Simplify:
1. 6 + {4/3 + (3/4 – 1/3)}
2. 8 – {3/2 + (3/5 – 1/2)}
(i) It is given that
6 + {4/3 + (3/4 – 1/3)}
We can write it as
= 6 + {4/3 + 3/4 – 1/3}
By further calculation
= 6/1 + 4/3 + 3/4 – 1/3
Here the LCM of 3 and 4 is 12
= (72 + 16 + 9 – 4)/ 12
So we get
= (97 – 4)/ 12
= 93/12
= 31/4
= 7 ¾
(ii) It is given that
8 – {3/2 + (3/5 – 1/2)}
We can write it as
= 8 – {3/2 + 3/5 – 1/2}
By further calculation
= 8/1 – 3/2 – 3/5 + 1/2
Here the LCM of 2 and 5 is 10
= (80 – 15 – 6 + 5)/ 10
So we get
= (85 – 21)/ 10
= 64/10
Dividing by 2
= 32/5
= 6 2/5