Question

Reenu got $\dfrac{2}{7}$ part of an apple while Sonal got $\dfrac{4}{5}$ part of it. Who got the larger part and by how much?

Answer 1

Hint: We first equate the denominators of the fractions to compare them. Then we compare the numerators. We subtract the lesser one from the greater one to find the difference. We can also convert the fraction to decimals to find the comparison.

Complete step by step solution:
We have to compare the fractions $\dfrac{2}{7}$ and $\dfrac{4}{5}$ to find out the greater one.
As the denominators of the fractions are different, we can’t compare them directly. We have to first make the denominators equal to compare the numerators.
To equal the denominators, we have to take the LCM of 5 and 7. As they are co-primes to each other the LCM will be $5\times 7=35$.
We multiply 5 for both the numerator and the denominator to the fraction $\dfrac{2}{7}$ and get \[\dfrac{2\times 5}{7\times 5}=\dfrac{10}{35}\].
Similarly, we multiply 7 for both the numerator and the denominator to the fraction $\dfrac{4}{5}$ and get \[\dfrac{4\times 7}{5\times 7}=\dfrac{28}{35}\].
Now that the denominators are equal, we can compare the fractions based on the numerators of the fractions.
The fractions are \[\dfrac{10}{35}\] and \[\dfrac{28}{35}\] which gives \[\dfrac{28}{35}\] as the greater one.
Now we subtract \[\dfrac{10}{35}\] from \[\dfrac{28}{35}\] to find the value by which \[\dfrac{28}{35}\] is greater.
Therefore, $\dfrac{4}{5}-\dfrac{2}{7}=\dfrac{28}{35}-\dfrac{10}{35}=\dfrac{18}{35}$.
Therefore, Sonal got the larger part and that is $\dfrac{18}{35}$ greater than Reenu.

Note: We can also convert the fractions into decimals to find the comparison between the fractions. We get $\dfrac{2}{7}=0.2857$ and $\dfrac{4}{5}=0.8$ which gives a clear idea about which one is greater and by same subtraction process we find by how much.