Question

How do you convert $7\dfrac{11}{12}$ to an improper fraction?

Answer 1

Hint: We first express the given fraction $7\dfrac{11}{12}$ as $7\dfrac{11}{12}=7+\dfrac{11}{12}$ . Then, after adding the two terms by assuming $7$ as $\dfrac{7}{1}$ and taking the LCM of $1$ and $12$ , we get our desired result.

Complete step-by-step solution:
Fractions are of various types. The three basic types of fractions are proper fractions, improper fractions and mixed fractions. Proper fractions are those whose numerator is less than its denominator, for example $\dfrac{11}{22}$ . Improper fractions are those whose numerator is greater than its denominator, for example $\dfrac{51}{2}$ . Mixed fractions are nothing but the improper fractions expressed as a whole number attached to a proper fraction, for example $3\dfrac{1}{2}$ is the mixed fraction corresponding to the improper fraction $\dfrac{10}{2}$ .
The given fraction is $7\dfrac{11}{12}$ . Clearly, it is a mixed fraction. It is asked to find the improper fraction corresponding to this mixed fraction. Now, by $7\dfrac{11}{12}$ , we mean that there are $7$ complete units along with an incomplete ${{\dfrac{11}{12}}^{th}}$ of an unit. This means, $7\dfrac{11}{12}$ can be expressed as
$7\dfrac{11}{12}=7+\dfrac{11}{12}$
We all know that a natural number can be expressed as a fraction with denominator $1$ . Similarly, $7$ can be expressed as $\dfrac{7}{1}$ . The mixed fraction thus becomes,
$\Rightarrow 7+\dfrac{11}{12}=\dfrac{7}{1}+\dfrac{11}{12}$
Since the denominators of the two fractions are not the same, we take the LCM of them, which is $12$ . The fractions can now be added as,
$\Rightarrow \dfrac{7}{1}+\dfrac{11}{12}=\dfrac{7\times 12}{12}+\dfrac{11}{12}$
Which becomes after simplification,
$\Rightarrow \dfrac{7}{1}+\dfrac{11}{12}=\dfrac{7\times 12}{12}+\dfrac{11}{12}=\dfrac{95}{12}$
Therefore, we can conclude that the improper fraction for the given mixed fraction $7\dfrac{11}{12}$ is $\dfrac{95}{12}$.

Note: We must be very careful while separating out the whole number of the mixed fraction and then adding it with the proper fraction, as most of the students directly add them without taking any LCM and this leads to wrong answers. A shortcut for solving mixed fractions to improper fractions is,
$a\dfrac{b}{c}=\dfrac{ac+b}{c}$