Question

Which of the following is the smallest ratio?
A.\[10:5,\]
B.\[10:25,\]
C.\[1:3,\]
D.\[19:25\]

Answer 1

Hint: We will write each ratio in fraction and then we will convert it into the simplest form. Then we will check the smallest fraction among all four fractions. The smallest fraction will be the smallest ratio.

Complete step-by-step answer:
We can write each ratio in fraction as:
We can write \[10:5\] as \[\dfrac{{10}}{5}\] .
Now we will write it in the simplest form and hence \[\dfrac{{10}}{5}\] becomes \[\dfrac{2}{1}\] .
Hence, \[10:5 = 2:1\].
We can write \[10:25\] as \[\dfrac{{10}}{{25}}\] .
Now we will convert it into the simplest form and hence \[\dfrac{{10}}{{25}}\] becomes \[\dfrac{2}{5}\] .
Hence, \[10:25 = 2:5\] .
We can write \[1:3\] as \[\dfrac{1}{3}\].
Now, we have to convert it into the simplest form.
But, we can clearly see that it is already in the simplest form.
Hence, \[1:3\] is already the simplest form of the given ratio.
Also, \[19:25\] can be written as \[\dfrac{{19}}{{25}}\] .
We can see that, among these four fractions
\[\dfrac{{10}}{5}\], \[\dfrac{{10}}{{25}}\], \[\dfrac{1}{3}\] and \[\dfrac{{19}}{{25}}\], the smallest fraction is \[\dfrac{1}{3}\] .
Hence the smallest ratio among \[10:5,\] \[10:25,\] \[1:3,\] \[19:25\] is \[1:3\].
Hence option C is correct.

Note: In mathematics, a ratio tells how many times one number contains another.
For example, there are 16 girls and 7 boys in the class.
So, the ratio of number of girls to number of boys is \[16:7\] .