Fraction calculator



This fraction calculator performs all fraction operations and evaluates expressions with fractions. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps find value from multiple fraction operations with two, three, or more fractions and numbers in one expression.

The result:

2 5/12 + 3 8/12 = 73/12 = 6 1/126.0833333

The spelled result in words is seventy-three twelfths (or six and one twelfth).

How do we solve fractions step by step?

  1. Conversion a mixed number 2 5/12 to a improper fraction: 2 5/12 = 2 5/12 = 2 · 12 + 5/12 = 24 + 5/12 = 29/12

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 12. Whole number 2 equally 2 * 12/12 = 24/12
    b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
    c) Write a previous answer (new numerator 29) over the denominator 12.

    Two and five twelfths is twenty-nine twelfths.
  2. Conversion a mixed number 3 8/12 to a improper fraction: 3 8/12 = 3 8/12 = 3 · 12 + 8/12 = 36 + 8/12 = 44/12

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 12. Whole number 3 equally 3 * 12/12 = 36/12
    b) Add the answer from the previous step 36 to the numerator 8. New numerator is 36 + 8 = 44
    c) Write a previous answer (new numerator 44) over the denominator 12.

    Three and eight twelfths is forty-four twelfths.
  3. Add: 29/12 + 44/12 = 29 + 44/12 = 73/12
    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(12, 12) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 12 × 12 = 144. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - twenty-nine twelfths plus forty-four twelfths is seventy-three twelfths.

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.

Fractions in word problems:



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