Question

There are three ropes of lengths $\frac{1}{4}m,\frac{1}{3}m,$ and $\frac{7}{5}m$. Lobo says that the rope of length $\frac{1}{4}m$ is the longest. Nana says that the rope of length $\frac{7}{5}m$ is the longest. Who is correct?

• A. Lobo
• B. Nana
• C. Both are correct
• D. Both are incorrect

Answer 1

The correct option is B Nana

Just like we compare fractions by making the denominators equal, we can also do it by making the numerators equal.

The first fraction has $1$ as its numerator, the second fraction has 1 as its numerator, and the third fraction has $7$ as its numerator. Let's make all the numerators the same.

Calculate the equivalent fraction of $\frac{1}{4}$ with $7$ as the numerator.

$=\frac{1\times 7}{4\times 7}=\frac{7}{28}$

Calculate the equivalent fraction of $\frac{1}{3}$ with $7$ as the numerator.

$=\frac{1\times 7}{3\times 7}=\frac{7}{21}$

The third fraction is $\frac{7}{5}$ . Now, all the fractions have the same numerator.

If fractions have the same numerator, the fraction having the smallest denominator has the highest value.

So, $\frac{7}{5}>\frac{7}{21}>\frac{7}{28}.$

Hence, Nana is correct.