Free Fractions 01 Practice Test - 6th grade 

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 $\frac{7}{8}$.

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

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.

No. of students failed = 65 - 57 = 8

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

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

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 $\frac{3}{4}$.

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.   

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