Mixed Fraction Calculator With Steps

Enter two or more mixed numbers in the boxes, or type the whole problem on one line, and the answer updates as you type. The calculator shows every step a teacher expects to see: converting to improper fractions, finding the least common denominator, cross-cancelling, simplifying with the greatest common factor and converting back to a mixed number. It also gives the answer as an improper fraction, a decimal and a percent.

How to use the mixed fraction calculator

1. Fill in the boxes. The big box is the whole number, the two small boxes are the numerator (top) and denominator (bottom). For a plain fraction such as 3/4, leave the whole-number box empty. For a whole number, leave the fraction boxes empty.
2. Pick the operation in the round button between two numbers: add (+), subtract (−), multiply (×) or divide (÷).
3. Add more numbers with “+ Add a number”. You can solve three, four or up to twelve mixed numbers in one problem.
4. Or type the problem. Write a mixed number with a space between the whole number and the fraction: 2 1/3 + 1 3/4. Use x or * for multiply and / with spaces around it, or ÷, for divide. Brackets work too: (1 1/2 + 2/3) x 1 1/5.
5. Read the steps under the answer. For addition and subtraction you can switch between two methods: converting to improper fractions, or working with the whole numbers and fractions separately (the borrowing method many classrooms teach).
6. Check your homework by typing your own answer in “Check your own answer”. The calculator tells you if it is right, right but not simplified, or wrong.

Copy link saves the problem in a web address, so you can send the exact problem and its solution to a classmate or student.

What is a mixed fraction?

A mixed fraction, also called a mixed number, is a whole number and a proper fraction written together. 2 1/3 means 2 + 1/3: two wholes and one third of another. The fraction part is always less than 1, so 2 4/3 is not written in mixed form; it is 3 1/3.

An improper fraction has a numerator that is equal to or larger than its denominator, such as 7/3. Every mixed number can be written as an improper fraction and every improper fraction with a remainder can be written as a mixed number. 2 1/3 and 7/3 are the same amount.

Type	Example	What it means
Proper fraction	3/4	Numerator smaller than the denominator, less than 1
Improper fraction	7/4	Numerator equal to or larger than the denominator, 1 or more
Mixed number	1 3/4	A whole number plus a proper fraction, the same as 7/4
Whole number	5	The same as 5/1

How to convert a mixed number to an improper fraction

Multiply the whole number by the denominator, add the numerator and put the result over the same denominator.

• 2 1/3: 2 × 3 + 1 = 7, so 2 1/3 = 7/3
• 1 3/4: 1 × 4 + 3 = 7, so 1 3/4 = 7/4
• 5 2/9: 5 × 9 + 2 = 47, so 5 2/9 = 47/9

To go back, divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator. 49/12: 49 ÷ 12 = 4 remainder 1, so 49/12 = 4 1/12.

How to add mixed fractions

Worked example: 2 1/3 + 1 3/4.

1. Convert both to improper fractions: 2 1/3 = 7/3 and 1 3/4 = 7/4.
2. Find the least common denominator (LCD) of 3 and 4. Counting in 4s gives 4, 8, 12, and 12 is the first number 3 also divides into. The LCD is 12.
3. Rewrite each fraction over 12: 7/3 = 28/12 and 7/4 = 21/12.
4. Add the numerators: 28/12 + 21/12 = 49/12.
5. Convert back: 49 ÷ 12 = 4 remainder 1, so the answer is 4 1/12.

The other method keeps the whole numbers apart. Add 2 + 1 = 3. Add the fractions with the LCD: 4/12 + 9/12 = 13/12. Since 13/12 is more than one whole, it becomes 1 1/12, and 3 + 1 1/12 = 4 1/12. Both methods give the same answer. The separate method keeps the numbers smaller when the whole numbers are large.

How to subtract mixed fractions

Worked example: 5 1/4 − 2 2/3.

Borrowing method. Give the fraction parts a common denominator: 5 3/12 − 2 8/12. You cannot take 8/12 away from 3/12, so borrow 1 from the 5. That 1 is 12/12, which turns 5 3/12 into 4 15/12. Now subtract the whole numbers (4 − 2 = 2) and the fractions (15/12 − 8/12 = 7/12). The answer is 2 7/12.

Improper fraction method. 5 1/4 = 21/4 and 2 2/3 = 8/3. Over the LCD of 12 that is 63/12 − 32/12 = 31/12, which is 2 7/12. This method never needs borrowing, which is why it is the calculator’s default.

If the second number is larger than the first, the answer is negative. 1 1/2 − 3 3/4 = −2 1/4.

How to multiply mixed fractions

Worked example: 1 1/2 × 2 2/3.

1. Convert to improper fractions: 3/2 × 8/3. You must convert first. Multiplying the whole numbers and the fractions separately gives a wrong answer.
2. Cross-cancel: the 3 on top and the 3 on the bottom cancel to 1, and 8 on top with 2 on the bottom share a factor of 2, leaving 4 and 1.
3. Multiply what is left: (1 × 4) / (1 × 1) = 4.

The answer is 4. Cross-cancelling before you multiply keeps the numbers small and means the result is already in lowest terms.

How to divide mixed fractions

Worked example: 3 3/4 ÷ 1 1/4.

