Fraction calculator

This fraction calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

The result:

17 4/9 - 12 2/3 = 43/9 = 4 7/9 ≅ 4.7777778

Spelled result in words is forty-three ninths (or four and seven ninths).

How do we solve fractions step by step?

Conversion a mixed number 17 4/9 to a improper fraction: 17 4/9 = 17 4/9 = 17 · 9 + 4/9 = 153 + 4/9 = 157/9

To find a new numerator:
a) Multiply the whole number 17 by the denominator 9. Whole number 17 equally 17 * 9/9 = 153/9
b) Add the answer from the previous step 153 to the numerator 4. New numerator is 153 + 4 = 157
c) Write a previous answer (new numerator 157) over the denominator 9.

Seventeen and four ninths is one hundred fifty-seven ninths.
Conversion a mixed number 12 2/3 to a improper fraction: 12 2/3 = 12 2/3 = 12 · 3 + 2/3 = 36 + 2/3 = 38/3

To find a new numerator:
a) Multiply the whole number 12 by the denominator 3. Whole number 12 equally 12 * 3/3 = 36/3
b) Add the answer from the previous step 36 to the numerator 2. New numerator is 36 + 2 = 38
c) Write a previous answer (new numerator 38) over the denominator 3.

Twelve and two thirds is thirty-eight thirds.
Subtract: 157/9 - 38/3 = 157/9 - 38 · 3/3 · 3 = 157/9 - 114/9 = 157 - 114/9 = 43/9
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, 3) = 9. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 9 × 3 = 27. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one hundred fifty-seven ninths minus thirty-eight thirds is forty-three ninths.

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)

Examples:

• adding fractions: 2/4 + 3/4
• subtracting fractions: 2/3 - 1/2
• multiplying fractions: 7/8 * 3/9
• dividing Fractions: 1/2 : 3/4
• reciprocal of a fraction: 1 : 3/4
• square of a fraction: 2/3^2
• cube of a fraction: 2/3^3
• exponentiation of a fraction: 1/2^4
• fractional exponents: 16 ^ 1/2
• adding fractions and mixed numbers: 8/5 + 6 2/7
• dividing integer and fraction: 5 ÷ 1/2
• complex fractions: 5/8 : 2 2/3
• decimal to fraction: 0.625
• Fraction to Decimal: 1/4
• Fraction to Percent: 1/8 %
• comparing fractions: 1/4 2/3
• multiplying a fraction by a whole number: 6 * 3/4
• square root of a fraction: sqrt(1/16)
• reducing or simplifying the fraction (simplification) : 4/22 - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction
• expression with brackets: 1/3 * (1/2 - 3 3/8)
• compound fraction: 3/4 of 5/7
• fractions multiple: 2/3 of 3/5
• divide to find the quotient: 3/5 ÷ 2/3

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 evaluate from left to right.