Question

How do you multiply $\dfrac{1}{2}\times \dfrac{2}{8}$?

Answer 1

Hint: We start solving the problem by assigning a variable to the given variable. We then make use of the fact that the multiplication of two numbers of the form $\dfrac{a}{b}$ and $\dfrac{c}{d}$ as $\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\times c}{b\times d}$ to proceed through the problem. We then check the common factors present in both numerator and denominator and then cancel it from both numerator and denominator to get the required answer.

Complete step-by-step solution:
According to the problem, we are asked to find the value of $\dfrac{1}{2}\times \dfrac{2}{8}$.
Let us assume $m=\dfrac{1}{2}\times \dfrac{2}{8}$ ---(1).
We know that the multiplication of two numbers of the form $\dfrac{a}{b}$ and $\dfrac{c}{d}$ is defined as $\dfrac{a}{b}\times \dfrac{c}{d}=\dfrac{a\times c}{b\times d}$. Let us use this result in equation (1).
$\Rightarrow m=\dfrac{1\times 2}{2\times 8}$ ---(2).
We can see that the common factor present in both the numerator and denominator of equation (2) is 2. Let us cancel that term to proceed.
$\Rightarrow m=\dfrac{1}{8}$.
So, we have found the value of the product $\dfrac{1}{2}\times \dfrac{2}{8}$ as $\dfrac{1}{8}$.
$\therefore $ The value of the product $\dfrac{1}{2}\times \dfrac{2}{8}$ is $\dfrac{1}{8}$.

Note: We can also solve this problem by making use of the law of exponents in the given problem. We should not confuse the division and multiplication of the terms $\dfrac{a}{b}$ and $\dfrac{c}{d}$ while solving these types of problems. Whenever we get this type of problem, we first multiply the terms present in the numerator of both terms and the terms in the denominator to proceed through the problem. We should not make mistakes while canceling the common terms present in both numerator and denominator. Similarly, we can expect problems to find the value of $\dfrac{9}{5}\div \dfrac{4}{3}$.