Question

How do you write \[10\dfrac{1}{2}\] as an improper fraction?

Answer 1

Hint: Let us see how we write the mixed fraction given by $a\dfrac{b}{c}$ in an improper fraction form.
We keep the denominator the same as the given which is equal to c.
In the numerator, we first multiply a and c and then add b to its multiplied resultant.
Therefore, the mixed fraction $a\dfrac{b}{c}$ is written as $\dfrac{{ca + b}}{c}$.

Complete step-by-step answer:
Now, if we replace a by 10, b by 1 and c by 2, we will get the mixed fraction to be: \[10\dfrac{1}{2}\].
Now, if we write this in an improper fraction format, we will get: $\dfrac{{10 \times 2 + 1}}{2}$.
Now, if we simplify the calculations in the improper fraction, we will get $\dfrac{{20 + 1}}{2}$.
Simplifying the improper fraction we obtained in the last step further to obtain: $\dfrac{{21}}{2}$.

Thus, we have got: \[10\dfrac{1}{2} \equiv \dfrac{{21}}{2}\].

Note:
The students must note that we basically have a mixed fraction and we are converting it into an improper fraction using the technique mentioned above.
The students must also note that, whatever be the values of a, b and c in the mixed fraction $a\dfrac{b}{c}$, we will always obtain an improper fraction. Because if you thoroughly observe the numerator in the fraction we obtain that is equal to ca + b but the denominator is c. Since, a and b can be natural numbers only, so the product of c and a will definitely be greater than or equal to c, now we have added a to it. So, it will be strictly greater than c. Therefore, we will obtain an improper fraction whenever we convert a mixed fraction.