Final answer:
The inequality (4/5) > 1 - (16/25) simplifies to (4/5) > (9/25) after subtracting the fractions on the right side. Multiplying and adding as instructed gives a new fraction of 100/14, which simplifies to 50/7. This is greater than the original (4/5).
Step-by-step explanation:
The comparison (4/5) > 1 - (16/25) is a mathematical inequality involving fractions. To solve this, we first need to evaluate the right side of the inequality. To do that, we find a common denominator for the fractions involved.
Since 5 is a factor of both 5 and 25, we can use 25 as the common denominator:
- Convert 1 to a fraction with a denominator of 25, which would be 25/25.
- Now subtract the two fractions 25/25 - 16/25.
- The subtraction yields (25 - 16)/25 = 9/25.
- This simplifies the inequality to (4/5) > (9/25).
Next, we multiply the first and last terms and add them to the second set of terms.
- Multiplying 4 and 25 gives us 100.
- Add the second set of numbers, which means adding 5 to 9, giving us 14.
- Now combine these results to create a new fraction 100/14.
- Simplify this fraction by dividing both numerator and denominator by the greatest common factor, which is 2, yielding the simplified result of 50/7.
To conclude, we find that the simplified fraction resulting from the given procedure is 50/7, which is indeed greater than the original (4/5).