Fraction calculator



This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step informations.

The result:

5 1/8 + 2 5/8 = 31/4 = 7 3/4 = 7.75

The spelled result in words is thirty-one quarters (or seven and three quarters).

How do we solve fractions step by step?

  1. Conversion a mixed number 5 1/8 to a improper fraction: 5 1/8 = 5 1/8 = 5 · 8 + 1/8 = 40 + 1/8 = 41/8

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
    b) Add the answer from the previous step 40 to the numerator 1. New numerator is 40 + 1 = 41
    c) Write a previous answer (new numerator 41) over the denominator 8.

    Five and one eighth is forty-one eighths.
  2. Conversion a mixed number 2 5/8 to a improper fraction: 2 5/8 = 2 5/8 = 2 · 8 + 5/8 = 16 + 5/8 = 21/8

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 8. Whole number 2 equally 2 * 8/8 = 16/8
    b) Add the answer from the previous step 16 to the numerator 5. New numerator is 16 + 5 = 21
    c) Write a previous answer (new numerator 21) over the denominator 8.

    Two and five eighths is twenty-one eighths.
  3. Add: 41/8 + 21/8 = 41 + 21/8 = 62/8 = 2 · 31/2 · 4 = 31/4
    It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the following intermediate step, cancel by a common factor of 2 gives 31/4.
    In other words - forty-one eighths plus twenty-one eighths is thirty-one quarters.

Rules for expressions with fractions:

Fractions - use a forward slash to divide the numerator by the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals (mixed numbers or fractions) keep one space between the integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both sign for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.


Math Symbols


OpSymbol nameSymbol MeaningExample
+plus signaddition 1/2 + 1/3
-minus signsubtraction 1 1/2 - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate expression inside first-3/5 - (-1/4)

See practise with fractions »