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:

3 4/5 * 1 5/7 = 228/35 = 6 18/35 ≅ 6.5142857

The spelled result in words is two hundred twenty-eight thirty-fifths (or six and eighteen thirty-fifths).

How do we solve fractions step by step?

Conversion a mixed number 3 4/5 to a improper fraction: 3 4/5 = 3 4/5 = 3 · 5 + 4/5 = 15 + 4/5 = 19/5

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 4. New numerator is 15 + 4 = 19
c) Write a previous answer (new numerator 19) over the denominator 5.

Three and four fifths is nineteen fifths.
Conversion a mixed number 1 5/7 to a improper fraction: 1 5/7 = 1 5/7 = 1 · 7 + 5/7 = 7 + 5/7 = 12/7

To find a new numerator:
a) Multiply the whole number 1 by the denominator 7. Whole number 1 equally 1 * 7/7 = 7/7
b) Add the answer from the previous step 7 to the numerator 5. New numerator is 7 + 5 = 12
c) Write a previous answer (new numerator 12) over the denominator 7.

One and five sevenths is twelve sevenths.
Multiple: 19/5 * 12/7 = 19 · 12/5 · 7 = 228/35
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(228, 35) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - nineteen fifths multiplied by twelve sevenths is two hundred twenty-eight thirty-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.