Question

Which ratio is larger in the following pairs?
$4:7\,\,or\,\,5:8$

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. Using the concept of LCM, we will make the denominator the same and then we will compare the numerator part.

Complete step by step answer:
Now, we have been given two ratios $4:7\,$ and $\,5:8$. We have to find which ratio is greater. To solve this, we first let the ratio $a = \dfrac{4}{7}$ and $b = \dfrac{5}{8}$. Now, to compare both the ratios we will make the denominator of both $a$ and $b$ the same and then compare their numerator to find which ratio is greater.

To make the denominator of both $a$ and $b$ the same we will take LCM of $7$ and $8$.Now, the LCM of $7$ and $8$ is $56$. We will now make the denominator of both a and b is $56$. Therefore,
$ \Rightarrow a = \dfrac{4}{7} = \dfrac{{4 \times 8}}{{7 \times 8}} = \dfrac{{32}}{{56}}$
$ \Rightarrow b = \dfrac{5}{8} = \dfrac{{5 \times 7}}{{8 \times 7}} = \dfrac{{35}}{{56}}$
Now, since the denominator is the same therefore the ratio becomes $32:35$.Now, since $35 > 32$. Therefore, $35:56$ is greater than originally $5:8$.

Hence, $5:8$ is greater than $4:7\,$.

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 $1:3$ can be said as $\dfrac{1}{3}$. One should not confuse how to find the HCF and LCM of a given number.