Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

The result:

51/6 * 22/7 = 248/21 = 11 17/21 ≅ 11.8095238

Spelled result in words is two hundred forty-eight twenty-firsts (or eleven and seventeen twenty-firsts).

How do we solve fractions step by step?

1. Conversion a mixed number 5 1/6 to a improper fraction: 5 1/6 = 5 1/6 = 5 · 6 + 1/6 = 30 + 1/6 = 31/6

To find a new numerator:
a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6
b) Add the answer from the previous step 30 to the numerator 1. New numerator is 30 + 1 = 31
c) Write a previous answer (new numerator 31) over the denominator 6.

Five and one sixth is thirty-one sixths.
2. Conversion a mixed number 2 2/7 to a improper fraction: 2 2/7 = 2 2/7 = 2 · 7 + 2/7 = 14 + 2/7 = 16/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 2. New numerator is 14 + 2 = 16
c) Write a previous answer (new numerator 16) over the denominator 7.

Two and two sevenths is sixteen sevenths.
3. Multiple: 31/6 * 16/7 = 31 · 16/6 · 7 = 496/42 = 248 · 2/21 · 2 = 248/21
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(496, 42) = 2. In the following intermediate step, cancel by a common factor of 2 gives 248/21.
In other words - thirty-one sixths multiplied by sixteen sevenths is two hundred forty-eight twenty-firsts.

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
-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.