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:

2 1/4 + 5 7/8 = 65/8 = 8 1/8 = 8.125

The spelled result in words is sixty-five eighths (or eight and one eighth).

How do we solve fractions step by step?

  1. 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.
  2. Conversion a mixed number 5 7/8 to a improper fraction: 5 7/8 = 5 7/8 = 5 · 8 + 7/8 = 40 + 7/8 = 47/8

    To find a new numerator:
    a) Multiply the whole number 5 by the denominator 8. Whole number 5 equally 5 * 8/8 = 40/8
    b) Add the answer from the previous step 40 to the numerator 7. New numerator is 40 + 7 = 47
    c) Write a previous answer (new numerator 47) over the denominator 8.

    Five and seven eighths is forty-seven eighths.
  3. Add: 9/4 + 47/8 = 9 · 2/4 · 2 + 47/8 = 18/8 + 47/8 = 18 + 47/8 = 65/8
    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(4, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 8 = 32. In the following intermediate step, it cannot further simplify the fraction result by canceling.
    In other words - nine quarters plus forty-seven eighths is sixty-five eighths.

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