Note: Let,`5/6 ÷ 6/7 xx x - 8/9 ÷ 8/5 + 3/4 xx 10/3` `= 25/9` Then,`5/6 xx 7/6 xx x - 8/9 xx 5/8 + 5/2` `= 25/9` or ` 35/36 x - 5/9 + 5/2` `= 25/9` or`35/36 x` `= 25/9 + 5/9 - 5/2` or`35/36 x` `= 10/3 - 5/2` `= 5/6` or`x 5/6 xx 36/35` `=6/7`.

Note: Requied excess, `= (2/3 xx 57 - 1/3 xx 90)` `= (38 - 30)` `= 8`.

Note: Let,`45 - [28 - {37 - (15 - x )}]= 58`. `Then 45 - [28 - {37 - 15 + x}] = 58` or `45 - [28 - (22 + x}]= 58` or `45 - [28 - 22 - x]= 58` or `45 - [6 - x]= 58` or `45 - 6 + x = 58` or ` 39 + x = 58` or `x = (58 - 39)= 19`.

Note: Substituting the given values ,we have ` 9 3/8 xx 1 7/9` `= 75/8 xx 16/9` `= 150/9` `= 50/3` `= 16 2/3`.

Note: Let,`33/4 - 21/5 + 28/10 + 4/x - 232/100 = 533/100` Then,`4/x = 533/100 + 232/100 + 21/5 - 33/4 - 28/10` or` 4/x = 765/100 + (84 - 165 - 56)/20` or `4/x = 765/100 - 137/20` or`4/x = (765 - 685)/20` or`4/x = 80/20` `= 4/1` So,`x = 1`.

Note: Let,`20/3 of 726/100 ÷ 45/100 of x = 968/117` `or 242/5 ÷ (45x)/100` `= 968/117` `0r 242/5 xx 100/(45x)` `= 968/117` `or x = 242/5 xx 100/45 xx 117/968` `or x = 13`

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

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`

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`

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`