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:

4 1/9 - 3 3/5 = 23/45 ≅ 0.5111111

The spelled result in words is twenty-three forty-fifths.

How do we solve fractions step by step?

Conversion a mixed number 4 1/9 to a improper fraction: 4 1/9 = 4 1/9 = 4 · 9 + 1/9 = 36 + 1/9 = 37/9

To find a new numerator:
a) Multiply the whole number 4 by the denominator 9. Whole number 4 equally 4 * 9/9 = 36/9
b) Add the answer from the previous step 36 to the numerator 1. New numerator is 36 + 1 = 37
c) Write a previous answer (new numerator 37) over the denominator 9.

Four and one ninth is thirty-seven ninths.
Conversion a mixed number 3 3/5 to a improper fraction: 3 3/5 = 3 3/5 = 3 · 5 + 3/5 = 15 + 3/5 = 18/5

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 3. New numerator is 15 + 3 = 18
c) Write a previous answer (new numerator 18) over the denominator 5.

Three and three fifths is eighteen fifths.
Subtract: 37/9 - 18/5 = 37 · 5/9 · 5 - 18 · 9/5 · 9 = 185/45 - 162/45 = 185 - 162/45 = 23/45
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(9, 5) = 45. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 5 = 45. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - thirty-seven ninths minus eighteen fifths is twenty-three forty-fifths.

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.