Insert five
rational numbers between:
(i) −45 and −23
(ii) −12 and 23
(i) −45
and −23
LCM of 5,3=15
∴−45=−4×35×3=−1215
and −23=−2×53×5=−1015
∵
Between -10 and −12, there are is one rational.
∴
Multiplying numerator and denominator by (5+1)=6
∴−1215=−12×615×6=−7290
and −1015=−10×615×6=−6090
∴5 rational numbers between −7290 and −6090
−7190,−7090,−6990,−6890,−6790
−7190,−79,−2330,−3445,−6790
(ii)−12
and 23
LCM of 2,3,=6
∴−12=−1×32×3=−36 and
23=2×23×2=46
Now 5
rational numbers between
−12 and 23
−26,−16,16,26,36