# 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:

### 54/7 ÷ 210/21 = 9/4 = 2 1/4 = 2.25

Spelled result in words is nine quarters (or two and one quarter).

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

1. Conversion a mixed number 5 4/7 to a improper fraction: 5 4/7 = 5 4/7 = 5 · 7 + 4/7 = 35 + 4/7 = 39/7

To find a new numerator:
a) Multiply the whole number 5 by the denominator 7. Whole number 5 equally 5 * 7/7 = 35/7
b) Add the answer from the previous step 35 to the numerator 4. New numerator is 35 + 4 = 39
c) Write a previous answer (new numerator 39) over the denominator 7.

Five and four sevenths is thirty-nine sevenths.
2. Conversion a mixed number 2 10/21 to a improper fraction: 2 10/21 = 2 10/21 = 2 · 21 + 10/21 = 42 + 10/21 = 52/21

To find a new numerator:
a) Multiply the whole number 2 by the denominator 21. Whole number 2 equally 2 * 21/21 = 42/21
b) Add the answer from the previous step 42 to the numerator 10. New numerator is 42 + 10 = 52
c) Write a previous answer (new numerator 52) over the denominator 21.

Two and ten twenty-firsts is fifty-two twenty-firsts.
3. Divide: 39/7 : 52/21 = 39/7 · 21/52 = 39 · 21/7 · 52 = 819/364 = 91 · 9 /91 · 4 = 9/4
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 52/21 is 21/52) 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 91 gives 9/4.
In other words - thirty-nine sevenths divided by fifty-two twenty-firsts is nine quarters.

#### 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
+plus signaddition 1/2 + 1/3
-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.