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:

4 1/7 - 2 1/3 + 3/4 = 215/84 = 2 47/84 ≅ 2.5595238

Spelled out: two hundred fifteen eighty-fourths (or two and forty-seven eighty-fourths).

How do we solve fractions step by step?

Conversion a mixed number 4 1/7 to an improper fraction: 4 1/7 = 4 1/7 = 4 · 7 + 1/7 = 28 + 1/7 = 29/7

To find a new numerator:
a) Multiply the whole number 4 by the denominator 7. Whole number 4 equals 4 ·7/7 = 28/7
b) Add the answer from the previous step 28 to the numerator 1. New numerator is 28 + 1 = 29
c) Write a previous answer (new numerator 29) over the denominator 7.

Four and one seventh is twenty-nine sevenths.
Conversion a mixed number 2 1/3 to an improper fraction: 2 1/3 = 2 1/3 = 2 · 3 + 1/3 = 6 + 1/3 = 7/3

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 1. New numerator is 6 + 1 = 7
c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds.
Subtract: 29/7 - 7/3 = 29 · 3/7 · 3 - 7 · 7/3 · 7 = 87/21 - 49/21 = 87 - 49/21 = 38/21
It is suitable to adjust both fractions to a common (equal) denominator for subtracting fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 3) = 21. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 3 = 21. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, twenty-nine sevenths minus seven thirds equals thirty-eight twenty-firsts.
Add: the result of step No. 3 + 3/4 = 38/21 + 3/4 = 38 · 4/21 · 4 + 3 · 21/4 · 21 = 152/84 + 63/84 = 152 + 63/84 = 215/84
It is suitable to adjust both fractions to a common (equal) denominator for adding fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(21, 4) = 84. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 21 × 4 = 84. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, thirty-eight twenty-firsts plus three quarters equals two hundred fifteen eighty-fourths.

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.