# Dividing Fractions with mixed Number

In this post we will learn to divide fractions with mixed numbers.

## How to divide fractions with mixed numbers?

To divide the numbers follow the below steps;

(a) Convert mixed number into simple fraction

(b) Convert division into multiplication by taking reciprocal of divisor fraction.

(c) Multiply numerator and denominator separately.

(d) If possible, simplify the fraction.

Given below are examples for further understanding.

Example 01
Divide \mathtt{\frac{2}{5} \ \div \ 2\frac{1}{3}}

Solution

(a) Convert mixed fraction into simple fraction

The mixed fraction is converted into simple fraction 7/3.

Now the fraction can be written as;

(b) Convert the division into multiplication by taking reciprocal of devisor.

Here the fraction 7/3 is a divisor, taking its reciprocal we get ;

(c) Multiply the numerator and denominator separately.

Hence, fraction 6/35 is the solution.

Example 02
Multiply the fraction, \mathtt{\frac{8}{24} \ \div \ 3\frac{4}{6}}

Solution

(a) Convert the mixed number into simple fraction.

The mixed number is converted into fraction 22/6

Now the division can be written as;

(b) Convert the division into multiplication by taking reciprocal of divisor.

(c) Multiply the numerator and denominator separately.

⟹ Number 8 in numerator can divide 24 in denominator leaving 3 as quotient.

Number 3 in denominator can divide 6 in numerator leaving 2 as quotient.

Number 2 in numerator can divide 22 in denominator leaving 11 as quotient.

After all the simplification we get;

Hence, 1/11 is the solution of given multiplication.

Example 03
Multiply \mathtt{5\frac{2}{7} \ \div \ \frac{4}{35}}

Solution

(a) Convert mixed number into simple fraction

The division can be represented as;

(b) Converting division into multiplication by taking reciprocal of divisor

Here fraction 4/35 is the divisor.

(c) Multiply the numerator and denominator separately.

Number 7 in denominator can divide 35 in numerator leaving 5 as quotient.

Multiplying the remaining numbers we get;

Hence, 18/4 is the solution.

Example 04
Multiply \mathtt{11\frac{1}{3} \ \div \ \frac{4}{15}}

Solution

(a) Convert the mixed number into simple fraction.

The division can be represented as;

(b) Convert the division into multiplication by taking reciprocal of divisor.

(c) Multiply the numerators and denominator separately.

Number 3 in denominator can divide 15 in numerator leaving 5 as quotient.

34 in numerator and 4 in denominator are both divisible by 2 leaving quotient 17 and 2 respectively.

Dividing numerator and denominator by 2 we get;

Multiplying the remaining number we get;

Hence, 85/2 is the final solution.

Example 05
Divide the fractions, \mathtt{6\frac{1}{2} \ \div \ \frac{13}{2}}

Solution

(a) Convert the mixed number into fraction.

\mathtt{\ 6\frac{1}{2} \ =\ \frac{2.6\ +1}{2} \ =\ \frac{13}{2}}

The division can be represented as;

\mathtt{\frac{13}{2} \ \div \ \frac{13}{2}}

(b) Convert division into multiplication by taking reciprocal of divisor.

\mathtt{\frac{13}{2} \ \div \ \frac{13}{2} \ =\frac{13}{2} \ \times \frac{2}{13}}

Cancel out 13 and 2 from numerator and denominator.

\mathtt{\Longrightarrow \ \frac{\cancel{13}}{\cancel{2}} \ \times \frac{\cancel{2}}{\cancel{13}}}\\\ \\ \mathtt{\Longrightarrow \ 1\ \ }

Hence for above division, we get 1 as solution.