# Fraction calculator

This fraction 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.

## The result:

### 73/25 - 64/15 = 64/75 ≅ 0.8533333

Spelled result in words is sixty-four seventy-fifths.

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

1. 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.
2. 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.
3. 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, identical) denominator for adding, subtracting, and comparing 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 is sixty-four seventy-fifths.

#### 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 sign 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 /) have the same priority and must evaluate from left to right.