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((7)/(16)- (1)/(2) Of (1)/(5))times(4)/(5)-(1)/(3)times(5)/(8)times 2(3)/(4)

2 min read Jun 16, 2024
((7)/(16)- (1)/(2) Of (1)/(5))times(4)/(5)-(1)/(3)times(5)/(8)times 2(3)/(4)

Solving the Expression: ((7)/(16)- (1)/(2) of (1)/(5))times(4)/(5)-(1)/(3)times(5)/(8)times 2(3)/(4)

This problem involves several operations: fractions, multiplication, and mixed numbers. Let's break it down step by step to find the solution.

Simplifying the Expression

  1. "of" means multiplication: (1/2) of (1/5) = (1/2) * (1/5) = 1/10
  2. Subtraction within the parentheses: (7/16) - (1/10) = (35/80) - (8/80) = 27/80
  3. Convert mixed number to fraction: 2(3/4) = (2*4 + 3)/4 = 11/4
  4. Multiplication:
    • (27/80) * (4/5) = 27/100
    • (1/3) * (5/8) * (11/4) = 55/96

Final Calculation

Now we have: (27/100) - (55/96)

To subtract these fractions, we need a common denominator:

  • (27/100) * (96/96) = 2592/9600
  • (55/96) * (100/100) = 5500/9600

Finally: (2592/9600) - (5500/9600) = -2908/9600

This fraction can be simplified by dividing both numerator and denominator by their greatest common factor, which is 4: -727/2400

Therefore, the solution to the expression is -727/2400.

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