Simplification, General Mathematics

Question: `5 2/5 of 140 + ? = 800`
A
`28`

B
`36`

C
`44`

D
`52`

Note: Let,`27/5 of 140 + x = 800` Then` 27 xx 28 + x = 800` `:. 756 + x 80` or `x = (800 - 756)` `= 44`
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Question: `1 + 1/` `1 + 1/` `1 - 1/6= ?`
A
`6/11`

B
`16/11`

C
`7/6`

D
`1/6`

Note: Given Exp. `1 + 1/` `1 + 1/` `1 - 1/6` `1 + 1/ 1 + 1/((5∕6))` `= 1 + 1/` ` 1 + 6/5` `= 1 + 1/((11∕5))` `= (1 + 5/11)` `= 16/11`
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Question: The value of `1 + 1/` `2 + 1/` `1 - 1/3` is :
A
`2/7`

B
`7/9`

C
`9/7`

D
`13/7`

Note: Given Exp, `= 1 + 1/` `2 + 1/` `1 - 1/3` `= 1 + 1/` `2 + 1/((2∕3))` `= 1 + 1/` `2 + 3/2` `= 1 + 1/((7∕2))` `= (1 + 2/7)` `= 9/7`
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Question: The simplification of `1/` `2 + 1/` `2 + 1/` `2 - 1/2`yields :
A
`4/9`

B
`8/19`

C
`4/18`

D
`8/21`

Note: Given Exp , `= 1/` `2 + 1/` `2 + 1/` `2 - 1/2` `= 1/` `2 + 1/` `2 + 1/((3∕2))` `= 1/` `2 + 1/` `2 + 2/3` `= 1/` `2 + 1/((8∕3))` `= 1/` `2 + 3/4` `= 1/((19∕8))` `= 8/19`
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Question: The value of `4 - 5/` `1 + 1/` `3 + 1/` `2 + 1/4` is :
A
`40/31`

B
`4/9`

C
`1/8`

D
`31/40`

Note: Given Exp , `= 4 - 5/` `1 + 1/` `3 + 1/` `2 + 1/4` `= 4 - 5/` `1 + 1/` `3 + 1/((9∕4))` `= 4 - 5/` `1 + 1/` `3 + 4/9` `= 4 - 5/` `1 + 1/((31/9))` `= 4 - 5/` `1 + 9/31` `= 4 - 5/((40∕31))` `= (4 - (5 xx 31)/40)` `= (4 - 31/8)` `= 1/8`
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Question: The simplification of `((75983 xx 75983 - 45983 xx 45983)/30000)`yeilds:
A
`121796`

B
`121866`

C
`121956`

D
`121966`

Note: Given Exp , `= ((75983)^2 - (45983)^2)/30000` `= ((75983 + 45983)(75983 - 45983))/30000` `= (121966 xx 30000)/30000` `= 121966`
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Question: The value of `((343 xx 343 xx 343 + 257 xx 257 xx 257)/(343 xx 343 - 343 xx 257 + 257 xx 257))` is :
A
`8600`

B
`800`

C
`600`

D
`2600`

Note: Given Exp , `= ((343)^3 + (257)^2)/((343)^2 - 343 xx 257 + (257)^2)` `= ((a^3 + b^3)/(a^2 - ab + b^2))`,`where a = 343 and b = 257` `= (a + b)` `= (343 + 257)` `= 600`.
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Question: Four children A,B,C and D divide a bag of sweets .A takes `1/3`of them ,B `2/5`th of the remainder and the rest is equally shared between C and D.What fraction of the sweets did c or D get ?
A
`1/5`

B
`1/17`

C
`1/6`

D
`1/4`

Note: A' s share = `1/3`. Remainder `= (1 - 1/3) = 2/3` B 's share `= 2/5 of 2/3 = 4/15`. Rest,`= (2/3 - 4/15)` `= 6/15` `= 2/5` `C s share `= D,s share `= 1/2 of 2/5 = 1/5`.
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Question: The value of `1 + 1/(4 xx 3) + 1/(4 xx 3^2) + 1/(4 xx 3^3)` is :
A
`121/108`

B
`3/2`

C
`31/2`

D
None of these

Note: Not available
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Question: The value of `1/4 + 1/(4 xx 5) + 1/(4 xx 5 xx 6)` correct to four decimal places is :
A
`0.3075`

B
`0.3082`

C
`0.3083`

D
`0.3085`

Note: Given Exp, `= (5 xx 6 + 6 +1)/(4 xx 5 xx 6)` `= 37/120` `= 0.3083`.
1. Report

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Question: `5 2/5 of 140 + ? = 800`

Question: `1 + 1/` `1 + 1/` `1 - 1/6= ?`

Question: The value of `1 + 1/` `2 + 1/` `1 - 1/3` is :

Question: The simplification of `1/` `2 + 1/` `2 + 1/` `2 - 1/2`yields :

Question: The value of `4 - 5/` `1 + 1/` `3 + 1/` `2 + 1/4` is :

Question: The simplification of `((75983 xx 75983 - 45983 xx 45983)/30000)`yeilds:

Question: The value of `((343 xx 343 xx 343 + 257 xx 257 xx 257)/(343 xx 343 - 343 xx 257 + 257 xx 257))` is :

Question: Four children A,B,C and D divide a bag of sweets .A takes `1/3`of them ,B `2/5`th of the remainder and the rest is equally shared between C and D.What fraction of the sweets did c or D get ?

Question: The value of `1 + 1/(4 xx 3) + 1/(4 xx 3^2) + 1/(4 xx 3^3)` is :

Question: The value of `1/4 + 1/(4 xx 5) + 1/(4 xx 5 xx 6)` correct to four decimal places is :