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 2/3) : (3/2) = 34/9 = 3 7/93.7777778

The spelled result in words is thirty-four ninths (or three and seven ninths).

How do we solve fractions step by step?

  1. Conversion a mixed number 5 2/3 to a improper fraction: 5 2/3 = 5 2/3 = 5 · 3 + 2/3 = 15 + 2/3 = 17/3

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 3. Whole number 5 equally 5 * 3/3 = 15/3
    b) Add the answer from the previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
    c) Write a previous answer (new numerator 17) over the denominator 3.

    Five and two thirds is seventeen thirds.
  2. Divide: 17/3 : 3/2 = 17/3 · 2/3 = 17 · 2/3 · 3 = 34/9
    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 3/2 is 2/3) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - seventeen thirds divided by three halfs is thirty-four ninths.

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:



more math problems »