Fraction calculator

This fractions calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.

The result:

8 1/5 + 9 1/2 = 177/10 = 17 7/10 = 17.7

The spelled result in words is one hundred seventy-seven tenths (or seventeen and seven tenths).

How do we solve fractions step by step?

Conversion a mixed number 8 1/5 to a improper fraction: 8 1/5 = 8 1/5 = 8 · 5 + 1/5 = 40 + 1/5 = 41/5

To find a new numerator:
a) Multiply the whole number 8 by the denominator 5. Whole number 8 equally 8 * 5/5 = 40/5
b) Add the answer from the previous step 40 to the numerator 1. New numerator is 40 + 1 = 41
c) Write a previous answer (new numerator 41) over the denominator 5.

Eight and one fifth is forty-one fifths.
Conversion a mixed number 9 1/2 to a improper fraction: 9 1/2 = 9 1/2 = 9 · 2 + 1/2 = 18 + 1/2 = 19/2

To find a new numerator:
a) Multiply the whole number 9 by the denominator 2. Whole number 9 equally 9 * 2/2 = 18/2
b) Add the answer from the previous step 18 to the numerator 1. New numerator is 18 + 1 = 19
c) Write a previous answer (new numerator 19) over the denominator 2.

Nine and one half is nineteen halfs.
Add: 41/5 + 19/2 = 41 · 2/5 · 2 + 19 · 5/2 · 5 = 82/10 + 95/10 = 82 + 95/10 = 177/10
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(5, 2) = 10. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 2 = 10. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-one fifths plus nineteen halfs is one hundred seventy-seven tenths.

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and 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 whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . 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.