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:

5 1/4 - 2 5/7 = 71/28 = 2 15/28 ≅ 2.5357143

Spelled out: seventy-one twenty-eighths (or two and fifteen twenty-eighths).

How do we solve fractions step by step?

Conversion a mixed number 5 1/4 to an improper fraction: 5 1/4 = 5 1/4 = 5 · 4 + 1/4 = 20 + 1/4 = 21/4

To find a new numerator:
a) Multiply the whole number 5 by the denominator 4. Whole number 5 equals 5 ·4/4 = 20/4
b) Add the answer from the previous step 20 to the numerator 1. New numerator is 20 + 1 = 21
c) Write a previous answer (new numerator 21) over the denominator 4.

Five and one quarter is twenty-one quarters.
Conversion a mixed number 2 5/7 to an improper fraction: 2 5/7 = 2 5/7 = 2 · 7 + 5/7 = 14 + 5/7 = 19/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equals 2 ·7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 5. New numerator is 14 + 5 = 19
c) Write a previous answer (new numerator 19) over the denominator 7.

Two and five sevenths is nineteen sevenths.
Subtract: 21/4 - 19/7 = 21 · 7/4 · 7 - 19 · 4/7 · 4 = 147/28 - 76/28 = 147 - 76/28 = 71/28
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(4, 7) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 7 = 28. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, twenty-one quarters minus nineteen sevenths equals seventy-one twenty-eighths.

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.