Question

Which ratio is greater? $7:16$ or $13:24$

Answer 1

Hint: In this question, we have been given the question of ratio and proportion. So we will use the properties of ratios to solve this question. We will first write the ratios in the fraction form and then we will take the LCM of the denominators of both the fractions. We have to make the denominator the same in both the fractions and then we will solve this question.

Complete answer:
Here we have the ratios i.e. $7:16$ or $13:24$
We can write the above ratios in the fraction form, so we have:
$\dfrac{7}{{16}},\dfrac{{13}}{{24}}$ .
Now we will first make the denominator the same by taking the LCM and we will multiply the ratios with the number. After that, we will try to compare the numerator of the fractions to get the larger fraction.
The LCM of $(16,24)$ is $48$ .
Therefore we will convert the fractions accordingly now, we have the first fraction:
$ \Rightarrow \dfrac{7}{{16}} = \dfrac{{7 \times 3}}{{16 \times 3}}$
So we have a new fraction which is $\dfrac{{21}}{{48}}$
Now the second fraction can be written as:
$ \Rightarrow \dfrac{{13}}{{24}} = \dfrac{{13 \times 2}}{{24 \times 2}}$
It gives us another fraction i.e.
$\dfrac{{26}}{{48}}$
Now we will compare the numerator of both the like fraction, so we can see that the numerator of the second fraction is greater than the numerator of the first fraction. We can write this as:
$26 > 21$
So we can say that
$\dfrac{{26}}{{48}} > \dfrac{{21}}{{48}}$
Hence we can write that the second fraction is greater than the first one i.e.
$\dfrac{{13}}{{24}} > \dfrac{7}{{16}}$

Note:
We should note that we can alternately solve this question also. We can find the values of the fractions in decimals instead of converting the fractions into the same denominators. This means that we can simply divide the value and write it. So the first fraction gives the value: $ \Rightarrow \dfrac{7}{{16}} = 0.4375$
And we have another fraction i.e.
$ \Rightarrow \dfrac{{13}}{{24}} = 0.5416$
We will compare the decimal value. So by comparing we can write that:
$0.5416 > 0.4375$
Therefore it gives us $\dfrac{{13}}{{24}} > \dfrac{7}{{16}}$ .