In this post we will learn how to convert mixed number to improper fraction.

Before learning the exact steps, let us review the concept of improper fraction and mixed number.

**What is Improper Fraction?**

Fraction number whose **numerator is greater than denominator** is called improper fraction (numerator > denominator)

Examples of improper fractions:

\mathtt{( a) \ \frac{60}{5}}\\\ \\ \mathtt{( b) \ \frac{6}{3}}\\\ \\ \mathtt{( c) \ \frac{2}{1}}\\\ \\ \mathtt{( d) \ \frac{7}{6}}\\\ \\ \mathtt{( e_{\ }) \ \frac{50}{49}}

Note that in all the above examples, numerator is greater than denominator.

**But why its called Improper?**

Generally fraction is considered to have value less than 1 and are considered “Proper”.

The fractions whose value is greater than 1 is considered “improper”.

**What is Mixed Number?**

Mixed number contain two components:

(a) A Whole number

(b) A fraction

Since it contains both categories of number, they are called ” Mixed Number” in mathematics.

Generally Mixed Number is represented as:

Where;

W is a Whole number and;

A/B is a fraction

Examples of Mixed Number:

\mathtt{( a) \ 1\frac{5}{6}}\\\ \\ \mathtt{( b) \ 2\frac{7}{9}}\\\ \\ \mathtt{( c) \ 1\frac{2}{6}}\\\ \\ \mathtt{( d) \ 3\frac{1}{2}}\\\ \\ \mathtt{( e_{\ }) \ 10\frac{5}{6}}

**Converting Mixed Number into Improper Fraction**

Let \mathtt{A\frac{B}{C}} be the given mixed number.

You can easily represent mixed number as improper fraction by following below steps:

(a) Multiply denominator with whole number; [C x A]

(b) Now add the number with numerator; [C x A] + B

(c) Express the number in fraction; \mathtt{\frac{( C\ x\ A) +B}{C}}

Hence, the formula for converting mixed number into improper fraction is expressed as:

Let us see some examples:

Example 01

Convert \mathtt{2\frac{3}{5}} into improper fraction.

**Solution**

Follow the below steps;

**(i) Multiply the whole number with denominator**

**(ii) Now add the numerator number**

**(iii) Retain the same denominator**

**Hence, 13/5 is the required fraction**.

**Example 02**

Convert the mixed number \mathtt{\ 6\frac{2}{3}} into improper fraction.

Solution

Follow the below steps;

**(a) Multiply whole number with denominator**

**(b) Add the numerator 2**

**(c) Retain the same denominator 3**

Hence, 20/3 is the required improper fraction.

**Example 03**

Convert the mixed number \mathtt{7\frac{4}{9}} into improper fraction.

**Solution**

Hence, 67/9 is the required fraction.

(04) Convert \mathtt{3\frac{1}{2}} into improper fraction.

\mathtt{\Longrightarrow \ \frac{( 2\ \times 3) +1}{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{6\ +\ 1}{2}}\\\ \\ \mathtt{\Longrightarrow \ \frac{7}{2}}

(05) Convert \mathtt{10\frac{3}{6}} into improper fraction

\mathtt{\Longrightarrow \ \frac{( 6\ \times 10) +3}{6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{60\ +\ 3}{6}}\\\ \\ \mathtt{\Longrightarrow \ \frac{63}{6}}

(06) Convert \mathtt{5\frac{1}{8}} into improper fraction

\mathtt{\Longrightarrow \ \frac{( 8\ \times 5) +1}{8}}\\\ \\ \mathtt{\Longrightarrow \ \frac{40\ +\ 1}{8}}\\\ \\ \mathtt{\Longrightarrow \ \frac{41}{8}}

(07) Convert \mathtt{1\frac{2}{9} \ }

\mathtt{\Longrightarrow \ \frac{( 9\ \times 1) +2}{9}}\\\ \\ \mathtt{\Longrightarrow \ \frac{9\ +\ 2}{9}}\\\ \\ \mathtt{\Longrightarrow \ \frac{11}{9}}

(08) Convert \mathtt{10\frac{11}{12} \ } into improper fraction

\mathtt{\Longrightarrow \ \frac{( 12\ \times 10) +11}{12}}\\\ \\ \mathtt{\Longrightarrow \ \frac{120\ +\ 11}{12}}\\\ \\ \mathtt{\Longrightarrow \ \frac{131}{12}}

**Why we convert the mixed number into improper fraction?**

We do this because algebraic expressions with mixed number is confusing and difficult to manage.

For example, consider the below expression:

\mathtt{1\ +\ 1\frac{1}{4}} \\\ \\ \mathtt{Out\ of\ confusion\ some\ calculate\ it\ as:}\\ \\ \mathtt{1\ +\ 1\ +\ \frac{1}{4} \ \ =\ \frac{9}{4}}\\\ \\ \mathtt{Others\ calculate\ it\ as:}\\ \\ \mathtt{1\ +\ \left( 1\times \frac{1}{4}\right) \ =\ \frac{5}{4}}

To avoid the complexity, its better to convert the number into fraction and do the rest of calculation.

\mathtt{1\ +\ \frac{5}{4} \ \ =\ \frac{9}{4}}

**Mixed Number to Improper Fraction – Practice Questions**

Convert the given mixed number into improper fraction

(a) \mathtt{1\frac{1}{3}} \\\ \\ Read Solution

\mathtt{\Longrightarrow \ \frac{( 3\ \times 1) +1}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{3\ +\ 1}{3}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{3}}

(b) \mathtt{3\frac{2}{7} \ } \\\ \\ Read Solution

\mathtt{\Longrightarrow \ \frac{( 7\ \times 3) +2}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{21\ +\ 2}{7}}\\\ \\ \mathtt{\Longrightarrow \ \frac{23}{7}}

(c) \mathtt{1\frac{3}{5}} \\\ \\ Read Solution

\mathtt{\Longrightarrow \ \frac{( 5\ \times \ 1) +3}{5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{5\ +\ 3}{5}}\\\ \\ \mathtt{\Longrightarrow \ \frac{8}{5}}

(d) \mathtt{3\frac{1}{11}} \\\ \\ Read Solution

\mathtt{\Longrightarrow \ \frac{( 11\ \times \ 3) +1}{11}}\\\ \\ \mathtt{\Longrightarrow \ \frac{33\ +\ 1}{11}}\\\ \\ \mathtt{\Longrightarrow \ \frac{34}{11}}

(e) \mathtt{2\frac{3}{15}} \\\ \\ Read Solution

\mathtt{\Longrightarrow \ \frac{( 15\ \times \ 2) +3}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{30\ +\ 3}{15}}\\\ \\ \mathtt{\Longrightarrow \ \frac{33}{15}}