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:

86 14/24 + 7 13/24 = 753/8 = 94 1/8 = 94.125

The spelled result in words is seven hundred fifty-three eighths (or ninety-four and one eighth).

How do we solve fractions step by step?

Conversion a mixed number 86 14/24 to a improper fraction: 86 14/24 = 86 14/24 = 86 · 24 + 14/24 = 2064 + 14/24 = 2078/24

To find a new numerator:
a) Multiply the whole number 86 by the denominator 24. Whole number 86 equally 86 * 24/24 = 2064/24
b) Add the answer from the previous step 2064 to the numerator 14. New numerator is 2064 + 14 = 2078
c) Write a previous answer (new numerator 2078) over the denominator 24.

Eighty-six and fourteen twenty-fourths is two thousand seventy-eight twenty-fourths.
Conversion a mixed number 7 13/24 to a improper fraction: 7 13/24 = 7 13/24 = 7 · 24 + 13/24 = 168 + 13/24 = 181/24

To find a new numerator:
a) Multiply the whole number 7 by the denominator 24. Whole number 7 equally 7 * 24/24 = 168/24
b) Add the answer from the previous step 168 to the numerator 13. New numerator is 168 + 13 = 181
c) Write a previous answer (new numerator 181) over the denominator 24.

Seven and thirteen twenty-fourths is one hundred eighty-one twenty-fourths.
Add: 2078/24 + 181/24 = 2078 + 181/24 = 2259/24 = 3 · 753/3 · 8 = 753/8
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(24, 24) = 24. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 24 × 24 = 576. In the following intermediate step, cancel by a common factor of 3 gives 753/8.
In other words - two thousand seventy-eight twenty-fourths plus one hundred eighty-one twenty-fourths is seven hundred fifty-three 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

Symbol	Symbol name	Symbol Meaning	Example
+	plus sign	addition	1/2 + 1/3
-	minus sign	subtraction	1 1/2 - 2/3
*	asterisk	multiplication	*2/3 3/4**
×	times sign	multiplication	2/3 × 5/6
:	division sign	division	1/2 : 3
/	division slash	division	1/3 / 5
:	colon	complex fraction	1/2 : 1/3
^	caret	exponentiation / power	1/4^3
()	parentheses	calculate 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.