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:

2.541 : 0.35 = 363/50 = 7 13/50 = 7.26

The spelled result in words is three hundred sixty-three fiftieths (or seven and thirteen fiftieths).

How do we solve fractions step by step?

Conversion a decimal number to a fraction: 2.541 = 2541/1000 = 2541/1000

a) Write down the decimal 2.541 divided by 1: 2.541 = 2.541/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
2.541/1 = 25.41/10 = 254.1/100 = 2541/1000
Note: 2541/1000 is called a decimal fraction.

c) Simplify and reduce the fraction
2541/1000 = 2541 * 1/1000 * 1 = 2541 * 1/1000 * 1
Conversion a decimal number to a fraction: 0.35 = 35/100 = 7/20

a) Write down the decimal 0.35 divided by 1: 0.35 = 0.35/1
b) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)
0.35/1 = 3.5/10 = 35/100
Note: 35/100 is called a decimal fraction.

c) Simplify and reduce the fraction
35/100 = 7 * 5/20 * 5 = 7 * 5/20 * 5 = 7/20
Divide: 2.541 / 0.35 = 2541/1000 · 20/7 = 2541 · 20/1000 · 7 = 50820/7000 = 140 · 363 /140 · 50 = 363/50
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 7/20 is 20/7) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 140 gives 363/50.
In other words - two thousand five hundred forty-one one-thousandths divided by seven twentieths is three hundred sixty-three fiftieths.

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.