Question

Identify the larger fraction between the fractions \[\dfrac{7}{{12}}\] and \[\dfrac{9}{{20}}\] by using Vedic mathematics.
A) \[\dfrac{7}{{12}}\]
B) \[\dfrac{9}{{20}}\]
B) Both are equal
D) None of these

Answer 1

Hint: To compare any two fractions \[\dfrac{a}{b},\dfrac{p}{q}\]. We have to do cross multiplication of both the fractions and have to compare the values found in the cross multiplication.

Complete step by step answer:
The given fractions are \[\dfrac{7}{{12}}\]and\[\dfrac{9}{{20}}\]. Now to find the larger fraction among the both we must do the cross multiplication of the two fractions first.
Let us consider the given fractions,
\[\dfrac{7}{{12}},\dfrac{9}{{20}}\]
Now we are going to cross multiply them . Now we are going to multiply$7$ with$20$and $9$with$12$.
$7 \times 20 = 140$
And
$9 \times 12 = 108$
By cross-multiplication we get two values they are $140$ and $108$ respectively,
Now let us compare the values which we have got in the cross multiplication.
It is clear that $140$ is greater than $108$
\[140 > 108\]
This will imply that
$7 \times 20 > 9 \times 12$
On further simplification of the multiplication we get the following result,
$\dfrac{7}{{12}} > \dfrac{9}{{20}}$
Therefore,
The larger fraction among the fractions \[\dfrac{7}{{12}}\] and \[\dfrac{9}{{20}}\]is\[\dfrac{7}{{12}}\].

Hence it is clear that the correct answer is option A, \[\dfrac{7}{{12}}\].

Additional information:
Vedic mathematics is a collection of Techniques/Sutras to solve mathematical arithmetic in an easy and faster way. It consists of 16 Sutras (Formulae) and 13 sub-sutras (Sub Formulae) which can be used for problems involved in arithmetic, algebra, geometry, calculus, conics.

Note:
It is easy to calculate the larger fraction; there is another method of simplification too.
That is we can simplify the fractions initially and then compare them,
First let us simplify the fraction\[\dfrac{7}{{12}}\]then we get \[\dfrac{7}{{12}} = 0.58333\].
Next let us simplify the fraction \[\dfrac{9}{{20}}\]then we get \[\dfrac{9}{{20}} = 0.45\].
Now let us compare the values of the fraction then we get,
\[0.58333 > 0.45\]
That is nothing but, $\dfrac{7}{{12}} > \dfrac{9}{{20}}$.
Hence we have found that the fraction \[\dfrac{7}{{12}}\] is larger than\[\dfrac{9}{{20}}\].
Therefore, option $(A)$ is the correct answer.