Multippcation of a mixed number and a whole number

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

Rules for multiplying 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.

Multippcation of the fractions is carried out and simppfication if required is done.

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

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

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

Solution

Step 1:

First, we write the mixed number $2frac{1}{3}$ as an improper fraction and rewrite whole number 7 as fraction $frac{7}{1}$.

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

Step 2:

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

Step 3:

Multiplying numerators and denominators

$frac{7}{3} imes frac{7}{1} = frac{(7 imes 7)}{(3 imes 1)} = frac{49}{3}$

Step 4:

$frac{49}{3}$ can be written as a mixed number as follows

$frac{49}{3} = 16frac{1}{3}$

Step 5:

So, $2frac{1}{3} imes 7 = 16frac{1}{3}$

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

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

Solution

Step 1:

First, we write the mixed number $1frac{3}{4}$ as an improper fraction and rewrite the whole number 5 as a fraction $frac{5}{1}$.

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

Step 2:

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

Step 3:

Multiplying numerators and denominators

$frac{7}{4} imes frac{5}{1} = frac{(7 imes 5)}{(4 imes 1)} = frac{35}{4}$

Step 4:

$frac{35}{4}$ can be written as a mixed number as follows

$frac{35}{4} = 8frac{3}{4}$

Step 5:

So, $1frac{3}{4} imes 5 = 8frac{3}{4}$