Question

In the equivalent rational number for \[\dfrac{-15}{36}\] with numerator -75, find the denominator.

Answer 1

Hint: In this question, we have a rational number and we have to find the equivalent denominator if the numerator is -75. Divide by -15 in -75, we get 5. So, multiply by 5 in both numerator and denominator and solve further.

Complete step-by-step solution -
According to the question we have a rational number \[\dfrac{-15}{36}\]. Rational number is of the form \[\dfrac{p}{q}\] , where q should not be equal to zero that is, \[q\ne 0\] .
Now, we have to find the denominator equivalent if the numerator is -75.
Finding the constant term which is to be multiplied in the numerator of the rational number \[\dfrac{-15}{36}\] to get -75.
Dividing by -15 in -75, we get
\[\dfrac{-75}{-15}=5\]
Now, multiplying by 5 in the numerator and denominator of the rational number \[\dfrac{-15}{36}\] , we get
\[\dfrac{-15\times 5}{36\times 5}\] …………(1)
We know that \[-15\times 5=-75\] and \[36\times 5=180\] .
Now, putting \[-15\times 5=-75\] and \[36\times 5=180\] in equation (1), we get
\[\dfrac{-15\times 5}{36\times 5}=\dfrac{-75}{180}\]
We have -75 as numerator and 180 as denominator of the rational number.
Hence, for the rational number \[\dfrac{-15}{36}\] , 180 is the equivalent denominator if the numerator is -75.

Note: In this question, one can do a mistake in dividing -75 by 36 and then multiply by \[\dfrac{-75}{36}\] in the numerator and denominator of the rational number \[\dfrac{-15}{36}\]. This is wrong. We need -75 as a numerator. So, we have to divide -75 by the numerator of the rational number\[\dfrac{-15}{36}\] which is -15. That is, we have to multiply by \[\dfrac{-75}{-15}=5\] in the numerator and denominator of \[\dfrac{-15}{36}\] .