Question

How do you write $11\dfrac{2}{3}$ into an improper fraction?

Answer 1

Hint: When we write a mixed fraction into an improper fraction, as we know, the denominator remains the same. But the numerator will become the sum of the numerator of the mixed fraction and the product of the whole number and the denominator of the mixed fraction.

Complete step by step solution:
Let us consider the given mixed fraction $11\dfrac{2}{3}.$
We are asked to write the given mixed fraction into an improper fraction.
We know that the mixed fraction and the corresponding improper fraction have the same denominator. So, we can say that the denominator of the improper fraction is also $3$ since it is the denominator of the given mixed fraction.
On the other hand, the numerator will become the sum of the numerator of the given mixed fraction and the product of the denominator and the whole number.
So, to convert the given mixed fraction into an improper fraction, we need to, first, multiply the denominator with the whole number.
Thus, we will get the product of the whole number and the denominator $11\times 3=33.$
Now, let us find the sum of the obtained product and the numerator of the mixed fraction.
As a result of the addition, we will get $33+2=35.$
Therefore, the numerator of the improper fraction will be $35.$

Hence the improper fraction that corresponds the given mixed fraction is $\dfrac{35}{3}.$

Note: An improper fraction is a fraction in which the numerator is greater than the denominator. A mixed fraction is a combination of a whole number and a proper fraction. The whole number is the quotient and the numerator is the remainder.