Mixed numbers and improper fractions

In a nutshell 

A mixed number is a number which consists of a whole number and a proper fraction.  An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Example 1

Below are some examples of mixed numbers:

$$2\frac{1}{2}, 5\frac{1}{4}, 8\frac{3}{10}$$​​

Below are some examples of improper fractions:

$$\frac{13}{2}, \frac{7}{7}, \frac{27}{5}$$​​

​

Writing a mixed number as an improper fraction

procedure

Example 2

Convert the following mixed number into an improper fraction:

$$2\frac{7}{9}$$​​

Multiply the denominator and the whole number:

$$2 \times 9 = 18$$​​

Add the answer to the previous step to the numerator:

$$18+7 = 25$$​​

Write the answer to the previous step above the denominator.

$$\underline{\frac{25}{9}} (= 2\frac{7}{9})$$​​

Writing an improper fraction as a mixed number

procedure

Example 3

Convert the following improper fraction into a mixed number:

$$\frac{23}{7}$$​​

Divide the numerator by the denominator:

$$23 \div 7 = 3\thinspace R\thinspace2$$​

The whole number part is 3. The remainder is written over the original denominator.

$$\underline{3\frac{2}{7}}(=\frac{23}{7})$$​​

Note: The fraction part in this example cannot be simplified.