Mixed fraction examples – Conversion to improper fractions

Mixed fraction examples

A fraction is a mixed fraction if it contains a whole number and a proper fraction. The value of this fraction is always greater than 1. A mixed fraction can also be written in the form of an improper fraction and vice-versa. Let us have a look at some mixed fraction examples.

Examples:

• 2 \frac{1}{7}
  2 is a whole number and \frac{1}{7} is a fraction.
  
  
• 1 \frac{2}{5}
  1 is a whole number and \frac{2}{5} is a fraction.
  
• 3 \frac{2}{35}

3 is a whole number and \frac{2}{35} is a fraction.

• 1 \frac{5}{6}

1 is a whole number and \frac{5}{6} is a fraction.

Converting mixed fraction into an improper fraction

A mixed fraction is written in the form of “ a\frac{b}{c}”,

a = whole number
b = numerator
c = denominator

The improper fraction form of this mixed fraction is written as  \frac{(a \times c)+b}{c}.

Converting improper fraction into a mixed fraction

An improper fraction is written in the form of \frac{p}{q}(\text { where } \mathrm{p}>\mathrm{q})

p = numerator
q = denominator

We have to then divide numerator by denominator.

Then the mixed fraction form of this improper fraction is written as \text { (Quotient } \frac{\text { Remainder }}{\text { Divisor }} \text { ) }

Solved Examples

1. Convert 1 \frac{1}{7} into an improper fraction.

Solution

• a = 1
• b = 1
• c = 7

Improper fraction form of 1 \frac{1}{7}= \frac{(a \times c)+b}{c}=\frac{(1 \times 7)+1}{7}=\frac{8}{7}.

2. Convert \frac{12}{5} into a mixed fraction

Solution

\frac{12}{5} is an improper fraction.

• p = 12
• q = 5

When we divide 12 by 5.

• Quotient = 2
• Remainder = 2
• Divisor = 5

Mixed fraction form of \frac{12}{5} =\text { Quotient } \frac{\text { Remainder }}{\text { Divisor }}=2 \frac{2}{5}.

3. Add 6 \frac{1}{5} \text { and } \frac{2}{5}.

Solution

First, we have to convert 6 \frac{1}{5} into an improper fraction.

\frac{2}{5} is already a proper fraction. 

Since denominators are the same, it will be easier to add them.

4. Subtract 1 \frac{1}{5} \text { from } \frac{9}{5} \text {. }

Solution

First, we have to convert 1 \frac{1}{5} into an improper fraction.

\frac{9}{5} is already an improper fraction. 

Since denominators are the same, it will be easier to add them.

5. Find the value of 3 \frac{1}{3}+\frac{2}{5}-1 \frac{1}{15}.

Solution

= \frac{10}{3}+\frac{2}{5}-\frac{16}{15}

= \frac{10 \times 5}{3 \times 5}+\frac{2 \times 3}{5 \times 3}-\frac{16}{15}

= \frac{50}{15}+\frac{6}{15}-\frac{16}{15}

= \frac{50+6-16}{15}=\frac{40}{15}=2 \frac{10}{15}=2 \frac{2}{3}