A rational number is a fraction indicating the quotient of two integers, excluding division by zero.
If (p/q) and (r/s) are any two rational numbers such as (p/q) < (r/s), then (p + r)/(q + s) is a rational number, such that (p/q) < (p + r)/(q + s) < (r/s).
Question 1 :
Which arrow best shows the position of 11/3 on the number line?
Solution :
Decimal form 11/3 is 3.666......
The arrow D represents this position.
Question 2 :
Find any three rational numbers between -7/11 and 2/11
Solution :
The given fractions are having same denominator. Rational numbers between the given fractions are
-6/11, -5/11, -4/11, -3/11, -2/11, -1/11, 0/11, 1/11
Question 3 :
Find any five rational numbers between
(i) 1/4 and 1/5
Solution :
a = 1/4, b = 1/5
To find the 1st rational number a and b, we have to find average of a and b.
c = (a + b)/2
3rd rational number :
= [(1/4) + (19/80)]/2
= (20 + 19)/160
= 39/160
4th rational number :
= [(1/4) + (39/160)]/2
= (40 + 39)/320
= 79/320
5th rational number :
= [(1/4) + (79/320)]/2
= (80 + 119)/640
= 159/640
Hence the 5 rational numbers are
9/40, 19/80, 39/160, 79/320, 159/640.
(ii) 0.1 and 0.11
Solution :
Decimals lie between 0.1 and 0.11 are
0.101, 0.102, 0.103, 0.104, 0.105, 0.106, ............
(iii) -1 and -2
Solution :
let a, b, c, d, e be the rational numbers between -1 and -2
a = [-1 + (-2)] /2 = -3/2
b = [-1 + (-3/2)]/2 = -5/4
c = [-1 + (-5/4)]/2 = -9/8
d = [-1 + (-9/8)]/2 = -17/16
e = [-1 + (-17/16)]/2 = -33/32
Hence 5 rational numbers between -1 and -2 are -3/2, -5/4, -9/8, -17/16 and -33/32.
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