# What is a Mixed Number ? Understanding Mixed Fractions

## What is a Mixed Number?

It is a number made of two components; a whole number and a fraction.

Given below are some examples of mixed number.

### Parts of Mixed Fraction

As stated above the Mixed fraction consists of whole number and a fraction.

Below image describes the parts of Mixed Fraction.

### Why we use Mixed Fractions?

Mixed fractions are used for better representation of improper fraction.

Consider the improper fraction 7/5.

The fraction 7/5 does not give proper value of the number.
To get the value, you have to divide numerator and denominator which is time consuming.

The Mixed Fraction tells you the value of improper fraction in no time.

For example,

The mixed fraction equivalent of 7/5 is \mathtt{1\frac{2}{5}}

Here;
Whole number ⟹ 1
Fraction ⟹ 2/5

The mixed number can be represented as; 1 + 2/5

It tells that the number lies between 1 and 2 on the number line.

Hence, just looking at the whole number part you will have an idea about the value of mixed fraction.

Example 02
Approximate Value of Fraction \mathtt{12\frac{3}{4}}

Solution
Mixed fraction consists of whole number and fraction.

Whole Number ⟹ 12
Fraction ⟹ 3/4

The mixed number can be represented as; 12 + 3/4

Since the whole number part is 12, it means that value of mixed number lies between 12 and 13.

In practical life also, mixed numbers are easy to understand.

Look at the two statement;

Statement 01
” I ate \mathtt{2\frac{1}{2}} apples “

Statement 02
” I ate 5/2 apples “

The 1st statement is easy to understand as it tells that the person had ate 2 full apple and 1/2 part of another apple.

The 2nd statement is not that clear to understand.

Conclusion
Mixed Fraction helps you find the approximate value of number without doing any form of calculation.

## Finding exact value of Mixed Fraction

We have already learnt to find approximate value of mixed fraction.

Lt us now learn the method to find the exact value of the mixed fraction step by step.

Let \mathtt{a\frac{b}{c}} be the mixed fraction.

(a) Convert the mixed number into simple fraction.

Multiply the whole number with denominator and then add the numerator

Using the above method the mixed fraction will be converted into improper fraction.

(b) Now divide the numerator and denominator of the fraction to get the exact value.

Let us look at some of the examples;

Example 01
Find the value of fraction \mathtt{3\frac{1}{2}}

Solution

(a) Convert Mixed Fraction into simple fraction

(b) Divide the numerator and denominator of fraction to get the exact value.

Hence, 3.5 is the value of given mixed fraction \mathtt{3\frac{1}{2}}

Example 02
Find the value of mixed fraction \mathtt{9\frac{4}{5}}

Solution

(a) Convert Mixed fraction into simple fraction

The mixed fraction \mathtt{9\frac{4}{5}} is converted into fraction 49/5.

(b) Divide numerator and denominator of fraction.

Hence, 9.8 is the value of mixed fraction \mathtt{9\frac{4}{5}} .

## Questions on Mixed Fractions

(01) Find the approximate value of mixed fractions;

\mathtt{( i) \ 6\frac{5}{7} \ }\\\ \\ \mathtt{( ii) \ 11\frac{3}{2}}\\\ \\ \mathtt{( iii) \ 5\frac{4}{5}}\\\ \\ \mathtt{( iv) \ 16\ \frac{7}{11} \ }\\\ \\ \mathtt{( v) \ 22\frac{3}{4}}

Solution
\mathtt{( i) \ 6\frac{5}{7} \ }

We know that mixed number is made of whole number and fraction.

Whole number ⟹ 6
Fraction ⟹ 5/7

The fraction can be written as : 6 + 5/7

Hence, the value of mixed number is between 6 and 7.

\mathtt{( ii) \ 11\frac{3}{2}}

Whole number ⟹ 11
Fraction ⟹ 3/2

Mixed fraction can be represented as : 11 + 3/2

Hence, the value of mixed fraction is between 11 and 12.

\mathtt{( iii) \ 5\frac{4}{5}}

Whole number ⟹ 5
Fraction ⟹ 4/5

The mixed fraction can be represented as: 5 + 4/5

Hence, the value of mixed fraction is between 5 and 6.

\mathtt{( iv) \ 16\ \frac{7}{11}}

Whole number ⟹ 16
Fraction ⟹ 7/11

Mixed fraction can be represented as: 16 + 7/11

Hence, the value of mixed fraction is between 16 and 17.

\mathtt{( v) \ 22\frac{3}{4}}

Whole number ⟹ 22
Fraction ⟹ 3/4

Mixed fraction can be represented as: 22 + 3/4

Hence, the value of fraction is between 22 and 23.

(02) Find the exact value of below mixed fraction

\mathtt{( i) \ 4\frac{3}{5} \ }\\\ \\ \mathtt{( ii) \ 6\frac{9}{10}}\\\ \\ \mathtt{( iii) \ 5\frac{2}{7}}

Solution

\mathtt{( i) \ 4\frac{3}{5} \ }

(i) Convert the Mixed fraction into simple fraction.

The mixed fraction is converted into 23/5

(ii) Divide numerator with denominator to find exact value.

Hence, 4.6 is the value of mixed fraction

\mathtt{( ii) \ 6\frac{9}{10}}

(a) Convert the mixed fraction into simple fraction

(b) Divide the numerator and denominator.

Hence, 6.9 is the value of fraction

\mathtt{( iii) \ 5\frac{2}{7}}

Solution
(a) Convert mixed fraction into simple fraction.

(b) Divide numerator and denominator of the fraction

Hence, 5.29 is the value of mixed fraction