Fraction calculator

This 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 fraction value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

Result:

- 3/8 * -4/9 = 1/6 ≅ 0.1666667

Spelled result in words is one sixth.

How do you solve fractions step by step?

Unary minus: -3/8 = -3/8
Multiple: the result of step No. 1 * (-4) = -3/8 * (-4) = -3 · (-4)/8 · 1 = 12/8 = 3 · 4/2 · 4 = 3/2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 8) = 4. In the following intermediate step, cancel by a common factor of 4 gives 3/2.
In other words - minus three eighths multiplied by minus four = three halfs.
Divide: the result of step No. 2 : 9 = 3/2 : 9 = 3/2 · 1/9 = 3 · 1/2 · 9 = 3/18 = 3 · 1 /3 · 6 = 1/6
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 9/1 is 1/9) 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 3 gives 1/6.
In other words - three halfs divided by nine = one sixth.

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 are using mixed numbers, leave a space between the whole and fraction part.

Mixed numerals (mixed fractions or mixed numbers) 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 signs for fraction line and division, use 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
• exponentiation of fraction: 3/5^3
• 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) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22
• 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 /) has the same priority and then must evaluate from left to right.