Question

What is $\dfrac{2}{3}\times \dfrac{7}{8}$?

Answer 1

Hint: Assume the given product of the two fractions as E. Now to simplify the value of E, first check if there are any common factors in the numerator and denominator. If there are then cancel them and simplify the fraction. After cancelling the common factors, consider the product of numerators to get the resultant numerator and similarly consider the product of denominators to get the resultant denominators.

Complete step by step solution:
Here we have been provided with the expression $\dfrac{2}{3}\times \dfrac{7}{8}$ and we are asked to find its value. That means we have to find the product of the two fractions.
Now, when we take the product of two fractions then first we check if the numerator and denominator have any factor in common or not. If there are common factors then we cancel them first and then multiply their numerators to get the resultant numerator and similarly to find the resultant denominator we consider the product of their denominators.
Let us come to the question. Assuming the required product as E we get,
$\Rightarrow E=\dfrac{2}{3}\times \dfrac{7}{8}$
Now we can write $8=4\times 2$ so we get,
$\Rightarrow E=\dfrac{2}{3}\times \dfrac{7}{4\times 2}$
Clearly we can see that factor 2 is common in both numerator and denominator so cancelling 2 we get the simplified form as:
$\Rightarrow E=\dfrac{1}{3}\times \dfrac{7}{4}$
Now there are no common factors that can be cancelled and the fractions cannot be simplified further. Therefore multiplying the numerators of the two fractions to get the resultant numerator and the denominators to get the resultant denominator we get,
$\therefore E=\dfrac{7}{12}$

Hence $\dfrac{7}{12}$ is the required product.

Note: Do not multiply the numerator of one fraction with the denominator of the other fraction otherwise you will get the wrong answer. While considering the product do not forget to cancel the common factors as it makes the calculation easy. If there are no common factors then we don’t have any other option but to directly consider the product.