Total number of slices = 6
Number of slices ate by friends = 5
So, the fraction of pizza ate by friends = $\frac{5}{6}$
We know that,
Fraction of pizza ate by friends + Fraction of left over pizza = 1
$\therefore$ Fraction of left over pizza 
 = 1 - Fraction of pizza ate by friends
$=1-\frac{5}{6}$
$=\frac{6}{6}-\frac{5}{6}$
$=\frac{6-5}{6}$
$=\frac{1}{6}$

Converting the given fractions into equivalent fractions with denominator 8, we have
​$\frac{1\times 4}{2\times 4}=\frac{4}{8}$

$\frac{1\times 2}{4\times 2}=\frac{2}{8}$
​$\frac{9\times 1}{8\times 1}=\frac{9}{8}$

​$\frac{20÷2}{16÷2}=\frac{10}{8}$
Since $3<4<8$, we have $\frac{3}{8}<\frac{4}{8}<\frac{7}{8}$
i.e., $\frac{3}{8}<\frac{1}{2}<\frac{7}{8}$
Thus, $\frac{1}{2}$ lies between $\frac{3}{8}$ and $\frac{7}{8}$.

The fractions having same denominators are called like fractions.
Numerators are subtracted directly keeping the denominator common for like fractions. 
So, $\frac{13}{7}-\frac{5}{7}=\frac{13-5}{7}=\frac{8}{7}$

Fraction of migratory birds $=\frac{45}{150}=\frac{3}{10}$
Fraction of birds of Indian origin
$=\frac{3}{5}=\frac{6}{10}$ ...(equivalent fractions)
And, we know, $\frac{6}{10}>\frac{3}{10}.$
$\therefore$ The Indian origin birds are greater in number in the zoo.

Two equivalent fractions can never have same denominators. And like fractions have same denominators. So, two equivalent fractions can never be like fractions. 

No. of students failed = 65 - 57 = 8

Fraction of students who failed = $\frac{8}{65}$

A proper fraction is a number that represents part of a whole. So, it is a fraction in which the numerator is lesser than the denominator.   

If there are two equivalent fractions, their simplest forms are equal. E.g. $\frac{45}{60}$ and $\frac{15}{20}$ are 

equivalent fractions. Both their simplest form is $\frac{3}{4}$.

We have $\frac{999}{13}=76\frac{11}{13}$ 
$\therefore a=76$ and $b=11$