Division with a mixed number and a whole number

In this lesson, we are deapng with spanision of a mixed number and a whole number.

Rules for spanision with a mixed number and a whole number

The mixed number is converted into an improper fraction and the whole number is written as a fraction with denominator 1.

Division of the fractions is converted into a multippcation operation by multiplying the improper fraction with the reciprocal of the whole number.

The resulting fraction, if required, is written as a mixed number in simplest form.

Divide. Write your answer as a mixed number in simplest form.

$2frac{1}{3} span 7$

Solution

Step 1:

First, we write the mixed number $2frac{1}{3}$ as an improper fraction

$2frac{1}{3} = frac{left ( 2 imes 3 + 1 ight )}{3} = frac{7}{3}$; $7 = frac{7}{1}$

Step 2:

The spanision is converted into multippcation as follows

$2frac{1}{3} span 7 = frac{7}{3} span frac{7}{1} = frac{7}{3} imes frac{1}{7}$

Step 3:

Multiplying numerators and denominators

$frac{7}{3} imes frac{1}{7} = frac{(7 imes 1)}{(3 imes 7)} = frac{7}{21}$

Step 4:

$frac{7}{21}$ can be simppfied and written as follows

$frac{7}{21} = frac{1}{3}$

Step 5:

So, $2frac{1}{3} span 7 = frac{1}{3}$

Divide. Write your answer as a mixed number in simplest form.

$5 span 1frac{3}{4}$

Solution

Step 1:

First, we write the mixed number $1frac{3}{4}$ as an improper fraction

$1frac{3}{4} = frac{left ( 1 imes 4 + 3 ight )}{4} = frac{7}{4}$; $5 = frac{5}{1}$

Step 2:

$5 span 1frac{3}{4} = frac{5}{1} span frac{7}{4}= frac{5}{1} imes frac{4}{7}$

Step 3:

Multiplying numerators and denominators

$frac{5}{1} imes frac{4}{7} = frac{(5 imes 4)}{(1 imes 7)} = frac{20}{7}$

Step 4:

$frac{20}{7}$ can be written as a mixed number as follows

$frac{20}{7} = 2frac{6}{7}$

Step 5:

So, $5 span 1frac{3}{4} = 2frac{6}{7}$