Fraction calculator

This fraction calculator performs all fraction operations - addition, subtraction, multiplication, division and evaluates expressions with fractions. It also shows detailed step-by-step information.

The result:

7 3/25 - 6 4/15 = 64/75 ≅ 0.8533333

The result spelled out in words is sixty-four seventy-fifths.

How do we solve fractions step by step?

Conversion a mixed number 7 3/25 to a 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 equally 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 a 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 equally 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, it cannot further simplify the fraction result by canceling.
In other words, one hundred seventy-eight twenty-fifths minus ninety-four fifteenths equals sixty-four seventy-fifths.

Rules for expressions with fractions:

Fractions - write a forward slash to separate the numerator and the denominator, i.e., for five-hundredths, enter 5/100. If you use mixed numbers, leave a space between the whole and fraction parts.

Mixed numerals (mixed numbers or fractions) - keep one space between the whole part and fraction and use a forward slash to input fraction i.e., 1 2/3 . A negative mixed fraction write for example as -5 1/2.
A slash is both a sign for fraction line and division, use a colon (:) for division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal dot . and they are automatically converted to fractions - i.e. 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)

The calculator follows well-known rules for the order of operations. The most common mnemonics for remembering this order are:

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 (brackets: `(){}`), Exponents, Multiplication, Division, Addition, Subtraction.
MDAS: Multiplication and Division (same precedence), Addition and Subtraction (same precedence). MDAS is a subset of PEMDAS.

Important Notes:
1. Multiplication/Division vs. Addition/Subtraction: Always perform multiplication and division *before* addition and subtraction.
2. Left-to-Right Rule: Operators with the same precedence (e.g., `+` and `-`, or `*` and `/`) must be evaluated from left to right.