Important Questions: Rational Numbers

Let us consider a fraction 3/5 and a rational number = 14/7
By definition, 3/5 is a rational number. So, p is true. By definition, -4/7 is not a fraction, since, −4 is not a natural number. So, q is false.

All fractions can be termed as rational numbers; however, all rational numbers cannot be termed as fractions. Only those rational numbers in which 'p' and 'q' are positive integers are termed as fractions.

√2/3 is not a rational number.

because √2 doesn't have an exact value, and on further division by 3, it goes more unstable. 

Since, every integer having a denominator 1 can be expressed in P/q form, p is true. Since, a rational number with denominator other than 1 is not an integer (e.g., 3/5), q is false.

Since, denominator is 0, it is not a rational number.

-12/32 = -3*4/8*4 = -3/8

-4/7 = -32/X

 X=32x7/4

X=56

L.C.M. of 5, 4 and 20 is 20. 
4/−5 × 4/4 = 16/−20;3/4 = 3×5/4×5 = 15/20
−2 < 4/−5 < −11/20 < 3/4
or 
3/4 > −11/20 > 4/−5 > −2
is the required descending order.
Rewrite equivalent fractions of the given fractions and then compare then.
Arrange them in descending order.

The ascending order of 4/7,1/3, 2/5 and 5/9 is 1/3<2/5<5/9<4/7. The two middle numbers are 2/5 and 5/9. 

∴  Average = = 43/90

The given numbers can be arranged in ascending order as1/5 < 3/5 < 7/5 < 9/5
The greatest number = 9/5;
The least number = 1/5
We have,  9/5 × x/100 = 1/5 
⇒ x = 10/09 =

The ascending order of given numbers is 1/9,5/9,11/9. 
∴  Required difference = 11/9 −1/9 = 10/9

−24/15 is the equivalent rational number of −8/5.

Since, 1/0 is not rational, the quotient of two integers is not always rational.

All the given statements are correct. Consider 
4/5 [a] Since 4/5 + 0 = 4/5,, 1 is the additive identity of rational numbers. [b] Since 
4/5 × 1= 4/5, is the  multiplicative identity of rational numbers. [c] Since 0+0=0,
0 is the additive inverse of 0.

Let x be the required number. So,  
x+(−7/5) = −3 
⇒ x = −3+7/5 = −1/5 + 7/5 = −8/5