Ex. 1. Simplify: (I0 5005 -5000 / 10 (ii) 18800 /470 / 20.
Sol. (I) 5005 – 500 /10 = 5005 – 5000/10 = 5005 – 500 =4505.
(II) 18800 / 470 / 20 = 18800 / 470 / 20 = 40 /20 = 2.
Ex. 2. Simplify: b- [b – (a + b) – (b – a – b)} + 2a].
Sol. given expression =b – (b – (a + b) – {b – a + b)} + 2a]
= b –[ b- a – b –{b – 2b + a } + 2 a]
= b-[- a – {b – 2b +a + 2a}]
= b – [ - a –{-b + 3a}] = b – [- [ - a +b – 3a]
= b – [= 4a + b] =b + 4a – b = 4a.
Ex.3 what value will replace the question mark in the following equation?
4 1/2 + 3 1/6 +? 2 1/3 = 13 2/5.
Sol. let 9/2 + 19/6 + x + 7/3 = 67/5
The, X =67/5 – (9/2 + 19/6 + 7/3) x = 67/5 (27 + 19 + 14/6) =67/5 – 60/6)
X = (67/5 – 1) = 17/5 = 32/5.
Ex. 4. 4/15 of 5/7 of a number is greater than 4/9 of 2/5 of the same number by 8. What is half of that number?
Sol. let the number be x. then, 4/15 of 5/7 of X – 4/9 of 2/5 of X = 8 4/21 X – 8/45 X = 8.
(4/21 – 8/45) X = 8. (60 – 56)/315) X = 8. 4/315 X = 8.
X = (8 x 325 / 315) x =8 4/315 x = 8.
Hence, required number =315.
Ex. 5. Simplify: [3 1/4 + {1 1/4 – 1.2 (2 1/2 – 1/4 - 1/6)}]