Question

How do you evaluate \[4\dfrac{2}{3}+112\]?

Answer 1

Hint: Assume the sum of given rational numbers as ‘E’. Now, convert the given mixed fraction into the improper fraction by using the relation: $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}$. In the next step take the L.C.M and simplify the sum to get the answer.

Complete step-by-step answer:
Here, we have been provided with the expression \[4\dfrac{2}{3}+112\] and we are asked to evaluate it. That means we have to add the two rational numbers and convert them into a single fraction.
Now, let us assume the given expression as ‘E’, so we have,
\[\Rightarrow E=4\dfrac{2}{3}+112\]
To take the sum of these rational numbers first we need to convert the given mixed fraction into the improper fraction. Now, any mixed fraction of the form $a\dfrac{b}{c}$ can be converted into an improper fraction by using the relation $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}$. Here, the denominator ‘c’ must not be 0 otherwise the fraction will become undefined. So we have,
$\begin{align}
  & \Rightarrow 4\dfrac{2}{3}=\dfrac{\left( 4\times 3 \right)+2}{3} \\
 & \Rightarrow 4\dfrac{2}{3}=\dfrac{12+2}{3} \\
 & \Rightarrow 4\dfrac{2}{3}=\dfrac{14}{3} \\
\end{align}$
Therefore, the given sum becomes:
\[\Rightarrow E=\dfrac{14}{3}+112\]
As we can see that there is nothing in the denominator of the number 112 so we can assume the denominator as 1, so we get,
\[\Rightarrow E=\dfrac{14}{3}+\dfrac{112}{1}\]
Now, we need to take the L.C.M of the denominators of the two fractions, clearly we can see that the numbers in the denominator of the two fractions are 1 and 3 whose L.C.M will be 3. Therefore, we get,
\[\begin{align}
  & \Rightarrow E=\dfrac{14+\left( 112\times 3 \right)}{3} \\
 & \Rightarrow E=\dfrac{14+336}{3} \\
 & \Rightarrow E=\dfrac{350}{3} \\
\end{align}\]
Hence, our answer is \[\dfrac{350}{3}\].

Note: You must know the conversion relation of a mixed fraction into an improper fraction otherwise it will be difficult to solve the above question. Note that the mixed fraction $a\dfrac{b}{c}$ is read as ‘a whole b divided by c’ and mathematically it is equivalent to the sum $a+\dfrac{b}{c}$. Here, the numbers in the denominator were small so it was easy to calculate the L.C.M, sometimes the numbers in the denominator of the fraction will be large so in such cases we need to use the prime factorization method to find the L.C.M.