Convert an improper fraction into a mixed number, or turn a mixed number back into an improper fraction, instantly, in either direction. Every quotient, remainder, and product is shown so you can follow exactly how the result was built.
Enter an improper fraction: the numerator on top, the denominator below.
Enter values above to see each step of the conversion.
An improper fraction is a fraction whose numerator is greater than or equal to its denominator. Examples include 7/3, 5/2, and 9/4. In each case the top number is at least as large as the bottom number, which means the fraction stands for a value of one whole or more. Improper fractions can look unusual at first, but they follow the exact same rules of arithmetic as any other fraction, and they are often easier to add, subtract, multiply, or divide than the equivalent mixed number.
The defining test is simple: compare the numerator to the denominator. If the numerator is bigger than, or equal to, the denominator, the fraction is improper. 7/3 is improper because 7 is bigger than 3. Even 4/4 counts as improper, since the numerator equals the denominator. It simply represents exactly one whole.
A proper fraction, like 2/3, has a numerator smaller than its denominator and always represents a value less than one whole. An improper fraction flips that relationship: 7/3 is more than two wholes, since 6/3 already equals 2 and there is 1/3 left over. Both kinds of fractions use the same numerator-over-denominator notation; only the size relationship between the two numbers changes what the value means.
7/3 is just another way of writing 2 1/3. The two forms represent the identical value, and converting between them is simply a matter of division. The calculator above, and the two methods below, show exactly how that conversion works in both directions.
To rewrite an improper fraction as a mixed number, divide the numerator by the denominator. The whole-number part of that division becomes the whole number in the mixed number, the remainder becomes the new numerator, and the denominator never changes.
Divide 7 by 3: 7 ÷ 3 = 2, with 1 left over. So the quotient 2 becomes the whole number, the remainder 1 becomes the new numerator, and the denominator stays 3. 7/3 becomes the mixed number 2 1/3.
To rewrite a mixed number as an improper fraction, multiply the whole number by the denominator, then add the numerator. That sum becomes the new numerator, placed over the original denominator.
Multiply the whole number, 2, by the denominator, 3: 2 × 3 = 6. Add the numerator, 1: 6 + 1 = 7. Keep the same denominator, 3. The mixed number 2 1/3 becomes the improper fraction 7/3.
Finding a least common denominator gets much more reliable once every mixed number has been rewritten as an improper fraction first. When a whole number and a fraction are still tangled together, it is easy to line up the wrong parts or forget to borrow correctly during subtraction. Converting removes that risk entirely.
Say you need to add 1 1/2 and 2 1/3. If you try to add the whole numbers and fractions separately without a clear plan, it is easy to add 1/2 and 1/3 using the wrong denominator, or to mishandle the whole numbers when a fraction sum rolls over into a new whole. Subtraction is even riskier, since borrowing from the whole number requires converting a piece of it into a fraction anyway. That is the exact operation this page performs.
Convert both mixed numbers to improper fractions first: 1 1/2 becomes 3/2, and 2 1/3 becomes 7/3. Now the problem is just two ordinary fractions. The LCD of 2 and 3 is 6, so 3/2 becomes 9/6 and 7/3 becomes 14/6. Adding gives 23/6, which converts back to the mixed number 3 5/6, a clean result with no borrowing and no ambiguity about which parts to combine.
Once you have your improper fractions, head to the LCD calculator to find the least common denominator, or straight to the fraction addition calculator or fraction subtraction calculator to finish the problem with full working shown.
Eight fully worked examples, four for each direction, showing every intermediate step so you can check your own work or simply see the pattern repeat with different numbers.