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:

10 5/7 - 5 2/3 = 106/21 = 5 1/21 ≅ 5.047619

The spelled result in words is one hundred six twenty-firsts (or five and one twenty-first).

How do we solve fractions step by step?

Conversion a mixed number 10 5/7 to a improper fraction: 10 5/7 = 10 5/7 = 10 · 7 + 5/7 = 70 + 5/7 = 75/7

To find a new numerator:
a) Multiply the whole number 10 by the denominator 7. Whole number 10 equally 10 * 7/7 = 70/7
b) Add the answer from the previous step 70 to the numerator 5. New numerator is 70 + 5 = 75
c) Write a previous answer (new numerator 75) over the denominator 7.

Ten and five sevenths is seventy-five sevenths.
Conversion a mixed number 5 2/3 to a improper fraction: 5 2/3 = 5 2/3 = 5 · 3 + 2/3 = 15 + 2/3 = 17/3

To find a new numerator:
a) Multiply the whole number 5 by the denominator 3. Whole number 5 equally 5 * 3/3 = 15/3
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 3.

Five and two thirds is seventeen thirds.
Subtract: 75/7 - 17/3 = 75 · 3/7 · 3 - 17 · 7/3 · 7 = 225/21 - 119/21 = 225 - 119/21 = 106/21
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(7, 3) = 21. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - seventy-five sevenths minus seventeen thirds is one hundred six twenty-firsts.

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.