Question

Which of the following is a rational number between 1/2 and 5/7 ? i. 1/3 ii. 2/5 iii. 0 iv. 4/7​

Answer 1

(i) 536+642

At first, we will calculate the LCM of 36 and 42. The prime factorisation is 36 and 42 is,

36 = 2 × 2 × 3 × 3

42 = 2 × 3 × 7

Now, LCM of 36 and 42 = 2 × 2 × 3 × 3 × 7 = 252

536+642=5×736×7+6×642×6=35252+36252=35+36252=71252

(ii) 123+245=1×3+23+2×5+45=53+145

Now, LCM of 3 and 5 is 15.

53+145=5×53×5+14×35×3=2515+4215=6715=4715

(iii) 1117+1319

Now, LCM of 17 and 19 is 323.

1117+1319=11×1917×19+13×1719×17=209323+221323=430323

(iv) 2311+1377=2×11+311+1×77+377=2511+8077

Now, LCM of 11 and 77 is 77.

2511+8077=25×711×7+80×177×1=17577+8077=25577=32477