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:

6 1/4 + 9 4/5 = 321/20 = 16 1/20 = 16.05

The spelled result in words is three hundred twenty-one twentieths (or sixteen and one twentieth).

How do we solve fractions step by step?

Conversion a mixed number 6 1/4 to a improper fraction: 6 1/4 = 6 1/4 = 6 · 4 + 1/4 = 24 + 1/4 = 25/4

To find a new numerator:
a) Multiply the whole number 6 by the denominator 4. Whole number 6 equally 6 * 4/4 = 24/4
b) Add the answer from the previous step 24 to the numerator 1. New numerator is 24 + 1 = 25
c) Write a previous answer (new numerator 25) over the denominator 4.

Six and one quarter is twenty-five quarters.
Conversion a mixed number 9 4/5 to a improper fraction: 9 4/5 = 9 4/5 = 9 · 5 + 4/5 = 45 + 4/5 = 49/5

To find a new numerator:
a) Multiply the whole number 9 by the denominator 5. Whole number 9 equally 9 * 5/5 = 45/5
b) Add the answer from the previous step 45 to the numerator 4. New numerator is 45 + 4 = 49
c) Write a previous answer (new numerator 49) over the denominator 5.

Nine and four fifths is forty-nine fifths.
Add: 25/4 + 49/5 = 25 · 5/4 · 5 + 49 · 4/5 · 4 = 125/20 + 196/20 = 125 + 196/20 = 321/20
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, 5) = 20. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 5 = 20. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-five quarters plus forty-nine fifths is three hundred twenty-one twentieths.

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.