Question

One morning, Mirna counted $15$ junk emails out of $21$ emails in her inbox. How do you write a ratio comparing the number of regular emails to the junk emails?

Answer 1

Hint: The ratio of a number $A$ to a number $B$ is the quotient $\dfrac{A}{B}$ or the proportion $A:B.$ We will subtract the number of junk emails from the total number of mails to find the regular emails. Then we will find the quotient or proportion accordingly.

Complete step by step solution:
Let us consider the given problem. According to the problem, the total number of emails Mirna has gotten is $21.$
Out of these $21$ emails $15$ emails are junk emails. So, to find out the number of regular emails, we will subtract $15$ from $21.$
So, the number of regular emails is $21-15=6.$ That is, there are $6$ emails in the inbox.
We are asked to find the ratio comparing the number of regular emails to the junk emails.
Since the number of regular emails is $6$ and the number of the junk emails are $15,$ the ratio comparing these numbers is the quotient $\dfrac{6}{15}$ or the proportion $6:15.$
There is a common factor of these two numbers. And that is, $3.$
So, we will get $\dfrac{2\times 3}{5\times 3}$ or $2\times 3:5\times 3.$
Now we can cancel $3$ from each of these numbers. We will get $\dfrac{2}{5}$ or $2:5.$
Hence the ratio of the number of regular emails to that of the junk emails is $2:5.$

Note: When we are finding the ratio of some quantities with the same unit, we find the quotient or proportion of those values in the respective order. The order of the quantities is very important. Because, if we write $5:2$ instead of $2:5$ in the above problem, then the answer is wrong.