Question

The ratio of 72 to 60 is?

Answer 1

Hint: The type of question which asks for a ratio of two values, means they are asking the simplest value of the ratio these values will have. For this we just need to divide them in the ratio and bring the simplest form, by dividing them both by Highest common factor.

Complete step by step answer:
So for our question we had two values i.e. 72 and 60. So highest common factor of 72 and 60 (other than one) are:
$\begin{align}
  & 72=1,2,4,6,8,9,12,18,36,72 \\
 & 60=1,2,3,4,5,6,10,12,15,20,30,60 \\
\end{align}$
$=2,4,6,12$
So for the ratio of 72 to 60 i.e.$\dfrac{72}{60}$ start dividing them by their common factors, we can divide them in any of the order, of common factor; for our ease let us divide them by first by 2, but you can divide them by 4, or by 6 or so on. But keep dividing till where we end with any of the common factors in the ratio.
So for $\dfrac{72}{60}=\dfrac{36}{30}$ when we will divide by their common factor 2,
Now 36 and 30 both have common factors 2,3,4,6. So we can divide by any of these four factors through which we will feel easy. So let us divide them by 6
So, $\dfrac{36}{30}=\dfrac{6}{5}$, so after dividing by 6 we get $\dfrac{6}{5}$, which now does not have any common factor. Other than 1, so the ratio of $\dfrac{72}{60}$ will be $\dfrac{6}{5}$
Hence the ratio of 72 to 60 is $\dfrac{6}{5}$

Note: Keep in mind that the number for which to is used will be in the denominator, as in our case it is 72 to 60, as ‘to’ is used for 60 so we had kept it in the denominator. And also keep dividing the value until you get the least value or until the values end with any common factor between them.