# 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:

### 92/5 ÷ 13/10 = 94/13 = 7 3/13 ≅ 7.2307692

Spelled result in words is ninety-four thirteenths (or seven and three thirteenths).

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

1. Conversion a mixed number 9 2/5 to a improper fraction: 9 2/5 = 9 2/5 = 9 · 5 + 2/5 = 45 + 2/5 = 47/5

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 the previous step 45 to the numerator 2. New numerator is 45 + 2 = 47
c) Write a previous answer (new numerator 47) over the denominator 5.

Nine and two fifths is forty-seven fifths.
2. Conversion a mixed number 1 3/10 to a improper fraction: 1 3/10 = 1 3/10 = 1 · 10 + 3/10 = 10 + 3/10 = 13/10

To find a new numerator:
a) Multiply the whole number 1 by the denominator 10. Whole number 1 equally 1 * 10/10 = 10/10
b) Add the answer from the previous step 10 to the numerator 3. New numerator is 10 + 3 = 13
c) Write a previous answer (new numerator 13) over the denominator 10.

One and three tenths is thirteen tenths.
3. Divide: 47/5 : 13/10 = 47/5 · 10/13 = 47 · 10/5 · 13 = 470/65 = 5 · 94 /5 · 13 = 94/13
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 13/10 is 10/13) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 5 gives 94/13.
In other words - forty-seven fifths divided by thirteen tenths is ninety-four thirteenths.

#### 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 be evaluated from left to right.