Multiplication of a mixed number and a whole number

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In this lesson, we are dealing with multiplication 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.

• Multiplication of the fractions is carried out and simplification if required is done.

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

$2\frac{1}{3} \times 7$

Solution

Step 1:

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

$2\frac{1}{3} = \frac{\left ( 2 \times 3 + 1 \right )}{3} = \frac{7}{3}$; $7 = \frac{7}{1}$

Step 2:

$2\frac{1}{3} \times 7 = \frac{7}{3} \times \frac{7}{1}$

Step 3:

Multiplying numerators and denominators

$\frac{7}{3} \times \frac{7}{1} = \frac{(7 \times 7)}{(3 \times 1)} = \frac{49}{3}$

Step 4:

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

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

Step 5:

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

$1\frac{3}{4} \times 5$

Solution

Step 1:

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

$1\frac{3}{4} = \frac{\left ( 1 \times 4 + 3 \right )}{4} = \frac{7}{4}$; $5 = \frac{5}{1}$

Step 2:

$1\frac{3}{4} \times 5 = \frac{7}{4} \times \frac{5}{1}$

Step 3:

Multiplying numerators and denominators

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

Step 4:

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

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

Step 5:

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