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:

7 3/25 - 6 4/15 = 64/75 ≅ 0.8533333

Spelled out: sixty-four seventy-fifths.

How do we solve fractions step by step?

Conversion a mixed number 7 3/25 to an improper fraction: 7 3/25 = 7 3/25 = 7 · 25 + 3/25 = 175 + 3/25 = 178/25

To find a new numerator:
a) Multiply the whole number 7 by the denominator 25. Whole number 7 equals 7 ·25/25 = 175/25
b) Add the answer from the previous step 175 to the numerator 3. New numerator is 175 + 3 = 178
c) Write a previous answer (new numerator 178) over the denominator 25.

Seven and three twenty-fifths is one hundred seventy-eight twenty-fifths.
Conversion a mixed number 6 4/15 to an improper fraction: 6 4/15 = 6 4/15 = 6 · 15 + 4/15 = 90 + 4/15 = 94/15

To find a new numerator:
a) Multiply the whole number 6 by the denominator 15. Whole number 6 equals 6 ·15/15 = 90/15
b) Add the answer from the previous step 90 to the numerator 4. New numerator is 90 + 4 = 94
c) Write a previous answer (new numerator 94) over the denominator 15.

Six and four fifteenths is ninety-four fifteenths.
Subtract: 178/25 - 94/15 = 178 · 3/25 · 3 - 94 · 5/15 · 5 = 534/75 - 470/75 = 534 - 470/75 = 64/75
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(25, 15) = 75. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 25 × 15 = 375. In the following intermediate step, the fraction cannot be simplified further by cancelling.
In other words, one hundred seventy-eight twenty-fifths minus ninety-four fifteenths equals sixty-four seventy-fifths.

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.