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 2/3 ÷ 1 4/5 = 40/27 = 1 13/27 ≅ 1.4814815

Spelled out: forty twenty-sevenths (or one and thirteen twenty-sevenths).

How do we solve fractions step by step?

Conversion a mixed number 2 2/3 to an improper fraction: 2 2/3 = 2 2/3 = 2 · 3 + 2/3 = 6 + 2/3 = 8/3

To find a new numerator:
a) Multiply the whole number 2 by the denominator 3. Whole number 2 equals 2 ·3/3 = 6/3
b) Add the answer from the previous step 6 to the numerator 2. New numerator is 6 + 2 = 8
c) Write a previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds.
Conversion a mixed number 1 4/5 to an improper fraction: 1 4/5 = 1 4/5 = 1 · 5 + 4/5 = 5 + 4/5 = 9/5

To find a new numerator:
a) Multiply the whole number 1 by the denominator 5. Whole number 1 equals 1 ·5/5 = 5/5
b) Add the answer from the previous step 5 to the numerator 4. New numerator is 5 + 4 = 9
c) Write a previous answer (new numerator 9) over the denominator 5.

One and four fifths is nine fifths.
Divide: 8/3 : 9/5 = 8/3 · 5/9 = 8 · 5/3 · 9 = 40/27
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 9/5 is 5/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, eight thirds divided by nine fifths equals forty 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.