Fraction Calculator

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

The result:

9 1/4 - 4 5/6 = 53/12 = 4 5/12 ≅ 4.4166667

Spelled out: fifty-three twelfths (or four and five twelfths).

How do we solve fractions step by step?

Conversion a mixed number 9 1/4 to a improper fraction: 9 1/4 = 9 1/4 = 9 · 4 + 1/4 = 36 + 1/4 = 37/4

To find a new numerator:
a) Multiply the whole number 9 by the denominator 4. Whole number 9 equally 9 * 4/4 = 36/4
b) Add the answer from the previous step 36 to the numerator 1. New numerator is 36 + 1 = 37
c) Write a previous answer (new numerator 37) over the denominator 4.

Nine and one quarter is thirty-seven quarters.
Conversion a mixed number 4 5/6 to a improper fraction: 4 5/6 = 4 5/6 = 4 · 6 + 5/6 = 24 + 5/6 = 29/6

To find a new numerator:
a) Multiply the whole number 4 by the denominator 6. Whole number 4 equally 4 * 6/6 = 24/6
b) Add the answer from the previous step 24 to the numerator 5. New numerator is 24 + 5 = 29
c) Write a previous answer (new numerator 29) over the denominator 6.

Four and five sixths is twenty-nine sixths.
Subtract: 37/4 - 29/6 = 37 · 3/4 · 3 - 29 · 2/6 · 2 = 111/12 - 58/12 = 111 - 58/12 = 53/12
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, 6) = 12. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 4 × 6 = 24. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words, thirty-seven quarters minus twenty-nine sixths equals fifty-three twelfths.

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.