Question

How do you multiply \[\dfrac{8}{7} \times \dfrac{3}{5}\]?

Answer 1

Hint: To solve this problem, we need to use the concept of multiplication of the fractions. In this, we first need to check if the given two fractions can be simplified or not. Here, both the fractions cannot be simplified further. So, we can directly apply the multiplication rule of fractions to get our answer.

Complete step-by-step solution:
We are given \[\dfrac{8}{7} \times \dfrac{3}{5}\].
If we consider the first fraction $ \dfrac{8}{7} $ , it cannot be simplified as both numerator and denominator have not any common factors.
And if we consider the second fraction $ \dfrac{3}{5} $ , it cannot be simplified as both numerator and denominator are prime numbers.
Therefore, we can directly apply the multiplication rule of the fraction.
According to this rule, both numerators $ 8 $ and $ 3 $ are multiplied with each other and both the depositors $ 7 $ and $ 5 $ are multiplied with each other.
\[ \Rightarrow \dfrac{8}{7} \times \dfrac{3}{5} = \dfrac{{8 \times 3}}{{7 \times 5}} = \dfrac{{24}}{{35}}\]
Now let us check whether \[\dfrac{{24}}{{35}}\]can be simplified or not. We will check this by factoring both the numbers and check if there are any common factors or not.
 $ 24 $ can be written as the product of its prime factor as $ 24 = 2 \times 2 \times 2 \times 3 $
 $ 35 $ can be written as the product of its prime factor as $ 35 = 5 \times 7 $
Thus, there are no common actors in both these numbers.
Thus, our final answer is \[\dfrac{{24}}{{35}}\].

Note: The general steps for multiplying two fractions which we have used here are:
Step 1: To multiply the two numerators.
Step 2: To multiply the two denominators.
Step 3: Finally, simplify the new fractions.
The fractions can also be simplified before multiplying by factoring out common factors in the numerator and denominator. Simplifying before multiplying helps avoid dealing with large numbers.