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 3/10 + 9 12/15 = 171/10 = 17 1/10 = 17.1

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

How do we solve fractions step by step?

Conversion a mixed number 7 3/10 to a improper fraction: 7 3/10 = 7 3/10 = 7 · 10 + 3/10 = 70 + 3/10 = 73/10

To find a new numerator:
a) Multiply the whole number 7 by the denominator 10. Whole number 7 equally 7 * 10/10 = 70/10
b) Add the answer from the previous step 70 to the numerator 3. New numerator is 70 + 3 = 73
c) Write a previous answer (new numerator 73) over the denominator 10.

Seven and three tenths is seventy-three tenths.
Conversion a mixed number 9 12/15 to a improper fraction: 9 12/15 = 9 12/15 = 9 · 15 + 12/15 = 135 + 12/15 = 147/15

To find a new numerator:
a) Multiply the whole number 9 by the denominator 15. Whole number 9 equally 9 * 15/15 = 135/15
b) Add the answer from the previous step 135 to the numerator 12. New numerator is 135 + 12 = 147
c) Write a previous answer (new numerator 147) over the denominator 15.

Nine and twelve fifteenths is one hundred forty-seven fifteenths.
Add: 73/10 + 147/15 = 73 · 3/10 · 3 + 147 · 2/15 · 2 = 219/30 + 294/30 = 219 + 294/30 = 513/30 = 3 · 171/3 · 10 = 171/10
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(10, 15) = 30. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 10 × 15 = 150. In the following intermediate step, cancel by a common factor of 3 gives 171/10.
In other words - seventy-three tenths plus one hundred forty-seven fifteenths is one hundred seventy-one 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.