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 informations.

The result:

5 1/4 + 3 2/5 = 173/20 = 8 13/20 = 8.65

The spelled result in words is one hundred seventy-three twentieths (or eight and thirteen twentieths).

How do we solve fractions step by step?

Conversion a mixed number 5 1/4 to a improper fraction: 5 1/4 = 5 1/4 = 5 · 4 + 1/4 = 20 + 1/4 = 21/4

To find a new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equally 5 * 4/4 = 20/4
b) Add the answer from the previous step 20 to the numerator 1. New numerator is 20 + 1 = 21
c) Write a previous answer (new numerator 21) over the denominator 4.

Five and one quarter is twenty-one quarters.
Conversion a mixed number 3 2/5 to a improper fraction: 3 2/5 = 3 2/5 = 3 · 5 + 2/5 = 15 + 2/5 = 17/5

To find a new numerator:
a) Multiply the whole number 3 by the denominator 5. Whole number 3 equally 3 * 5/5 = 15/5
b) Add the answer from the previous step 15 to the numerator 2. New numerator is 15 + 2 = 17
c) Write a previous answer (new numerator 17) over the denominator 5.

Three and two fifths is seventeen fifths.
Add: 21/4 + 17/5 = 21 · 5/4 · 5 + 17 · 4/5 · 4 = 105/20 + 68/20 = 105 + 68/20 = 173/20
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-one quarters plus seventeen fifths is one hundred seventy-three twentieths.

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.