Final answer:
The simplified form of 22.5/1000 is obtained by dividing both the numerator and the denominator by the same factor. After correctly identifying the factor as 2.5, the fraction simplifies to 9/400, which is answer choice (a).
Step-by-step explanation:
The simplified form of 22.5⁄1000 is found by dividing both the numerator and the denominator by their greatest common divisor (GCD). By identifying the GCD as 22.5, we can divide both the numerator and the denominator by this number, which simplifies the fraction:
- Numerator: 22.5 ÷ 22.5 = 1
- Denominator: 1000 ÷ 22.5 = 40
This gives us the fraction 1⁄40, which is not one of our choices. However, we realize we've simplified incorrectly because 22.5 is not the GCD—it is actually the numerator itself. We need to find the GCD that reduces the fraction correctly. Upon further examination, it's easier to see that the correct GCD is 0.225, which if we divide both numerator and denominator by, gives us:
- Numerator: 22.5 ÷ 0.225 = 100
- Denominator: 1000 ÷ 0.225 = 4000
Upon further reducing by dividing both top and bottom by the factor of 100 you get the fraction 1⁄40. However, this is still not one of the answer choices given. If we return to the original fraction and reduce it by dividing top and bottom by 2.5, we get:
- Numerator: 22.5 ÷ 2.5 = 9
- Denominator: 1000 ÷ 2.5 = 400
The fraction 9⁄400 corresponds to answer choice (a) and is the correct simplified form of 22.5⁄1000.