3 + 5) ÷ (4 + 6) = 0.8, is a common mistake: fractions need a common denominator, which dividing each one out first takes care of.
  • Here 3 ÷ 4 + 5 ÷ 6 = gives the same answer without brackets, because ÷ comes before +. With subtraction or longer fractions the brackets matter, so keep them as a habit.
  • A calculator shows a rounded decimal. For the exact fraction, use the fraction calculator above.

How this is checked: an automated test presses these keys on this site's scientific calculator, checks every display along the way, and confirms the answer matches the calculator on this page (last checked 2026-10-19). It has not been checked on any particular brand or model, and real calculators label some keys differently.

What this calculator does

Add, subtract, multiply or divide two fractions, and see every step of how to do it yourself. It works with mixed numbers too, like 2 1/3. The steps follow the way it's taught in class. For adding and subtracting, you find a common bottom number, rewrite each fraction, combine them, then simplify.

You get the answer in lowest terms, which means as simple as it can be. If it's bigger than 1, you also get it as a mixed number. You get it as a decimal and a percent, too. Negative fractions and mixed numbers both work. So you can check homework, scale a recipe or add up measurements without converting anything first.

Where it's used

Why this math matters outside the classroom:

  • Scaling recipes. Cooks halving a recipe that calls for 3/4 cup of sugar multiply 3/4 by 1/2 to get 3/8 cup.
  • Woodworking. Carpenters add boards 2 3/8 in and 1 5/16 in wide by rewriting both in sixteenths, giving 3 11/16 in.
  • Sharing food. Splitting 3/4 of a pizza equally among 3 friends gives each person 1/4 of the pizza.
  • Cutting fabric. Sewers find how many 3/8-yard strips fit in 3 yards of fabric by dividing 3 by 3/8, which gives 8 strips.
  • Music rhythm. Musicians check that a half note and two quarter notes fill one bar of 4/4 time, since 1/2 + 1/4 + 1/4 = 1.

Grade level and standards: Grades 5–7; Common Core State Standards for Mathematics 5.NF.A.1, 5.NF.B.4, 6.NS.A.1, 7.NS.A.1, 7.NS.A.2. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. For each fraction, enter the top number (the numerator) and the bottom number (the denominator) as whole numbers.
  2. For a mixed number such as 2 1/3, also fill in the whole number box. Put 2 in the whole number, 1 in the top and 3 in the bottom. Leave the whole number blank for an ordinary fraction.
  3. Choose add, subtract, multiply or divide.
  4. Read the simplified answer. Then open the working to follow each step.

What the inputs mean

First whole number (optional)
The whole-number part of a mixed number. For a negative mixed number, put the minus sign here: −2 with 1/3 means −(2 1/3). Leave it blank if the first value is a plain fraction.
First numerator
The top number of the first fraction. Whole numbers only. It can be negative for a plain fraction.
First denominator
The bottom number of the first fraction. It must be a whole number other than zero.
Operation
What to do with the two fractions, working from the first to the second.
Second whole number (optional)
The whole-number part of the second value, if it's a mixed number.
Second numerator
The top number of the second fraction. It can't be zero when you divide, because you can't divide by zero.
Second denominator
The bottom number of the second fraction. It must be a whole number other than zero.

Formula and method

mixed number: w n/d = (w × d + n) ÷ d
a/b + c/d: rewrite both over LCD(b, d), then add the numerators
a/b − c/d: rewrite both over LCD(b, d), then subtract the numerators
a/b × c/d = (a × c) ÷ (b × d)
a/b ÷ c/d = a/b × d/c

In the formulas, a/b is the first fraction and c/d is the second. So a and c are the top numbers, and b and d are the bottoms. In the mixed-number line, w is the whole number, n is the top and d is the bottom. LCD stands for least common denominator, explained next.

To add or subtract, both fractions need the same bottom number, so you're combining pieces of the same size. The working uses the least common denominator (LCD). That's the smallest number both bottom numbers go into evenly, which keeps the numbers as small as possible. Each fraction is multiplied top and bottom by whatever turns its bottom number into the LCD.

