# Calculator complex fractions

### 5/8 : 2 2/3 = 1564 = 0.234375

Spelled result in words is fifteen sixty-fourths.### How do you solve fractions step by step?

- Conversion a mixed number 2 23 to a improper fraction: 2 2/3 = 2 23 = 2 · 3 + 23 = 6 + 23 = 83

To find new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 33 = 63

b) Add the answer from previous step 6 to the numerator 2. New numerator is 6 + 2 = 8

c) Write previous answer (new numerator 8) over the denominator 3.

Two and two thirds is eight thirds - Divide: 58 : 83 = 58 · 38 = 5 · 38 · 8 = 1564

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 83 is 38) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step the fraction result cannot be further simplified by cancelling.

In words - five eighths divided by eight thirds = fifteen sixty-fourths.

### Calculate next expression:

#### Rules for expressions with fractions:

**Fractions**- use the slash “/” between the numerator and denominator, i.e. for five-hundredths enter

**5/100**. If you are using mixed numbers be sure to leave a single space between the whole number and fraction part.

The slash separates the numerator (number above a fraction line) and denominator (number below).

**Mixed numerals**(mixed fractions or mixed numbers) write as non-zero integer separated by one space and fraction i.e.,

**1 2/3**(having the same sign). An example of a negative mixed fraction:

**-5 1/2**.

Because slash is both signs for fraction line and division, we recommended use colon (:) as operator of division fractions i.e.,

**1/2 : 3**.

Decimals (decimal numbers) enter with a decimal point

**.**and they are automatically converted to fractions - i.e.

**1.45**.

Colon

**:**and slash

**/**is the symbol of division. Can be used to divide mixed numbers

**1 2/3 : 4 3/8**or can be used for write complex fractions i.e.

**1/2 : 1/3**.

An asterisk

*****or

**×**is the symbol for multiplication.

Plus

**+**is addition, minus sign

**-**is subtraction and

**()[]**is mathematical parentheses.

The exponentiation/power symbol is

**^**- for example:

**(7/8-4/5)^2**= (7/8-4/5)

^{2}

#### Examples:

• addition of fractions: 2/4 + 3/4• adds proper and improper fractions: 4/6+1/8

• adding fractions and mixed numbers: 8/5 + 6 2/7

• subtraction fractions: 2/3 - 1/2

• multiplying a fraction by another fraction - multiplication: 7/8 * 3/9

• division of fractions: 1/2 : 3/4

• dividing integer and fraction: 5 ÷ 1/2

• complex fractions: 5/8 : 2 2/3

• what is: 1/12 divided by 1/4

• converting a decimal to a fraction: 0.125 as a fraction

• 0.625 as a fraction

• comparing fractions: 1/4 2/3

• multiplying a fraction by a whole number: 6 * 3/4

• exponentiation of fraction: 3/5^3

• fractional exponents: 16 ^ 1/2

• square root of a fraction: sqrt(1/16)

• reducing or simplifying the fraction (simplification) - dividing the numerator and denominator of a fraction by the same non-zero number - equivalent fraction: 4/22

• mixed numbers and decimals: 1.5 - 1 1/5

• subtracting mixed number and fraction: 1 3/5 - 5/6

• operations with mixed fractions: 8 1/5 + 9 1/2

• expression with brackets: 1/3 * (1/2 - 3 3/8)

• convert a fraction to a percentage: 3/8 %

• conversion between fractions and decimals: 5/8

• compound fraction: 3/4 of 5/7

• fractions multiple: 2/3 of 3/5

• divide to find the quotient: 3/5 ÷ 2/3

• change decimal into a fraction : 3.875

• viral Japanese fraction problem (order of operations with fractions) : 9 - 3 ÷ 1/3 + 1

Calculator follows well-known rules for

**order of operations**. 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.

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.