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:

8 5/6 ÷ 2 1/4 = 106/27 = 3 25/27 ≅ 3.9259259

Spelled out: one hundred six twenty-sevenths (or three and twenty-five twenty-sevenths).

How do we solve fractions step by step?

Conversion a mixed number 8 5/6 to an improper fraction: 8 5/6 = 8 5/6 = 8 · 6 + 5/6 = 48 + 5/6 = 53/6

To find a new numerator:
a) Multiply the whole number 8 by the denominator 6. Whole number 8 equals 8 ·6/6 = 48/6
b) Add the answer from the previous step 48 to the numerator 5. New numerator is 48 + 5 = 53
c) Write a previous answer (new numerator 53) over the denominator 6.

Eight and five sixths is fifty-three sixths.
Conversion a mixed number 2 1/4 to an improper fraction: 2 1/4 = 2 1/4 = 2 · 4 + 1/4 = 8 + 1/4 = 9/4

To find a new numerator:
a) Multiply the whole number 2 by the denominator 4. Whole number 2 equals 2 ·4/4 = 8/4
b) Add the answer from the previous step 8 to the numerator 1. New numerator is 8 + 1 = 9
c) Write a previous answer (new numerator 9) over the denominator 4.

Two and one quarter is nine quarters.
Divide: 53/6 : 9/4 = 53/6 · 4/9 = 53 · 4/6 · 9 = 212/54 = 2 · 106 /2 · 27 = 106/27
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 9/4 is 4/9) 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 2 gives 106/27.
In other words, fifty-three sixths divided by nine quarters equals one hundred six twenty-sevenths.

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

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)

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.