Question

Subtract the sum of (-36/11) and (49/22) from the sum of (33/8) and (-19/4).

Answer 1

First we have to find the sum of (-36/11) and (49/22)

= (-36/11) + (49/22)

LCM of 11 and 22 is 22

Express each of the given rational numbers with the above LCM as the common denominator.

Now,

= [(-36×2)/ (11×2)] = (-72/22)

= [(49×1)/ (22×1)] = (49/22)

Then,

= (-72/22) + (49/22)

= (-72+49)/22

= (-23/22)

Now we have to find the sum of (33/8) and (-19/4)

= (33/8) + (-19/4)

LCM of 8 and 4 is 8

Express each of the given rational numbers with the above LCM as the common denominator.

Now,

= [(33×1)/ (8×1)] = (33/8)

= [(-19×2)/ (4×2)] = (-38/8)

Then,

= (33/8) + (-38/8)

= (33-38)/8

= (-5/8)

Now,

= (-5/8) – (-23/22)

We have:

= (-5/8) – (-23/22)

= (-5/8) + (additive inverse of -23/22)

= (-5/8) + (23/22)

LCM of 8 and 22 is 88

Express each of the given rational numbers with the above LCM as the common denominator.

Now,

= [(-5×11)/ (8×11)] = (-55/88)

= [(23×4)/ (22×4)] = (92/88)

Then,

= (-55/88) + (92/88)

= (-55+92)/88

= (37/88)