Question

How do you write $10\dfrac{5}{{12}}$ as an improper equivalent function.

Answer 1

Hint: We will first right the general mixed fraction which is $a\dfrac{b}{c}$, then convert it to improper fraction which will be $\dfrac{{ca + b}}{c}$ and thus we have the answer.

Complete step by step answer:
We are given that we are required to convert $10\dfrac{5}{{12}}$ as an improper equivalent function.
We know that a general mixed fraction is given by $a\dfrac{b}{c}$, where a, b and c are natural numbers.
While we convert it to an improper fraction, we will have to take c times a and add b to it as the numerator and c as it is in the denominator.
Therefore, we will get $\dfrac{{ca + b}}{c}$ as the improper fraction which is equivalent to $a\dfrac{b}{c}$.
Replacing a by 10, b by 5 and c by 12 in the above equation, we will then obtain the following equation:-
So, the given mixed fraction $10\dfrac{5}{{12}}$ is equivalent to the improper fraction $\dfrac{{12 \times 10 + 5}}{{12}}$.
Simplifying the calculations in the numerator of the above equation, we will then obtain the following equation:-
So, the given mixed fraction $10\dfrac{5}{{12}}$ is equivalent to the improper fraction $\dfrac{{120 + 5}}{{12}}$.
Simplifying the calculations in the numerator of the above equation further, we will then obtain the following equation:-
So, the given mixed fraction $10\dfrac{5}{{12}}$ is equivalent to the improper fraction $\dfrac{{125}}{{12}}$.
Hence, the answer is $\dfrac{{125}}{{12}}$.

Note: Whenever you convert a mixed fraction into an improper fraction, you will no matter what the fraction is, always obtain an improper fraction.
The reason behind it is because whenever we convert a mixed fraction, in the numerator it will be c times a, which will be definitely greater than c and on top of it, we are adding b to it as well. Therefore, the numerator of the obtained fraction is always greater than the denominator of it.