What this fraction calculator does
Enter two fractions, whole numbers or mixed numbers, choose add, subtract, multiply or divide, and the calculator returns the answer in lowest terms, as a mixed number when that is natural, and as a decimal. It also shows each step of the working and draws bar models for both inputs and the answer. All arithmetic is done with exact whole numbers, so 1/2 + 1/3 is exactly 5/6, never 0.8333333 stored as a rounded decimal. The decimal is only a display of the exact fraction, rounded to six places and marked "about" when rounding was needed.
How to type fractions and mixed numbers
Write a fraction as numerator/denominator, for example 3/4. Write a mixed number with a space between the whole part and the fraction, for example 2 3/4 (two and three quarters). A leading minus sign makes the whole value negative, so -1 1/2 means minus one and a half. The calculator rejects input it could misread rather than guessing: decimals such as 0.5, a denominator of zero, spaces around the slash, a sign in the denominator and mixed numbers whose fraction part is not proper (such as 1 5/3). Each value can have up to 15 digits in any whole part, numerator or denominator.
Adding and subtracting fractions
Fractions can only be added or subtracted when they are cut into pieces of the same size, so the first job is a common denominator. The smallest one is the least common denominator, the least common multiple of the two denominators. For 1/2 + 1/3 the denominators 2 and 3 give 6, so the sum is 3/6 + 2/6 = 5/6. For 3/4 + 5/6 the least common denominator is 12 and the sum is 9/12 + 10/12 = 19/12, which the calculator shows as 19/12 and as the mixed number 1 7/12. Subtraction works the same way: 5/6 − 1/4 uses 12 and gives 10/12 − 3/12 = 7/12, and the tool reports 7/12. If you want to see how a common denominator is found, use the LCM calculator.
Mixed numbers are handled by converting them to improper fractions first, doing the arithmetic, then converting back. For example 2 3/4 + 1 2/3 becomes 11/4 + 5/3 = 33/12 + 20/12 = 53/12, which is 4 5/12.
Multiplying and dividing fractions
To multiply, multiply the numerators and multiply the denominators: 2/3 × 3/4 = 6/12, which reduces to 1/2. No common denominator is needed. A mixed number is converted first: 1 1/2 × 2/3 is 3/2 × 2/3 = 6/6 = 1. To divide, multiply by the reciprocal of the second fraction, the fraction turned upside down: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, shown as 15/8 or 1 7/8. Dividing by a fraction whose value is zero is undefined, and the calculator says so instead of returning an answer.
Simplifying to lowest terms
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. The calculator divides both by their greatest common factor, found with Euclid's remainder method, and tells you which factor it used. 6/12, for instance, has a greatest common factor of 6 and reduces to 1/2. You can check any pair of numbers with the GCF calculator. Because the arithmetic is exact, the reduction is exact too, even for large values: 123456789/987654321 + 1/3 comes out as 150891632/329218107 with no rounding.
Negative fractions and the sign of the answer
The sign always belongs to the whole fraction, and the calculator writes it in front of the numerator. A mixed number such as -1 1/2 is read as −(1 + 1/2) = −3/2, not as −1 + 1/2. Adding 1/2 gives -1. Dividing a negative by a positive, or the reverse, gives a negative answer, and two negatives multiply or divide to a positive.
From fractions to decimals and percentages
A fraction is a division: 3/8 means 3 divided by 8, which is 0.375. Some fractions terminate, like 3/8, and others repeat forever, like 1/3 = 0.333... The calculator shows up to six decimal places and marks a rounded value with "about". To turn a decimal into a percentage multiply by 100, or use the percentage calculator. To watch the digits of a repeating decimal appear one at a time, open the long division calculator.
The school standards that introduce these operations, including adding and subtracting fractions with unlike denominators and dividing with unit fractions, are set out in the Common Core State Standards for Mathematics, Grade 5, Number and Operations: Fractions.
Common mistakes
Adding the numerators and the denominators separately (1/2 + 1/3 = 2/5) is the classic error: the pieces are different sizes, so the answer 2/5 is actually smaller than 1/2. Forgetting to invert the second fraction when dividing is the next most common. Reading 2 3/4 as 2 × 3/4 is another, because the space in a mixed number means addition. Last, a fraction is not finished until it is reduced, so check the answer against the lowest-terms form shown above.
Fraction calculator questions
How do you add fractions with different denominators?
Rewrite both fractions with the same denominator, preferably the least common denominator, add the numerators, keep the denominator and reduce. For 1/2 + 1/3 that gives 5/6.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole part and the remainder is the new numerator over the same denominator. For 15/8 that gives 1 7/8.
How do you divide fractions?
Multiply the first fraction by the reciprocal of the second. Dividing by 2/5 is the same as multiplying by 5/2.
Can the calculator handle mixed numbers and negatives?
Yes. Type a mixed number with a space, such as 2 3/4, and put a minus sign in front for a negative value. The answer is shown as a simplified fraction, a mixed number and a decimal.
Why does the calculator refuse some inputs?
It only accepts forms that have one clear meaning: whole numbers, fractions and mixed numbers with a proper fraction part. Decimals, a zero denominator and ambiguous spacing are rejected with a message instead of being guessed.