Mixed Number to Improper Fraction || How to convert Mixed number into improper fraction

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

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

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

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

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