Question

Yesterday, \[\dfrac{7}{8}\] of the \[64\] students in a contest gave their speeches. How many students gave their speeches?

Answer 1

Hint: As we know that a fraction of some part gives the part which we want. Also, if we subtract \[1\] from fraction we will get a part left out. If we need to find some fraction of a whale then we need to perform cross multiplication.

Complete step by step solution:
As we know that \[\dfrac{7}{8}\] of the \[64\] students gave speeches. In mathematics, the ward ‘of’ is translated to “multiply”.
Thus the number of students who gave speeches \[=\dfrac{7}{8}\times 64\]
\[=\dfrac{448}{8}=56\].
Therefore, There were \[56\] students who gave speeches.

Additional information:
Alternate way,
No. of students gave speeches \[=64-\left( 1-\dfrac{7}{8} \right)\times 64\]
\[=64-\left( \dfrac{8-7}{8} \right)\times 64\]
\[=64-\dfrac{1}{8}\times 64\]
\[=64-8=56\]
Here, the alternative way is difficult to find an answer, but is an important concept of fraction.

Note: As we are dealing with proper fraction, therefore we must get the solution less than the total number of students. We can define formula as:-
No. of students gave speeches \[=\] total- [(\[1-\]fraction)\[\times \]Total]
Where, ‘Total’ is the total number of students.