Question

Find the numerator in the equivalent rational number for $\dfrac{-15}{36}$ with the denominator –12?

Answer 1

Hint: We start solving the problem by assigning the variable for the numerator of the equivalent rational number. We then find the equivalent rational number using this variable and then equate it to the given rational number. We then make the necessary calculations involving division, multiplication to find the required value of the numerator of the equivalent rational number.

Complete step by step answer:
According to the problem, we need to find the numerator in the equivalent rational number for $\dfrac{-15}{36}$ with the denominator –12.
Let us assume the numerator of the equivalent rational number be ‘x’.
So, we have the equivalent numerator as $\dfrac{x}{-12}$ and we know that this will be equal to $\dfrac{-15}{36}$.
Now, we have $\dfrac{-15}{36}=\dfrac{x}{-12}$.
Let us multiply with –12 on both sides.
$\Rightarrow \dfrac{x}{-12}\times -12=\dfrac{-12\times -15}{36}$.
$\Rightarrow x=\dfrac{180}{36}$.
$\Rightarrow x=5$.
So, we have found the numerator of the equivalent rational number as 5.

∴ The numerator of the equivalent rational number is 5.

Note: Whenever we get this type of problems, we should first assume variables for the unknowns to avoid confusion. We should keep in mind that the denominator of the rational number must not be equal to 0 while solving the problem. We should not make mistakes while doing the calculations involving the signs for the given numbers. We can also find the equivalent rational number using the obtained numerator and given denominator. Similarly, we can expect problems to find the equivalent rational number such that the denominator is 6.