write 3 rational numbers equivalent to given rational numbers: 2/5,-5/7,17/3
Answers
Answer:
(i) -1 and 0
Let us write -1 and 0 as rational numbers with denominator 6.
=> -1 = -6/6 and 0 = 0/6
So, -6/6 < -5/6 < -4/6 < -3/6 < -2/6 < -1/6 < 0/6
=> -1 < -5/6 < -2/3 < -1/2 < -1/3 < -1/6 < 0
Hence, the five rational numbers between -1 and 0 are:
-5/6 < -2/3 < -1/2 < -1/3 < -1/6
(ii) -2 and -1
Let us write -2 and -1 as rational numbers with denominator 6.
=> -2 = -12/6 and -1 = -6/6
So, -12/6 < -11/6 < -10/6 < -9/6 < -8/6 < -7/6 < -6/6
=> -2 < -11/6 < -5/3 < -3/2 < -4/3 < -7/6 < -1
Hence, the five rational numbers between -2 and -1 are:
-2 < -11/6 < -5/3 < -3/2 < -4/3 < -7/6 < -1
(iii) -4/3 and -2/3
Let us write -4/3 and -2/3 as rational numbers with the same denominator.
=> -4/5 = -36/45 and -2/3 = -30/45
=> -36/45 < -35/45 < -34/45 < -33/45 < -32/45 < -31/45 < -30/45
=> -4/5 < -7/9 < -34/45 < -11/15 < -32/45 < -31/45 < -2/3
Step-by-step explanation:
2/5 = 4/10,
-5/7= -25/35
17/3= 34/6