Question

Which ratio is greater?
7 : 8 or 2 : 3

Answer 1

Hint: We will be using the concept of ratio and proportion to solve the problem. We will also be using the concept of LCM of two numbers to further simplify the problem.

Complete step-by-step solution -

Now, we have been given two ratios 7 : 8 and 2 : 3. We have to find which ratio is greater. To solve this we first let the ratio $a={\displaystyle \frac{7}{8}}andb={\displaystyle \frac{2}{3}}$.
Now, to compare both the ratio we will make the denominator of both a and b same and then compare their numerator to find which ratio is greater. To make the denominator of both a and b same we will take LCM of 8 and 3.
Now, the LCM of 8 and 3 is 24.
We will now make the denominator of both a and b is 24. Therefore,
$\begin{array}{rl}& a={\displaystyle \frac{7}{8}}={\displaystyle \frac{7\times 3}{8\times 3}}={\displaystyle \frac{21}{24}}\\ & b={\displaystyle \frac{2}{3}}={\displaystyle \frac{2\times 8}{3\times 8}}={\displaystyle \frac{16}{24}}\end{array}$
Now, since the denominator is the same therefore the ratio becomes 21 : 24 and 16 : 24.
Now, since 21 > 16. Therefore, 21 : 24 is greater which is originally 7 : 8.
Hence, 7 : 8 is greater than 2 : 3.

Note: To solve these types of questions one must have a knowledge of ratio and proportional also it has to be noted that a ratio can be represented as a rational number like 2 : 3 can be said as ${\displaystyle \frac{2}{3}}$.