Question

Multiply the following and explain your answer in form of mixed fraction:
$3\times 5\dfrac{1}{5}$

Answer 1

Hint: Convert the expression to proper fraction i.e by multiplying the whole number part with the denominator of the fractional part and add it to the numerator and solve the expression. After solving don’t forget to convert it back to mixed fraction i.e by dividing the numerator by the denominator, the quotient becomes the whole number part, the remainder is the numerator of the mixed fraction and the denominator is the same as the proper fraction form.

Complete step-by-step answer:
First, let us see how to convert a mixed fraction to proper fraction:
For example: let us consider a mixed fraction: $a\dfrac{b}{c}$ . Here, $a$ is the whole number part and $\dfrac{b}{c}$ is the fractional part.
Now, to convert this to proper fraction we need to multiply the whole number part with the denominator of the fractional part and add it to the numerator.
So, converting we get,
\[a\dfrac{b}{c}=\dfrac{\left( c\times a \right)+b}{c}\]
Similarly, our question turns out to be:
$3\times 5\dfrac{1}{5}=3\times \left( \dfrac{\left( 5\times 5 \right)+1}{5} \right)=3\times \dfrac{\left( 25+1 \right)}{5}=3\times \dfrac{26}{5}=\dfrac{78}{5}$
Now, to convert it back to a mixed fraction, divide the numerator by the denominator, the quotient becomes the whole number part, the remainder is the numerator of the mixed fraction and the denominator is the same as the proper fraction form.
So, on dividing 78 by 5 we get 3 as remainder, 15 as the quotient and 5 is the denominator.
$\therefore 3\times 5\dfrac{1}{5}=\dfrac{78}{5}=15\dfrac{3}{5}$
Hence, the answer to the expression $3\times 5\dfrac{1}{5}$ is$\dfrac{78}{5}=15\dfrac{3}{5}$ .

Note: Alternately, you can break the mixed fraction as $a\dfrac{b}{c}$ = $a+\dfrac{b}{c}$ .
So, using this the alternate solution to our question can be:
$3\times 5\dfrac{1}{5}=3\times \left( 5+\dfrac{1}{5} \right)=15+\dfrac{3}{5}$
Now, while converting it to mixed fraction first convert the proper fraction part of addition to mixed one and then add the integer part of addition to the whole number part to get the answer.
So, on dividing 3 by 5 we get 3 as remainder, 0 as the quotient and 5 is the denominator. And 15 is the integer part in the addition, making the whole number part of mixed fraction=15+0=15.
\[\therefore 15+\dfrac{3}{5}=15\dfrac{3}{5}\]