Multiplying works straight across: top times top, and bottom times bottom. To divide, keep the first fraction, change ÷ to ×, and flip the second fraction upside down. The flipped fraction is called its reciprocal.

At the end, the top and bottom are divided by the biggest number that goes into both evenly, called the greatest common divisor. Any minus sign is moved to the top. So 6/−8 is shown as −3/4.

Worked example

A recipe calls for 3/4 cup of milk and 5/6 cup of water. How much liquid is that in total?

  1. The least common denominator of 4 and 6 is 12.
  2. Rewrite each fraction over 12: 3/4 = 9/12 (times 3 top and bottom) and 5/6 = 10/12 (times 2).
  3. Add the numerators: 9/12 + 10/12 = 19/12.
  4. No number except 1 goes into both 19 and 12, so 19/12 is already as simple as it gets. As a mixed number, 12 goes into 19 once with 7 left over: 1 7/12.

Result: 3/4 + 5/6 = 19/12, which is 1 7/12 cups, or about 1.583333 as a decimal (158.33%).

Understanding the result

The simplified fraction is the exact answer. The decimal may be rounded. For example, 1/3 + 1/3 = 2/3 is exact, but 0.666667 is not.

A mixed number splits a top-heavy fraction into a whole part and a fraction smaller than 1. That's often easier to picture for measurements. A negative mixed number such as −1 3/4 means −(1 + 3/4).

Assumptions and limitations

  • Top numbers, bottom numbers and whole-number parts are whole numbers. Enter a decimal like 0.5 as 1/2.
  • In a mixed number, the minus sign goes on the whole number, and you enter the fraction part as positive.
  • Answers are always reduced to lowest terms, with a positive bottom number.
  • After any mixed number is converted, top and bottom numbers can be up to 10,000,000. That limit keeps the math exact.
  • It handles two fractions and one operation at a time. For longer problems, work one operation at a time, in the usual order of operations.

Frequently asked questions

How do I find the least common denominator?

Count up by the larger bottom number until you reach one the smaller bottom number goes into evenly. For 4 and 6, counting by 6 gives 6, 12, 18… Since 4 goes into 12, the LCD is 12. When the two numbers share no factor, as with 3 and 5, the LCD is their product, 15.

How do I add or subtract mixed numbers?

First turn each one into a single fraction: multiply the whole number by the bottom, then add the top. So 2 1/3 becomes 7/3, and 1 3/4 becomes 7/4. Then add as usual with 12 on the bottom: 28/12 + 21/12 = 49/12, which is 4 1/12.

Why does dividing by a fraction make the answer bigger?

Dividing asks how many of the second amount fit into the first. Half a cake divided by a quarter is 2, because two quarters fit into one half. Dividing by anything between 0 and 1 gives a bigger answer.

Do I have to use the lowest common denominator?

No. Any shared bottom number works, including the two bottom numbers multiplied together. The lowest one keeps the numbers smaller, so there's less to simplify at the end. Either way, the simplified answer is the same.

How do I turn a fraction into a decimal or a percent?

Divide the top by the bottom to get the decimal. Then multiply by 100 for the percent. For example, 3/8 = 3 ÷ 8 = 0.375, which is 37.5%.

How is a negative mixed number written?

The minus sign applies to the whole value. −7/4 is written −1 3/4, which means −(1 + 3/4), not −1 + 3/4.

Can I cancel before multiplying?

Yes. If a top number and the other fraction's bottom number share a factor, you can divide both by it first. In 4/9 × 3/8, cancel 4 with 8 and 3 with 9 to get 1/3 × 1/2 = 1/6. The calculator multiplies first and simplifies at the end, and you get the same answer.

How this calculator is checked

Method: Standard rules of fraction arithmetic; least common denominator via the least common multiple; reduction by the greatest common divisor. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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