Question

(i) Provide the number in the box \[\square \], such that \[\dfrac{2}{5}\times \square =\dfrac{10}{30}\].
(ii) The simplest form of the numerator obtained in \[\square \] is _______.

Answer 1

Hint: Put \[\square \] as numerator and denominator. Take the entire numerator part of the expression and get the numerator of \[\square \]. Similarly take the entire denominator part and get the denominator of \[\square \]. Write them together to get the value of \[\square \].
Step- By-Step answer:
(i)We have been given, \[\dfrac{2}{5}\times \square =\dfrac{10}{30}\].
We need to find the fraction in the box such that the final answer becomes \[\dfrac{10}{30}\].
\[\dfrac{2}{5}\times \square =\dfrac{10}{30}\]
The \[\square \] = numerator / denominator – (1).
Thus we can write that, \[\dfrac{2}{3}\times \] numerator / denominator = \[\dfrac{10}{30}\] - (2).
Thus let us check the numerator parts of the above expression, equation (2).
\[2\times \] numerator = 10.
Thus numerator \[=\dfrac{10}{2}=5\].
Thus we got numerator = 5.
Now let us find the denominator of the expression by considering the denominator of equation (2).
\[\therefore 3\times \] denominator = 30.
\[\therefore \] denominator \[=\dfrac{30}{3}=10\].
Thus we got the denominator = 10.
Now let us substitute the values of numerator and denominator in equation (1).
\[\therefore \square \]= numerator / denominator = \[\dfrac{5}{10}\].
Thus \[\square \] = \[\dfrac{5}{10}\].
Now, let us check if our answer is right or not.
\[\dfrac{2}{5}\times \square =\dfrac{2}{5}\times \dfrac{5}{10}=\dfrac{10}{30}\]
Thus the answer is the same.
\[\therefore \square =\dfrac{5}{10}\]
Thus we got the required values.
(ii) We have been asked to find the simplest form of \[\square =\dfrac{5}{10}\].
Simplest form of \[\dfrac{5}{10}\]. Divide the numerator and denominator by 5. We get,
\[\dfrac{5\div 5}{10\div 5}=\dfrac{1}{2}\]
Thus the simplest form of \[\square =\dfrac{1}{2}\].
Thus we got, \[\square =\dfrac{5}{10}\].
The simplest form of \[\square =\dfrac{1}{2}\].

Note: We can also find the value of \[\square \] by using cross multiplication property.
\[\dfrac{2}{5}\times \square =\dfrac{10}{30}\]
\[\therefore \square =\dfrac{\dfrac{10}{30}}{\dfrac{2}{3}}=\dfrac{10}{30}\times \dfrac{3}{2}=\dfrac{5}{10}\]
Thus we got, \[\square =\dfrac{5}{10}\], which is the same as what we got earlier.