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)}]
Sol. given exp. = [13/4 + {5/4 – ½ (5/2 – 3.2/12)}] = [13/4 /{5/4 – ½ (5.2 – 1/12)}]
= [13/4 / {5/4 – ½ (30-1/12)}] = [13/4 / {5/4 – 29 /24}]
= 13/4 / {30 – 29 / 24}] = [13/4 /1/24] = [13/4 x 24] = 78.
Ex.6. simplify: 108 / 36 of ¼ + 2/5 x 3 1/4
Sol. given exp. = 108 / 9 + 2/5 x 13/4 = 108 / 9 + 13/10 = (12+12/10) = 133/10 = 13/3/10.
Ex.7. simplify: 7/2 / 5/2 x 3/2
7/2 + 5/2 of 3/2 \5.25.
Sol. given exp. = 7/2 x 2/5 x 3/2 / 7/2 / 15/4 \ 5.25 = 21/10 / 7/2 x 4/15 \ 525 / 100 = 21 / 10 x
15/14 x 100/525 =6/14 = 3.7
Ex.8. simplify: (I0 12.05 x 5.4 \0.6 (II).6 x .6 + .6 + 6.
Sol. (I) given exp. = 12.05 x 5.4 /0.6 =12.05 x 9 = 108. 45.
(II) Given exp. = .6 x.6 +.6/6 = .36 + .1 = .46.
Ex. 9. Find the value of X in each of the following equations:
(I) 17.28 \ X/ 3.6 x 0.2 = 2
(II) (II)3648.24 + 364.824 \ X -36.4824 = 3794.1697
(III) 8.5 – {5 ½ -(7 ½ + 2.8 + 2.8 \ X )} x 4.25 \ (0.2)² = 306.
Sol. (I) 17.28/X = 2 x 3.6 x 0.2 X = 17.28 /1.44 = 1728/144 = 12.
(II) 364. 824/X =(3794.1696 + 36.4824) – 3648.24 = 3830.652 – 3648.24 = 182.412.
X = 364.824/182.412 = 2.
(III). 8.5 {5.5 (7.5 + 2.8/X)} x 4.25/0.04 = 306 8.5 – {5.5 – (7.5 X + 2.8/X)} x 425 / 4 = 306.
= 8.5 – {5.5 X – 7.5 X – 2.8/X} x 425/4 = 306 8.5 – {-2x – 2.8/X} x 106.25 = 306
= 8.5 – {-212.5X – 297.5/x) = 306 8.5X + 212.5X + 297.5/X = 306.
= (306 – 221) X = 297.5 X =297.5/85 = 3.5.
Ex.10. If X/y = 6/5, find the value of x²+ y²/x² - y².
Sol. X²+ y²/x² - y² =x²/² +1/x²/y²-1 = (x/y)²+1 / (x/y)²-1 = (6/5)²+1/(6/5)²-1 = 63/25
+ 1/ 36/25 – 1 = 61/25 x 25/11 = 61/11.
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