Question

Multiply and express as a mixed fraction $3\dfrac{2}{5}\times 8$?

Answer 1

Hint: From the question we have been asked to multiply the $3\dfrac{2}{5}\times 8$ and the final answer should be expressed in the mixed fraction. To solve the above question first we have to convert $3\dfrac{2}{5}$ into a simple fraction then we have to multiply with the $8$ and again the final answer should be converted into the mixed fraction.

Complete step by step solution:
Mixed fraction means fraction represented with its quotient and remainder is a mixed fraction. For example, in the given question $3\dfrac{2}{5}$ is a mixed fraction, where 3 is the quotient, 2 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

From the question we have to multiply the
$\Rightarrow 3\dfrac{2}{5}\times 8$
First, we have to convert the $3\dfrac{2}{5}$ into the simple fraction.
Conversion of mixed fraction into simple fraction is
$\Rightarrow \dfrac{divisor\times quotient+remainder}{divisor}$
Here in the question the mixed fraction is $3\dfrac{2}{5}$.
$\Rightarrow divisor=5$
$\Rightarrow quotient=3$
$\Rightarrow remainder=2$
So, from the formula by substituting in their respective positions we will get
$\Rightarrow \dfrac{5\times 3+2}{5}$
$\Rightarrow \dfrac{15+2}{5}$
$\Rightarrow \dfrac{17}{5}$
Now we will multiply the above simple fraction with the $8$
By multiplying we will get,
$\Rightarrow \dfrac{17}{5}\times 8$
$\Rightarrow \dfrac{17\times 8}{5}$
$\Rightarrow \dfrac{136}{5}$
Again, we will have to convert this improper fraction into mixed fraction.
Now we have to divide $136$ with $5$,
by dividing we will get,
$\Rightarrow divisor=5$
$\Rightarrow quotient=27$
$\Rightarrow remainder=1$
From this three we can write mixed fraction is in the form,
$\Rightarrow quotient\dfrac{remainder}{divisor}$
$\Rightarrow 27\dfrac{1}{5}$
The final answer in mixed fraction is $27\dfrac{1}{5}$

Note: Students should know the definition of mixed fraction along with the mixed fraction students should know about the definition of proper fraction and improper fraction. Proper fraction means in this the denominator is greater than the numerator, for example $\dfrac{1}{5}$. Improper fraction means in this denominator is less than the numerator, for example $\dfrac{136}{5}$. Student should also know about the conversion of fraction to mixed fraction and vice versa.