Comparing a Proper Fraction with it's Square

Q. If a proper fraction in its lower form is subtracted from its reciprocal, the value of difference is $\frac{45}{14}$. What is the value of the square of the proper fraction?

1. $-\frac{7}{2}$
   
2. $\frac{2}{7}$
   
3. $\frac{49}{4}$
   
4. $\frac{4}{49}$
   

Q. Which among the following is NOT a proper fraction?

1. $\frac{2}{3}$
   
2. $\frac{29}{31}$
   
3. $\frac{72}{83}$
   
4. $\frac{64}{63}$
   

Q.

Write the fractions in number form, Three - tenths.

Q. If we multiply a proper fraction with another proper fraction, then the value of the product would be what in comparison to the individual values of the proper fractions?

1. Greater than the values of individual proper fractions
2. Less than the values of individual proper fractions
3. Equal to the values of individual proper fractions
4. Cannot be determined

Q. Select the bubble which contains proper fraction.
(Proper fractions are fractions that are less than 1)

1. 1/4
2. 9/4
3. 16/9
4. 9/49
5. 4/49
6. 64/81
7. 25/16
8. 16/81

Q. Rachel lives $5\frac{3}{4}$ miles away from her school. In the morning, she covers $5\frac{1}{2}$ miles by foot and the remaining distance by local bus. Find the square of the distance covered by Rachel by local bus.

1. $\frac{1}{8}$ km
   
2. $\frac{1}{32}$ km
   
3. $\frac{1}{4}$ km
   
4. $\frac{1}{16}$ km
   

Q.

Replace $\square$by an appropriate sign $<,=\mathrm{or}>$ between the given fractions:

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

Q. Which among the following statements is true?

1. The value of a proper fraction is always larger than the value of its square.
2. The value of a proper fraction is always smaller than the value of its square.
3. The value of a proper fraction is always equal to the value of its square.
4. None of the above

Q.

Express the relation between the following numbers with the help of the less than or greater than inequalities. Also, verify it :

$-\frac{7}{3}$ and $\frac{4}{3}$

Q.

Replace $\square$by an appropriate sign $<,=\mathrm{or}>$ between the given fractions:

$\frac{3}{4}\square \frac{2}{8}$