Fraction calculator



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

The result:

1/3 * 3/5 * 2 1/4 = 9/20 = 0.45

The spelled result in words is nine twentieths.

How do we solve fractions step by step?

  1. Multiple: 1/3 * 3/5 = 1 · 3/3 · 5 = 3/15 = 1 · 3/5 · 3 = 1/5
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 15) = 3. In the following intermediate step, cancel by a common factor of 3 gives 1/5.
    In other words - one third multiplied by three fifths is one fifth.
  2. Conversion a mixed number 2 1/4 to a improper fraction: 2 1/4 = 2 1/4 = 2 · 4 + 1/4 = 8 + 1/4 = 9/4

    To find a new numerator:
    a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/4 = 8/4
    b) Add the answer from the previous step 8 to the numerator 1. New numerator is 8 + 1 = 9
    c) Write a previous answer (new numerator 9) over the denominator 4.

    Two and one quarter is nine quarters.
  3. Multiple: the result of step No. 1 * 9/4 = 1/5 * 9/4 = 1 · 9/5 · 4 = 9/20
    Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(9, 20) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - one fifth multiplied by nine quarters is nine twentieths.

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: October 9, 2024