-(2)%2F(5)times(-(3)%2F(7))-(1)%2F(6)times(3)%2F(2)%2B(1)%2F(14)times(2)%2F(5).jpeg "(ii) (2)/(5)times(-(3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)")
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
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Multiplication:
- (2/5) * (-3/7) = -6/35
- (1/6) * (3/2) = 3/12 = 1/4
- (1/14) * (2/5) = 2/70 = 1/35
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Substitution: Now we can substitute these values back into the original expression: -6/35 - 1/4 + 1/35
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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
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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.