1. Convert to improper fractions: 15/4 ÷ 5/4.
2. Keep, change, flip: keep the first fraction, change ÷ to × and flip the second fraction to its reciprocal. 15/4 × 4/5.
3. Cross-cancel: 15 and 5 share a factor of 5, and the two 4s cancel. That leaves 3/1 × 1/1.
4. Multiply: 3.

3 3/4 divided by 1 1/4 is 3, which you can check: 3 × 1 1/4 = 3 3/4. Dividing by zero, or by a fraction equal to zero, has no answer, and the calculator says so.

Three or more mixed fractions

To add three mixed numbers, find one common denominator for all of them. For 1 1/2 + 2 1/3 + 3 1/4 the LCD of 2, 3 and 4 is 12:

• Improper fractions: 3/2 + 7/3 + 13/4
• Over 12: 18/12 + 28/12 + 39/12 = 85/12
• As a mixed number: 85 ÷ 12 = 7 remainder 1, so 7 1/12

When a problem mixes operations, the order of operations applies: brackets first, then multiplication and division, then addition and subtraction from left to right. In 1 1/2 + 2 2/3 × 3/4 the multiplication comes first (2 2/3 × 3/4 = 2), then 1 1/2 + 2 = 3 1/2. Working left to right instead gives 3 1/8, which is wrong. The calculator follows the correct order and shows each part as its own step.

How to simplify a mixed fraction

Simplify only the fraction part. Divide its numerator and denominator by their greatest common factor (GCF). In 4 6/8 the GCF of 6 and 8 is 2, so 6/8 becomes 3/4 and 4 6/8 = 4 3/4. If the fraction part is improper, carry the extra whole into the whole number: 2 7/4 = 2 + 1 3/4 = 3 3/4.

Enter a single number with no operation and the calculator simplifies it and converts it, so it also works as a fraction simplifier and as an improper fraction to mixed number converter.

Common mistakes with mixed numbers

Mistake	Wrong	Right
Adding numerators and denominators	1/2 + 1/3 = 2/5	3/6 + 2/6 = 5/6
Multiplying wholes and fractions separately	2 1/2 × 2 1/2 = 4 1/4	5/2 × 5/2 = 25/4 = 6 1/4
Dividing without flipping	3/4 ÷ 1/2 = 3/8	3/4 × 2/1 = 3/2 = 1 1/2
Applying a minus sign to the whole number only	−2 1/3 = −2 + 1/3 = −1 2/3	−2 1/3 = −(2 + 1/3) = −7/3
Subtracting the smaller fraction from the larger instead of borrowing	5 1/4 − 2 2/3 = 3 5/12	4 15/12 − 2 8/12 = 2 7/12

Mixed numbers as decimals and percents

Divide the numerator of the improper fraction by the denominator. 2 7/12 = 31/12 = 2.58333…, where the 3 repeats forever. The calculator writes repeating digits with a bar over them (2.583) instead of cutting them off, so you can see the exact value. A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5: 3 3/4 = 3.75, but 1 1/3 = 1.333… For the percent, multiply the decimal by 100: 3 3/4 = 375%.

Fractions are rational numbers. If you want to see where they sit among the other kinds of numbers, read our guides to examples of real numbers and irrational numbers. For more calculators, converters and printables, see all of our science and math tools.

Frequently asked questions

Is a mixed fraction the same as a mixed number?

Yes. Mixed fraction and mixed number are two names for a whole number written with a proper fraction, such as 3 1/2. Textbooks in the US mostly say mixed number.

Can this calculator add 3 mixed fractions?

Yes. Press “+ Add a number” or type all three on one line, for example 1 1/2 + 2 1/3 + 3 1/4. It finds one common denominator for all three and shows each step. It handles up to 12 numbers and brackets.

How do you add mixed fractions with different denominators?

Convert each mixed number to an improper fraction, rewrite them over the least common denominator, add the numerators and convert back. 2 1/3 + 1 3/4 = 28/12 + 21/12 = 49/12 = 4 1/12.

How do you multiply mixed fractions?

Convert them to improper fractions, cancel common factors between any numerator and any denominator, then multiply straight across. 1 1/2 × 2 2/3 = 3/2 × 8/3 = 4.

How do you divide mixed fractions?

Convert them to improper fractions, then multiply the first by the reciprocal of the second. 3 3/4 ÷ 1 1/4 = 15/4 × 4/5 = 3.

What is 39/12 as a mixed number?

39/12 = 3 1/4. 39 divided by 12 is 3 remainder 3, which gives 3 3/12, and 3/12 simplifies to 1/4.

Is 5/3 a mixed fraction?

No. 5/3 is an improper fraction because the numerator is larger than the denominator. As a mixed number it is 1 2/3.

How do you write a whole number as a fraction?

Put it over 1. 5 = 5/1. To add it to a fraction, rewrite it over the other denominator: 5 = 20/4.

What does a negative mixed number mean?

The minus sign applies to the whole mixed number. −2 1/3 means −(2 + 1/3), which is −7/3, not −2 + 1/3.

Why does my answer have a line over a digit?

The line marks digits that repeat forever. 4 1/12 = 4.083 means 4.08333… with the 3 repeating.