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:

163/8 - 95/8 = 27/4 = 6 3/4 = 6.75

The spelled result in words is twenty-seven quarters (or six and three quarters).

How do we solve fractions step by step?

1. Conversion a mixed number 16 3/8 to a improper fraction: 16 3/8 = 16 3/8 = 16 · 8 + 3/8 = 128 + 3/8 = 131/8

To find a new numerator:
a) Multiply the whole number 16 by the denominator 8. Whole number 16 equally 16 * 8/8 = 128/8
b) Add the answer from the previous step 128 to the numerator 3. New numerator is 128 + 3 = 131
c) Write a previous answer (new numerator 131) over the denominator 8.

Sixteen and three eighths is one hundred thirty-one eighths.
2. Conversion a mixed number 9 5/8 to a improper fraction: 9 5/8 = 9 5/8 = 9 · 8 + 5/8 = 72 + 5/8 = 77/8

To find a new numerator:
a) Multiply the whole number 9 by the denominator 8. Whole number 9 equally 9 * 8/8 = 72/8
b) Add the answer from the previous step 72 to the numerator 5. New numerator is 72 + 5 = 77
c) Write a previous answer (new numerator 77) over the denominator 8.

Nine and five eighths is seventy-seven eighths.
3. Subtract: 131/8 - 77/8 = 131 - 77/8 = 54/8 = 2 · 27/2 · 4 = 27/4
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(8, 8) = 8. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 8 × 8 = 64. In the following intermediate step, cancel by a common factor of 2 gives 27/4.
In other words - one hundred thirty-one eighths minus seventy-seven eighths is twenty-seven quarters.

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.