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:

3 56/34 - 5 1/2 = -29/34 ≅ -0.8529412

The spelled result in words is minus twenty-nine thirty-fourths.

How do we solve fractions step by step?

Conversion a mixed number 3 56/34 to a improper fraction: 3 56/34 = 3 56/34 = 3 · 34 + 56/34 = 102 + 56/34 = 158/34

To find a new numerator:
a) Multiply the whole number 3 by the denominator 34. Whole number 3 equally 3 * 34/34 = 102/34
b) Add the answer from the previous step 102 to the numerator 56. New numerator is 102 + 56 = 158
c) Write a previous answer (new numerator 158) over the denominator 34.

Three and fifty-six thirty-fourths is one hundred fifty-eight thirty-fourths.
Conversion a mixed number 5 1/2 to a improper fraction: 5 1/2 = 5 1/2 = 5 · 2 + 1/2 = 10 + 1/2 = 11/2

To find a new numerator:
a) Multiply the whole number 5 by the denominator 2. Whole number 5 equally 5 * 2/2 = 10/2
b) Add the answer from the previous step 10 to the numerator 1. New numerator is 10 + 1 = 11
c) Write a previous answer (new numerator 11) over the denominator 2.

Five and one half is eleven halfs.
Subtract: 158/34 - 11/2 = 158/34 - 11 · 17/2 · 17 = 158/34 - 187/34 = 158 - 187/34 = -29/34
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(34, 2) = 34. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 34 × 2 = 68. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - one hundred fifty-eight thirty-fourths minus eleven halfs is minus twenty-nine thirty-fourths.

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.