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 1/6 * 2 2/7 * 7 1/5 = 480/7 = 68 4/7 ≅ 68.5714286

Spelled out: four hundred eighty sevenths (or sixty-eight and four sevenths).

How do we solve fractions step by step?

Conversion a mixed number 4 1/6 to a improper fraction: 4 1/6 = 4 1/6 = 4 · 6 + 1/6 = 24 + 1/6 = 25/6

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 1. New numerator is 24 + 1 = 25
c) Write a previous answer (new numerator 25) over the denominator 6.

Four and one sixth is twenty-five sixths.
Conversion a mixed number 2 2/7 to a improper fraction: 2 2/7 = 2 2/7 = 2 · 7 + 2/7 = 14 + 2/7 = 16/7

To find a new numerator:
a) Multiply the whole number 2 by the denominator 7. Whole number 2 equally 2 * 7/7 = 14/7
b) Add the answer from the previous step 14 to the numerator 2. New numerator is 14 + 2 = 16
c) Write a previous answer (new numerator 16) over the denominator 7.

Two and two sevenths is sixteen sevenths.
Multiply: 25/6 * 16/7 = 25 · 16/6 · 7 = 400/42 = 200 · 2/21 · 2 = 200/21
Multiply both numerators and both denominators. Then simplify the resulting fraction to its lowest terms GCD(400, 42) = 2. In the following intermediate step, cancel by a common factor of 2 gives 200/21.
In other words, twenty-five sixths multiplied by sixteen sevenths equals two hundred twenty-firsts.
Conversion a mixed number 7 1/5 to a improper fraction: 7 1/5 = 7 1/5 = 7 · 5 + 1/5 = 35 + 1/5 = 36/5

To find a new numerator:
a) Multiply the whole number 7 by the denominator 5. Whole number 7 equally 7 * 5/5 = 35/5
b) Add the answer from the previous step 35 to the numerator 1. New numerator is 35 + 1 = 36
c) Write a previous answer (new numerator 36) over the denominator 5.

Seven and one fifth is thirty-six fifths.
Multiply: the result of step No. 3 * 36/5 = 200/21 * 36/5 = 200 · 36/21 · 5 = 7200/105 = 480 · 15/7 · 15 = 480/7
Multiply both numerators and both denominators. Then simplify the resulting fraction to its lowest terms GCD(7200, 105) = 15. In the following intermediate step, cancel by a common factor of 15 gives 480/7.
In other words, two hundred twenty-firsts multiplied by thirty-six fifths equals four hundred eighty 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.