Insert three rational numbers between 3/5 and 2/3
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The "n" rational numbers between a and
b are a+b , a+2d , a+3d,............a+nd.
d=b-a/n+1 (b>a) here a=2/3 , b=3/5 and
n=3 (a>b) ,therefore d=a-b/n+1 (since
a>b) = 2/3-3/5/3+1 = 1/15/4 = 1/15×4 =
1/60 . d= 1/60, therefore Required 3
rational numbers between 2/3 and 3/5
are a+d,a+2d,a+3d.a
+d=2/3+1/60=40+1/60=41/60 (L.C.M of
3,60),a+2d=2/3+1/30=20+1/30=21/30, a
+3d=2/3+1/10=23/30.
b are a+b , a+2d , a+3d,............a+nd.
d=b-a/n+1 (b>a) here a=2/3 , b=3/5 and
n=3 (a>b) ,therefore d=a-b/n+1 (since
a>b) = 2/3-3/5/3+1 = 1/15/4 = 1/15×4 =
1/60 . d= 1/60, therefore Required 3
rational numbers between 2/3 and 3/5
are a+d,a+2d,a+3d.a
+d=2/3+1/60=40+1/60=41/60 (L.C.M of
3,60),a+2d=2/3+1/30=20+1/30=21/30, a
+3d=2/3+1/10=23/30.
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