Question

If we have an expression as $\dfrac{5}{8} = \dfrac{{20}}{p}$, then what is the value of $p$?

Answer 1

Hint: In this question, we are given an equation in which we have been asked to find the value of $p$. Simply, cross multiply in such a way that $p$ comes to the numerator from the denominator and all other terms are towards the other side. Then simplify the equation and you will have the required value of $p$.

Complete step-by-step solution:
We have an equation in terms of $p$.
$ \Rightarrow \dfrac{5}{8} = \dfrac{{20}}{p}$
In this equation, $p$ is in the denominator. We will shift $p$to the other side such that it is in the numerator. We will also send the remaining digits to RHS.
$ \Rightarrow p = \dfrac{{20 \times 8}}{5}$
Now, we will simplify the equation.
$ \Rightarrow p = 4 \times 8$
We have, $p = 32$.
Hence, the required value of $p$ is 32.

Note: We can also solve the given equation in the following way.
If we observe, we will notice that the given ratio is an equivalent ratio.
What are equivalent ratios?
Equivalent ratios are those ratios that give equal and same simplest form. For example: If we find the simplest form of $\dfrac{4}{8}$, it will give us $\dfrac{1}{2}$. On the same hand, if we find the simplest form of $\dfrac{{12}}{{24}}$, we will again get $\dfrac{1}{2}$. Therefore, $\dfrac{1}{2} = \dfrac{4}{8} = \dfrac{{12}}{{24}}$. Hence, all these ratios are equivalent ratios as their simplest ratios are the same.
Moving towards the question, we have to find the value of $p$ in $\dfrac{5}{8} = \dfrac{{20}}{p}$. Since the two sides are equal, they are also equivalent ratios.
We have to think of such a number which when multiplied with 5 will give us 20. This is because LHS is the simplest form of RHS.
$ \Rightarrow \dfrac{{5 \times x}}{{8 \times x}} = \dfrac{{20}}{p}$
The value of x is 4. If we multiply by 4 on numerator and denominator, we will get the required value.
$ \Rightarrow \dfrac{{5 \times 4}}{{8 \times 4}} = \dfrac{{20}}{p}$
Hence, $p = 8 \times 4 = 32$