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:

12 5/8 ÷ 3 19/24 = 303/91 = 3 30/913.3296703

The spelled result in words is three hundred three ninety-firsts (or three and thirty ninety-firsts).

How do we solve fractions step by step?

  1. Conversion a mixed number 12 5/8 to a improper fraction: 12 5/8 = 12 5/8 = 12 · 8 + 5/8 = 96 + 5/8 = 101/8

    To find a new numerator:
    a) Multiply the whole number 12 by the denominator 8. Whole number 12 equally 12 * 8/8 = 96/8
    b) Add the answer from the previous step 96 to the numerator 5. New numerator is 96 + 5 = 101
    c) Write a previous answer (new numerator 101) over the denominator 8.

    Twelve and five eighths is one hundred one eighths.
  2. Conversion a mixed number 3 19/24 to a improper fraction: 3 19/24 = 3 19/24 = 3 · 24 + 19/24 = 72 + 19/24 = 91/24

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 24. Whole number 3 equally 3 * 24/24 = 72/24
    b) Add the answer from the previous step 72 to the numerator 19. New numerator is 72 + 19 = 91
    c) Write a previous answer (new numerator 91) over the denominator 24.

    Three and nineteen twenty-fourths is ninety-one twenty-fourths.
  3. Divide: 101/8 : 91/24 = 101/8 · 24/91 = 101 · 24/8 · 91 = 2424/728 = 8 · 303 /8 · 91 = 303/91
    Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 91/24 is 24/91) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 8 gives 303/91.
    In other words - one hundred one eighths divided by ninety-one twenty-fourths is three hundred three ninety-firsts.

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: July 13, 2024