%2F(1-1%2F7).jpeg "(2/7-5)/(1-1/7)")
Simplifying a Complex Fraction: (2/7-5)/(1-1/7)
This article will guide you through the process of simplifying the complex fraction (2/7-5)/(1-1/7).
Understanding Complex Fractions
A complex fraction is a fraction where either the numerator, denominator, or both contain fractions. Our example fits this description, with fractions present in both the numerator and denominator.
Simplifying the Numerator and Denominator
The first step involves simplifying the numerator and denominator separately:
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Numerator: (2/7 - 5)
- To subtract, we need a common denominator. The common denominator for 7 and 1 is 7.
- (2/7 - 35/7) = -33/7
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Denominator: (1 - 1/7)
- Again, we need a common denominator.
- (7/7 - 1/7) = 6/7
Combining the Simplified Parts
Now, our fraction is: (-33/7) / (6/7)
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 6/7 is 7/6.
Therefore, we have: (-33/7) * (7/6)
Final Calculation and Simplification
Multiplying the numerators and denominators, we get: (-33 * 7) / (7 * 6)
This simplifies to -231/42.
To express in its simplest form, we can divide both numerator and denominator by their greatest common factor, which is 21. This gives us the final answer: -11/2.
Conclusion
By breaking down the problem into simpler parts and utilizing the rules of fraction operations, we were able to simplify the complex fraction (2/7-5)/(1-1/7) to its simplest form: -11/2.