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:

4 1/6 + 2 3/4 = 83/12 = 6 11/126.9166667

The spelled result in words is eighty-three twelfths (or six and eleven twelfths).

How do we solve fractions step by step?

  1. Conversion a mixed number 4 1/6 to a improper fraction: 4 1/6 = 4 1/6 = 4 · 6 + 1/6 = 24 + 1/6 = 25/6

    To find a new numerator:
    a) Multiply the whole number 4 by the denominator 6. Whole number 4 equally 4 * 6/6 = 24/6
    b) Add the answer from the previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
    c) Write a previous answer (new numerator 25) over the denominator 6.

    Four and one sixth is twenty-five sixths.
  2. Conversion a mixed number 2 3/4 to a improper fraction: 2 3/4 = 2 3/4 = 2 · 4 + 3/4 = 8 + 3/4 = 11/4

    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 3. New numerator is 8 + 3 = 11
    c) Write a previous answer (new numerator 11) over the denominator 4.

    Two and three quarters is eleven quarters.
  3. Add: 25/6 + 11/4 = 25 · 2/6 · 2 + 11 · 3/4 · 3 = 50/12 + 33/12 = 50 + 33/12 = 83/12
    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(6, 4) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 4 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - twenty-five sixths plus eleven quarters is eighty-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.


Last Modified: July 22, 2024