Question

Out of the ratios $7:20,$ $13:25,$$7:30$ and $11:15$, the smallest one is
A. $11:15$
B. $7:30$
C. $7:20$
D. $13:25$

Answer 1

Hint: To find the smallest ratio first we will convert the given ratios into fractions by using the concept $x:y=\dfrac{x}{y}$. Then we will divide the obtained fractions and convert them into decimals. Then by comparing the obtained values we will get the desired answer.

Complete step by step solution:
We have been given the ratios $7:20,$ $13:25,$$7:30$ and $11:15$.
We have to find the smallest one.
Now, let us first convert the given ratios into fractions. We know that $x:y=\dfrac{x}{y}$, so we will get
$\Rightarrow 7:20=\dfrac{7}{20}$
$\Rightarrow 13:25=\dfrac{13}{25}$
$\Rightarrow 7:30=\dfrac{7}{30}$
$\Rightarrow 11:15=\dfrac{11}{15}$
Now, dividing each fraction and converting them in to decimals we will get
$\Rightarrow \dfrac{7}{20}=0.35$
\[\Rightarrow \dfrac{13}{25}=0.52\]
$\Rightarrow \dfrac{7}{30}=0.233$
$\Rightarrow \dfrac{11}{15}=0.733$
Now, when we compare the values obtained by simplifying the fractions we get that 0.233 is the smallest value.
Hence $7:30$ is the smallest ratio.

So, the correct answer is “Option B”.

Note: Alternatively to compare fractions we can either make their denominators or numerators equal. Then the fractions will be easily comparable. Fractions with larger denominators are smaller, if numerators are equal. If denominators of fractions are equal then the fraction with least numerator is the smaller. It is easy to compare fractions with the same numerator or denominator, so students may try this method also.