List five rational numbers between: (1.) -1 and 0 (2.) -2 and -1 (3.) -4/5 and -2/3 (4.) -1/2 and 2/3

i) Rational numbers between -1 and 0:
(-1/1) and (0/1)
Since we need 5 numbers, multiply both the numerator and the denominator by 6.
After multiplication, we get;
-1 and 0
Following five rational numbers:
(-5/6), (-2/3), (-1/2), (-1/3), (-1/6)

ii) Rational numbers between -2 and -1:
The given negative integers are written as:
(-2/1) and (-1/1)
Multiplying both the numerator and denominator by 6, we get;
(-12/6) and (-6/6)
Following five rational numbers:
(-11/6), (-5/3), (-3/2), (-4/3), (-7/6)

iii) Rational numbers between -4/5 and -2/3
Since denominators are different, take LCM of 5 and 3 and we get
(-12/15) and (-10/15)
Now multiply both numerator and denominator by 6, we get
(-72/90) and (-60/90)
Following five rational numbers:
(-71/90), (-70/90), (-69/70), (-68/70), (-67/70)

iv) Rational numbers between -1/2 and 2/3
Taking LCM of 2 and 3, we get
(-3/6) and (-4/6)
Multiplying the numerator and denominator by 6, we get
(-18/36) and (-24/36)
Following five rational numbers:
(-19/36), (-20/36), (-21/36), (-22/36), (-23/36)

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