Question

What is \[\dfrac{2}{3}\] of \[\dfrac{7}{8}\]?

Answer 1

Hint: From the given question we are asked to find that \[\dfrac{2}{3}\] of \[\dfrac{7}{8}\]. We are given a fraction which is of the form \[\dfrac{a}{b}\] and we know that \[\dfrac{a}{b}\] fraction of some value will be the multiplication of both. For solving this question we will use the basic operation in mathematics which is multiplication. After finding the product of the two that is both the given values we will simplify the answer by using the basic operation in mathematics which is division. So, we proceed with our solution as follows.

Complete step-by-step solution:
We are given the fraction \[\dfrac{2}{3}\] of the form \[\dfrac{a}{b}\].
We know that \[\dfrac{a}{b}\] fraction of value \[x\] formulae will be as follows.
\[\Rightarrow \dfrac{a}{b}\times x\]
By comparing the parameters given in the question to the above formula we get the values as follows.
\[\Rightarrow \dfrac{a}{b}=\dfrac{2}{3},x=\dfrac{7}{8}\]
Now we will substitute the values we got after comparing in the formulae. So, we get the equation reduced or simplified as follows.
\[\Rightarrow \dfrac{a}{b}\times x\]
\[\Rightarrow \dfrac{2}{3}\times \dfrac{7}{8}\]
Now we will multiply the numerator with the numerator and denominator with the denominator term. So, we get the expression reduced as follows.
\[\Rightarrow \dfrac{14}{24}\]
Now we will divide the both terms in denominator and numerator with the number two. So, we get the expression reduced as follows.
\[\Rightarrow \dfrac{\dfrac{14}{2}}{\dfrac{24}{2}}\]
\[\Rightarrow \dfrac{7}{12}\]
Therefore, the answer to the question is \[ \dfrac{7}{12}\].

Note: Students must understand the question very properly. We must do the calculation very accurately. We must know that \[\dfrac{a}{b}\] fraction of some value will be the multiplication of both values but not division of them. If we do division to those values instead of multiplication then our solution is not correct.