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:

7 2/3 + 2 1/5 = 148/15 = 9 13/15 ≅ 9.8666667

The spelled result in words is one hundred forty-eight fifteenths (or nine and thirteen fifteenths).

How do we solve fractions step by step?

Conversion a mixed number 7 2/3 to a improper fraction: 7 2/3 = 7 2/3 = 7 · 3 + 2/3 = 21 + 2/3 = 23/3

To find a new numerator:
a) Multiply the whole number 7 by the denominator 3. Whole number 7 equally 7 * 3/3 = 21/3
b) Add the answer from the previous step 21 to the numerator 2. New numerator is 21 + 2 = 23
c) Write a previous answer (new numerator 23) over the denominator 3.

Seven and two thirds is twenty-three thirds.
Conversion a mixed number 2 1/5 to a improper fraction: 2 1/5 = 2 1/5 = 2 · 5 + 1/5 = 10 + 1/5 = 11/5

To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/5 = 10/5
b) Add the answer from the previous step 10 to the numerator 1. New numerator is 10 + 1 = 11
c) Write a previous answer (new numerator 11) over the denominator 5.

Two and one fifth is eleven fifths.
Add: 23/3 + 11/5 = 23 · 5/3 · 5 + 11 · 3/5 · 3 = 115/15 + 33/15 = 115 + 33/15 = 148/15
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(3, 5) = 15. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 3 × 5 = 15. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - twenty-three thirds plus eleven fifths is one hundred forty-eight fifteenths.

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.