Question

Which ratio is greater? $13:24$ or $17:32$ ?

Answer 1

Hint: In order to solve these types of problems, we will be requiring the concept of ratios and proportions. We first make the denominators the same by taking the LCM of them and then multiplying the ratios with the number accordingly. We then compare the numerators to get the larger fraction.

Complete step by step solution:
Now, we have been given two ratios $13:24$ and $17:32$ . We have to find which ratio is greater. To solve this, we first let the ratio,
$a=\dfrac{13}{24}$ and $b=\dfrac{17}{32}$
Now, to compare both the ratios we will make the denominator of both “a” and “b” same and then compare their numerator to find out which ratio is greater. To make the denominator of both a and b same, we will take LCM of $24,32$ . The LCM is $96$ .
We will now make the denominator of both a and b $96$ . Thus,
$a=\dfrac{13}{24}=\dfrac{13\times 4}{24\times 4}=\dfrac{52}{96}$
$b=\dfrac{17}{32}=\dfrac{17\times 3}{32\times 3}=\dfrac{51}{96}$
Now, since the denominator is the same, the ratio becomes $52:96$ and $51:96$ . Since, $52 > 51$ , so $\begin{align}
  & 52:96 > 51:96 \\
 & \Rightarrow 13:24 > 17:32 \\
\end{align}$
Thus, we can conclude that $13:24 > 17:32$ .

Note: We can also solve the problem in another way. Instead of making the denominators the same, we find the value of the respective fractions in decimals. In other words, we find out what is the value of “ $13$ divided by $24$ “ and “ $17$ divided by $32$ “. The respective values are \[0.541\] and $0.531$ . Since, \[0.541 > 0.531\] , the fraction $\dfrac{13}{24}$ is greater which means that the ratio $13:24$ is the greater ratio. We should be very careful in carrying out the calculations as this problem involves a lot of fractions.