Question

What is $\dfrac{9}{16}\cdot \dfrac{2}{3}$?

Answer 1

Hint: When we have to multiply two fractions we need to multiply their numerators to get the resultant numerator and multiply the denominators to get the resultant denominator.
Assume two fractions $\dfrac{a}{b}\cdot \dfrac{c}{d}$.
The numerators are $a,c$.
The denominators are $b,d$ .
Therefore, we have their multiplication as $\dfrac{ac}{bd}$ .
We can further simplify the fraction obtained if there are any common factors by representing them in the form of factors and cancelling the common terms.

Complete step by step answer:
Given,
$\dfrac{9}{16}\cdot \dfrac{2}{3}$
To find the value of $\dfrac{9}{16}\cdot \dfrac{2}{3}$
We have,
$\dfrac{9}{16}\cdot \dfrac{2}{3}$ …(1)
We multiply the numerators and denominators of the two fraction and the new fraction is as shown below:
$\dfrac{9\times 2}{16\times 3}$ …(2)
On multiplying the terms of numerator and denominator in equation (2)we get,
$\dfrac{18}{48}$ …(3)
Now we can represent the above equation in form of factors which are common to both numerator and denominator therefore we observe that the common factor is 6 hence the above equation (3) can be written as:
$\dfrac{3\times 6}{8\times 6}$ …(4)
Now we can eliminate the common term 6 from equation (4) we get,
$\dfrac{3}{8}$

Thus, we have $\dfrac{9}{16}\cdot \dfrac{2}{3}=\dfrac{3}{8}$

Note: There is another method to solve this question. We can skip the step of multiplying the numerator and denominator and directly look for the common factors in order to simplify the multiplication of two fractions.
$\dfrac{9}{16}\cdot \dfrac{2}{3}$ …(1)
Here we can see that 9 can be written as $9=3\times 3$ and $16=2\times 8$.
Thus, the equation (1) becomes:
$\dfrac{3\times 3}{2\times 8}\cdot \dfrac{2}{3}$ …(2)
Thus, we cancel the common terms in equation (2) we get:
$\dfrac{3}{8}$
Hence, we see that the answer obtained in both the cases is the same hence any method that is found convenient can be used.