How the fraction calculator works
The four operations
Add / subtract: rewrite both fractions over a common denominator, then combine the numerators. Multiply: multiply straight across — numerators together, denominators together. Divide: flip the second fraction and multiply. In every case the result is then simplified by dividing the top and bottom by their greatest common divisor.
Mixed numbers and decimals
When the numerator is bigger than the denominator, the fraction is 'improper' and can also be written as a mixed number — a whole part plus a proper fraction. The decimal form is the numerator divided by the denominator, rounded to six places; some, like 1/3 = 0.333333…, repeat forever and are shown rounded.
Worked example
1/2 + 1/3: the common denominator is 6, so 3/6 + 2/6 = 5/6 — already in lowest terms, and 0.833333 as a decimal. Compare multiplying: 1/2 × 1/3 = 1/6, and dividing: 1/2 ÷ 1/3 = 3/2 = 1½.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator — the least common multiple of the two denominators — and rewrite both fractions over it. For 1/2 + 1/3 the common denominator is 6: 3/6 + 2/6 = 5/6.
How do you divide fractions?
Flip the second fraction (its reciprocal) and multiply: 1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2. 'Keep, change, flip' is the memory aid: keep the first, change ÷ to ×, flip the second.
What does simplifying mean?
Dividing the numerator and denominator by their greatest common divisor (GCD) until no common factor remains. 6/8 simplifies to 3/4 because both divide by 2. A fraction in lowest terms has exactly the same value.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole part is the quotient, and the remainder stays over the original denominator: 7/4 = 1¾, because 7 ÷ 4 = 1 remainder 3.
Can denominators be negative?
They can, but by convention the sign is moved to the numerator (or in front of the fraction). This calculator keeps the denominator positive and carries the sign on the numerator.
More free study tools
Final Grade Calculator
See exactly what score you need on the final exam to finish the course with the grade you want.
Weighted Grade Calculator
Add each assignment with its score and weight to see your current course grade as a percentage and a letter.
Result & Grade Checker
Type in your own subject marks to get your total, percentage, letter grades, and GPA points — checked by you, stored nowhere.
Attendance Calculator
Find your attendance percentage and how many classes you must attend in a row — or can safely miss — to hit your target.
CGPA to Percentage Converter
Convert a 10-point CGPA to a percentage with the ×9.5 formula, and move between a 4.0 GPA and percentage with a standard table.
Quadratic Equation Solver
Solve ax² + bx + c step by step: discriminant, both roots, and the vertex of the parabola.
Percentage Tools for Marks
Quick percentage help for schoolwork: score change between two tests, average of several scores, and what percent one mark is of another.
Study Plan Calculator
Turn a pile of chapters and pages into a calm day-by-day plan that fits the days and hours you actually have.
School Age Calculator
Check a child's age on the school cutoff date and the likely kindergarten or Grade 1 entry year. Informational only — districts vary.