Question

Multiply and express $5 \times 6\dfrac{3}{4}$ as a mixed fraction.

Answer 1

Hint: In this question first we will convert the mixed fraction part into a proper fraction and then we will multiply the remaining integer part with the proper fraction. Now, after multiplying we will again convert the result into mixed fraction. So, by this method we will be able to find the answer to this question.

Complete step-by-step solution:
We have to express $5 \times 6\dfrac{3}{4}$ as a mixed fraction. We know that mixed fraction is the combination of whole numbers and a proper fraction.
The mixed fraction can be converted to a proper fraction by multiplying the whole number with the denominator and then adding that result to the numerator. Now, put the result in the numerator and the denominator will remain unchanged. Example: $1\dfrac{1}{5}$ can be converted into proper fraction by multiplying $1$ with $5$ and then add the result to numerator $1$ i.e. $1 \times 5 + 1 = 6$ . Now put this result i.e. $6$ in numerator and the denominator will remain unchanged. Therefore, the mixed fraction $1\dfrac{1}{5}$ can be written as a proper fraction $\dfrac{6}{5}$ . Now we can write the mixed fraction part of $5 \times 6\dfrac{3}{4}$ as:
$ \Rightarrow 5 \times \dfrac{{27}}{4}$
Now, do the multiplication in the above equation. Therefore, $5 \times \dfrac{{27}}{4}$ can be written as:
$ \Rightarrow \dfrac{{135}}{4}$
Now, we will convert $\dfrac{{135}}{4}$ into mixed fraction.
$ \Rightarrow \dfrac{{135}}{4} = 33\dfrac{3}{4}$

Hence, the mixed fraction of $5 \times 6\dfrac{3}{4}$ is $33\dfrac{3}{4}$.

Note: There are 3 types of fraction: Proper fractions, Improper fractions and Mixed fractions.Proper fraction is a part of whole. Improper fractions are greater than whole. An improper fraction written as the sum of a whole number and a proper fraction is known as Mixed Friction.Actually mixed friction is not a different friction it's just a friction which we are writing in a different way.
Fractions are useful to find out a part of a whole number and for distributions.