# Fraction calculator

This calculator performs basic and advanced fraction operations, expressions with fractions combined with integers, decimals, and mixed numbers. It also shows detailed step-by-step information about the fraction calculation procedure. The calculator helps in finding value from multiple fractions operations. Solve problems with two, three, or more fractions and numbers in one expression.

## Result:

### 93/5 - 77/15 = 32/15 = 2 2/15 ≅ 2.1333333

Spelled result in words is thirty-two fifteenths (or two and two fifteenths).

### How do we solve fractions step by step?

1. Conversion a mixed number 9 3/5 to a improper fraction: 9 3/5 = 9 3/5 = 9 · 5 + 3/5 = 45 + 3/5 = 48/5

To find a new numerator:
a) Multiply the whole number 9 by the denominator 5. Whole number 9 equally 9 * 5/5 = 45/5
b) Add the answer from previous step 45 to the numerator 3. New numerator is 45 + 3 = 48
c) Write a previous answer (new numerator 48) over the denominator 5.

Nine and three fifths is forty-eight fifths
2. Conversion a mixed number 7 7/15 to a improper fraction: 7 7/15 = 7 7/15 = 7 · 15 + 7/15 = 105 + 7/15 = 112/15

To find a new numerator:
a) Multiply the whole number 7 by the denominator 15. Whole number 7 equally 7 * 15/15 = 105/15
b) Add the answer from previous step 105 to the numerator 7. New numerator is 105 + 7 = 112
c) Write a previous answer (new numerator 112) over the denominator 15.

Seven and seven fifteenths is one hundred twelve fifteenths
3. Subtract: 48/5 - 112/15 = 48 · 3/5 · 3 - 112/15 = 144/15 - 112/15 = 144 - 112/15 = 32/15
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 15) = 15. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 5 × 15 = 75. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - forty-eight fifths minus one hundred twelve fifteenths is thirty-two fifteenths.

#### Rules for expressions with fractions:

Fractions - use a forward slash to divide the numerator by 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 integer and
fraction and use a forward slash to input fractions i.e., 1 2/3 . An example of a negative mixed fraction: -5 1/2.
Because slash is both signs for fraction line and division, use a colon (:) as the operator of division fractions i.e., 1/2 : 1/3.
Decimals (decimal numbers) enter with a decimal point . and they are automatically converted to fractions - i.e. 1.45.

### Math Symbols

SymbolSymbol nameSymbol MeaningExample
-minus signsubtraction 1 1/2 - 2/3
*asteriskmultiplication 2/3 * 3/4
×times signmultiplication 2/3 × 5/6
:division signdivision 1/2 : 3
/division slashdivision 1/3 / 5
:coloncomplex fraction 1/2 : 1/3
^caretexponentiation / power 1/4^3
()parenthesescalculate 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 of operations are:
PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
BEDMAS - Brackets, Exponents, Division, Multiplication, Addition, Subtraction
BODMAS - Brackets, Of or Order, Division, Multiplication, Addition, Subtraction.
GEMDAS - Grouping Symbols - brackets (){}, Exponents, Multiplication, Division, Addition, Subtraction.
MDAS - Multiplication and Division have the same precedence over Addition and Subtraction. The MDAS rule is the order of operations part of the PEMDAS rule.
Be careful; always do multiplication and division before addition and subtraction. Some operators (+ and -) and (* and /) has the same priority and then must evaluate from left to right.