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:

8 4/6 - 5 8/12 = 3/1 = 3

The spelled result in words is three.

How do we solve fractions step by step?

  1. Conversion a mixed number 8 4/6 to a improper fraction: 8 4/6 = 8 4/6 = 8 · 6 + 4/6 = 48 + 4/6 = 52/6

    To find a new numerator:
    a) Multiply the whole number 8 by the denominator 6. Whole number 8 equally 8 * 6/6 = 48/6
    b) Add the answer from the previous step 48 to the numerator 4. New numerator is 48 + 4 = 52
    c) Write a previous answer (new numerator 52) over the denominator 6.

    Eight and four sixths is fifty-two sixths.
  2. Conversion a mixed number 5 8/12 to a improper fraction: 5 8/12 = 5 8/12 = 5 · 12 + 8/12 = 60 + 8/12 = 68/12

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 12. Whole number 5 equally 5 * 12/12 = 60/12
    b) Add the answer from the previous step 60 to the numerator 8. New numerator is 60 + 8 = 68
    c) Write a previous answer (new numerator 68) over the denominator 12.

    Five and eight twelfths is sixty-eight twelfths.
  3. Subtract: 52/6 - 68/12 = 52 · 2/6 · 2 - 68/12 = 104/12 - 68/12 = 104 - 68/12 = 36/12 = 12 · 3/12 · 1 = 3
    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(6, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 12 = 72. In the following intermediate step, cancel by a common factor of 12 gives 3/1.
    In other words - fifty-two sixths minus sixty-eight twelfths is three.

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


SymbolSymbol 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)

The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) have the same priority and must be evaluated from left to right.


Last Modified: June 4, 2024