Question

What is two third of half of 369?

Answer 1

Hint: Word ‘of’ in mathematical expression can be replaced by the multiplication sign i.e. ‘x’. So, replace ‘of’ by ‘x’ in the given expression. Replace ‘two third’ and half by the mathematical fractions of them. Get the answer in simplified fraction form by dividing numerator and denominator by a number which can divide both of them.

Complete step-by-step answer:
As we need to determine the value of the relation given as
Two third of half of 369 = ?
So, first of all we need to convert the given expression in words to mathematical relation. As we know, the meaning of the word ‘of’ in mathematics represents the sign of multiplication $\left( \times \right)$ between two numbers. So, we have two ‘of’ words in the given expression, so we need to put two $\left( '\times ' \right)$ multiplication signs between the numbers ‘of’ is present.
Now, we know that the word ‘half’ represents $\dfrac{1}{2}$ in mathematical expression and the word ‘two third’ will represent $\dfrac{2}{3}$ in mathematical terms. So, we can replace ‘two third’ by $\dfrac{2}{3}$ and ‘half’ by $\dfrac{1}{2}$ and the word ‘of’ by sign of multiplication $\left( '\times ' \right)$.
So, we can represent the expression in mathematical relation as
$\dfrac{2}{3}\times \dfrac{1}{2}\times 369$
Now, we can put the denominator of 369 as ‘1’ and multiply the denominators of fractions and numerator of fractions individually. So, we get expression as
$\dfrac{2\times 1\times 369}{3\times 2\times 1}=\dfrac{738}{6}$
Now, we know that the fraction of $\dfrac{738}{6}$ is not in the simplest form. We can convert it to the simplest form by dividing the numerator and denominator by 6 as both are divisible by 6. So, we get expression $\dfrac{738}{6}$ as
$\dfrac{738}{6}=123$
Hence, we get the answer as 123. It means two third of half of 369 $=123$

Note: One may go wrong if he/she uses any other sign $\left(\text {mathematical}, {{Ex}}:+,-,\div \right)$ in place of word ‘of’ except multiplication sign $\left( \times \right)$. So, knowing the term ‘of’ in mathematics is the key point of this question.
Another approach for this question would be that one can put multiplication sign after solving the expression between two numbers by replacing one ‘of’ by $'\times '$ one by one in following way:-
Replace second ‘of’ by $'\times '$, we get
$=$ two third of $\dfrac{1}{2}\times \dfrac{369}{1}$
$=$ two third of $\dfrac{369}{2}$
Replace of by $'\times '$ now again
$=\dfrac{2}{3}\times \dfrac{369}{2}=123$