Question

On sports day , Nitin jumped $4\dfrac{7}{{12}}$ feet and Anil jumped $3\dfrac{1}{6}$ feet. How much farther did Nitin jump than Anil?
A) 2 feet
B) $1\dfrac{5}{6}$ feet
C) $1\dfrac{5}{{12}}$ feet
D) $\dfrac{5}{{12}}$ feet

Answer 1

Hint:
We are given the distances jumped by nitin and anil . we need to convert the given mixed fractions into improper fractions and we need to find the difference between the heights to get the required answer.

Complete step by step solution:
We are given that Nitin jumped $4\dfrac{7}{{12}}$ feet and Anil jumped $3\dfrac{1}{6}$ feet
We can see that we are given two mixed fractions. So first lets convert them into improper fractions. In order to convert them we need to multiply the denominator with the given whole number and the add the numerator to it and once again divide it by the denominator
$ \Rightarrow 4\dfrac{7}{{12}} = \dfrac{{12 \times 4 + 7}}{{12}} = \dfrac{{48 + 7}}{{12}} = \dfrac{{55}}{{12}}$
Hence we get that Nitin jumped $\dfrac{{55}}{{12}}$feet
And now
 $ \Rightarrow 3\dfrac{1}{6} = \dfrac{{6 \times 3 + 1}}{6} = \dfrac{{18 + 1}}{6} = \dfrac{{19}}{6}$
Hence we get that Anil jumped $\dfrac{{19}}{6}$feet
Now we are asked to find how much farther did Nitin jump than Anil and it is given by the difference between the heights jumped by Nitin and Anil
$ \Rightarrow \dfrac{{55}}{{12}} - \dfrac{{19}}{6}$
We can see that our denominators are different hence we need to take lcm
The LCM of 6 and 12 is 12
Hence we get
$
   \Rightarrow \dfrac{{55 - 38}}{{12}} \\
   \Rightarrow \dfrac{{17}}{{12}} \\
\ $
Hence we get a improper fraction and lets convert it into mixed fraction
When 17 is divided by 12 we get the quotient to be 1 and the remainder to be 5
Hence the quotient becomes the whole part and the remainder becomes the numerator and the divisor becomes the denominator
$ \Rightarrow \dfrac{{17}}{{12}} = 1\dfrac{5}{{12}}$
Hence Nitin jumped $1\dfrac{5}{{12}}$ feet farther than Anil

The correct option is c.

Note:
1) Every fraction has a numerator that equals the number of parts we have and a denominator equaling the total number of parts in a whole.
2) A mixed number is the combination of a whole number and a fraction.
3) An improper fraction is a fraction whose numerator is larger than its denominator therefore having a value greater than one.