Given expression = ?0.5 x .5 x a = .5 x .05 x ? b
? ?.025 x a = 0.25 x ? b
? 0.025a = 0.25 x .025 x b
? a/b = (.025 x .025) /.025
= .025
a / b = 0.04 / 1.5
= 4 / 150
= 2 / 75
? Given Exp. (b - a) / ( b + a)
= (1- a/b ) / (1 + a/b)
= (1- 2 / 75) / (1 + 2 / 75)
= ( 73/75 ) / ( 77/75)
= 73/77
0.6 + . 7 + .8 + .3
= ( 6/9 + 7/9 + 8/9 + 3/9)
= 24 / 9
= 8 / 3
= 22/3
4.12 = 4 + 0.12
= 4 + (12 - 1) / 90
= 411/90
Given Exp. = 247 + 353 + 0.05
= 5 + (47 / 99) + (53 / 99) + (05 / 99)
= 5 + (105 / 99)
= 5+106/99
=606/99
= 6.06
Given Exp. = 3.57 - 2.14
= 3 + (57 / 99) - 2 - (14 / 99)
= 1 + (57 / 99) - (14 /99)
= 1 + 43/99
= 1.43
Given expression = (.23 - .023) / ( .0023 / 23 )
= .207 / (.0023 / 23)
= .207 / .0001
=.2070 / .0001
= 2070
Given expression = [(3.537 - .948)2 + (3.537 + .948)2] / [(3.537)2 + (.948)2]
= [(a - b)2 + (a + b)2] / (a2 + b2)
(Where a = 3.537 and b = 0.948)
= 2(a2 +b2) / (a2 +b2)
= 2
Given Expression = (6.5 x 4.7 + 6.5 x 5.3 ) / (1.3 x 7.9 - 1.3 x 6.9)
= [6.5 x (4.7 + 5.3 )] / [13 x (7.9 - 6.9)]
= (6.5 x 10) / (1.3 x 1)
= 50
2/5 = 0.4 , 5/6 = 0.833, 11/12 = 0.916 and 7/8 = 0.875
Clearly, the greatest fraction is 0.916, i, e . 11/12.
Given expression =(.6)3 + (.4) 3 + 3 x .6 x .4 x (.6 + .4)
= a3 + b3 + 3ab (a+b)
= (a+b)3
= (.6 + .4)3
= 13
= 1
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