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:

1 2/3 + 3 3/4 = 65/12 = 5 5/125.4166667

The spelled result in words is sixty-five twelfths (or five and five twelfths).

How do we solve fractions step by step?

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

    To find a new numerator:
    a) Multiply the whole number 1 by the denominator 3. Whole number 1 equally 1 * 3/3 = 3/3
    b) Add the answer from the previous step 3 to the numerator 2. New numerator is 3 + 2 = 5
    c) Write a previous answer (new numerator 5) over the denominator 3.

    One and two thirds is five thirds.
  2. Conversion a mixed number 3 3/4 to a improper fraction: 3 3/4 = 3 3/4 = 3 · 4 + 3/4 = 12 + 3/4 = 15/4

    To find a new numerator:
    a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/4 = 12/4
    b) Add the answer from the previous step 12 to the numerator 3. New numerator is 12 + 3 = 15
    c) Write a previous answer (new numerator 15) over the denominator 4.

    Three and three quarters is fifteen quarters.
  3. Add: 5/3 + 15/4 = 5 · 4/3 · 4 + 15 · 3/4 · 3 = 20/12 + 45/12 = 20 + 45/12 = 65/12
    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(3, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 4 = 12. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - five thirds plus fifteen quarters is sixty-five 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.


Last Modified: June 4, 2024