Free Fractions 02 Practice Test - 6th grade 

$\frac{101}{7}$ and $\frac{99}{7}$ are like fractions as they have the same denominator. 
Hence, we can directly add the numerators keeping the denominator as it is.
$\therefore \frac{101}{7}+\frac{99}{7}=\frac{101+99}{7}=\frac{200}{7}$

A proper fraction is a number that represents part of a whole.

Let us take the full length of the train as L.

24 compartments---------------L

1 compartment--------------= $\frac{1}{24}\times L$

When numerator of a fraction is greater than its denominator, it is known as the improper fraction.

If $\frac{9}{7}$ and $\frac{a}{63}$ are equivalent fractions,then 9 x 63 = a x 7.

Solving, we get a = 81.

There are infinite fractions on a number line. The two fractions given in the question are two points on the number line. Between these two points, there exists infinite points. So, infinite fractions exist between two points on a number line.

Let us first convert the mixed fractions $15\frac{5}{3}$ and $17\frac{3}{2}$ to improper fractions.
i.e.,  $15\frac{5}{3}=\frac{15\times 3+5}{3}=\frac{50}{3}$ and $17\frac{3}{2}=\frac{17\times 2+3}{3}=\frac{37}{2}$
Now, $17\frac{3}{2}-15\frac{5}{3}=\frac{37}{2}-\frac{50}{3}=\frac{111-100}{6}=\frac{11}{6}=1\frac{5}{6}$

For like fractions, the denominators should be the same.

Total distance to be covered =  5 km

Distance covered by Manish = 2 km

$\Rightarrow$ Fraction of the distance covered by Manish = $\frac{2}{5}$ 

Fraction of the distance covered by Kushagra =$\frac{1}{2}$

To compare these fractions, we write them as like fractions.

$\frac{2}{5}=\frac{2\times 2}{5\times 2}=\frac{4}{10}$

$\frac{1}{2}=\frac{1\times 5}{2\times 5}=\frac{5}{10}$


Since $\frac{4}{10}<\frac{5}{10}$,

$\frac{2}{5}<\frac{1}{2}$

Therefore, Kushagra ran more.

Old animals = 40 - 10 = 30

Fraction of old animals presently in the zoo = $\frac{30}{40}=\frac{3}{4}$