Fraction Calculator

This fraction calculator performs all basic fraction operations – addition, subtraction, multiplication, and division – and evaluates expressions with fractions. Each calculation includes a detailed step-by-step explanation.

The result:

2 2/7 * 5 1/6 = 248/21 = 11 17/21 ≅ 11.8095238

Spelled out: two hundred forty-eight twenty-firsts (or eleven and seventeen twenty-firsts).

How do we solve fractions step by step?

Conversion a mixed number 2 2/7 to a improper fraction: 2 2/7 = 2 2/7 = 2 · 7 + 2/7 = 14 + 2/7 = 16/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 2. New numerator is 14 + 2 = 16
c) Write a previous answer (new numerator 16) over the denominator 7.

Two and two sevenths is sixteen sevenths.
Conversion a mixed number 5 1/6 to a improper fraction: 5 1/6 = 5 1/6 = 5 · 6 + 1/6 = 30 + 1/6 = 31/6

To find a new numerator:
a) Multiply the whole number 5 by the denominator 6. Whole number 5 equally 5 * 6/6 = 30/6
b) Add the answer from the previous step 30 to the numerator 1. New numerator is 30 + 1 = 31
c) Write a previous answer (new numerator 31) over the denominator 6.

Five and one sixth is thirty-one sixths.
Multiply: 16/7 * 31/6 = 16 · 31/7 · 6 = 496/42 = 248 · 2/21 · 2 = 248/21
Multiply both numerators and both denominators. Then simplify the resulting fraction to its lowest terms GCD(496, 42) = 2. In the following intermediate step, cancel by a common factor of 2 gives 248/21.
In other words, sixteen sevenths multiplied by thirty-one sixths equals two hundred forty-eight twenty-firsts.

Rules for expressions with fractions:

Fractions - Use a forward slash to separate the numerator and denominator. For example, for five-hundredths, enter 5/100.

Mixed numbers Leave one space between the whole number and the fraction part, and use a forward slash for the fraction. For example, enter 1 2/3 . For negative mixed numbers, write the negative sign before the whole number, such as -5 1/2.

Division of fractions - Since the forward slash is used for both fraction lines and division, use a colon (:) to divide fractions. For example, to divide 1/2 by 1/3, enter 1/2 : 1/3.

Decimals Enter decimal numbers using a decimal point (.), and they will be automatically converted to fractions. For example, enter 1.45.

Math Symbols

Op	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)

Order of Operations

Ever wondered why calculators don't just work left to right? This calculator follows the mathematical order of operations — a set of rules that ensures everyone solves expressions the same way, every time.

Popular Memory Tricks

Different regions use different mnemonics to remember this order:

* PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
* BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
* BODMAS - Brackets, Order (or "Of"), Division, Multiplication, Addition, Subtraction
* GEMDAS - Grouping symbols (parentheses, brackets, braces: (){}), Exponents, Multiplication, Division, Addition, Subtraction

The Golden Rules

Rule 1: Multiplication and division always come before addition and subtraction. Think of them as the VIPs that skip to the front of the line!

Rule 2: When operations have equal priority (like × and ÷, or + and −), work from left to right—just like reading a book.

Rule 3: Parentheses change the natural order of evaluation of operations.