Simplifying the Expression: (ii) (2)/(5)times((3)/(7))(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)
This problem involves performing arithmetic operations with fractions. Let's break it down step by step.
Understanding the Order of Operations
We need to follow the order of operations (PEMDAS/BODMAS):
 Parentheses/ Brackets
 Exponents/ Orders
 Multiplication and Division (from left to right)
 Addition and Subtraction (from left to right)
Simplifying the Expression

Multiplication:
 (2/5) * (3/7) = 6/35
 (1/6) * (3/2) = 3/12 = 1/4
 (1/14) * (2/5) = 2/70 = 1/35

Substitution: Now we can substitute these values back into the original expression: 6/35  1/4 + 1/35

Addition/Subtraction: To add/subtract fractions, they need a common denominator. The least common multiple of 35 and 4 is 140.
 (6/35) * (4/4) = 24/140
 (1/4) * (35/35) = 35/140
 (1/35) * (4/4) = 4/140
Now we have: 24/140  35/140 + 4/140
Finally, adding the fractions: 24/140  35/140 + 4/140 = 55/140

Simplification: The fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 5: 55/140 = 11/28
Conclusion
Therefore, the simplified form of the expression (2/5) * (3/7)  (1/6) * (3/2) + (1/14) * (2/5) is 11/28.