For whole numbers a, b you can convert them to a percentage a/b that is then rounded to a whole percent.
Suppose you know a/b = 24%, it may be that b=21 since 5/21 = .238095... but b could not be 22 since 5/22=23% and 6/22=27%.
Still using 24%:
[1] What is the smallest possible value of b?
[2] What is the largest value that b could not be?
Now find the 5 percentages between 0 and 50
[3] that give the largest answers to part [1]?
[4] that give the smallest answers to part [2]?
The concept of converting whole numbers a and b into percentages and exploring the smallest and largest possible values of b based on a given percentage is an interesting mathematical exercise. Here are the answers to the questions posed:
- [1] The smallest possible value of b, given a/b = 24%, is 21. This is because 5/21 ≈ 23.81%, and rounding it to the nearest whole percent gives 24%.
- [2] The largest value that b could not be, given a/b = 24%, is 22. As mentioned, 5/22 = 22.73%, and it rounds up to 23%.
To find the five percentages between 0 and 50 that give the largest answers to part [1], we need to look for fractions where the numerator (a) is as small as possible while keeping the denominator (b) relatively large. Here are the percentages and their corresponding fractions:
- 1% (a/b = 1/100)
- 2% (a/b = 2/100)
- 3% (a/b = 3/100)
- 4% (a/b = 4/100)
- 5% (a/b = 5/100)
These percentages have the smallest possible denominators while staying within the 0 to 50 range and will result in the smallest values of b.
Conversely, to find the five percentages between 0 and 50 that give the smallest answers to part [2], we should look for fractions where the numerator (a) is as large as possible. Here are the percentages and their corresponding fractions:
- 48% (a/b = 48/100)
- 47% (a/b = 47/100)
- 46% (a/b = 46/100)
- 45% (a/b = 45/100)
- 44% (a/b = 44/100)
These percentages have the largest
homework answers websites possible denominators while staying within the 0 to 50 range and will result in the largest values of b that could not be.
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