Math
I am a fraction in simplest form. I am
greater than1/3 and less than 1/2.
The sum of all my digitsb is 8. the difference between my numerator and denominator is 7. What fraction am I?
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The thing that may be keeping you from solving the problem is thinking that you are only dealing with two digits. Breaking this set should help.
To solve this problem, you need to find a fraction that satisfies the given conditions. Let's start by breaking down the given information:
1. The fraction is greater than 1/3 and less than 1/2.
To determine which fractions satisfy this condition, let's list some fractions between 1/3 and 1/2:
1/3, 2/5, 3/7, 4/9, 5/11, 6/13, 7/15, 8/17, 9/19, 10/21, 11/23, ...
2. The sum of all its digits is 8.
To fulfill this condition, we need to find a numerator and denominator with digits that sum up to 8. Let's check the fractions from our previous list:
1/3: 1 + 3 = 4
2/5: 2 + 5 = 7
3/7: 3 + 7 = 10
4/9: 4 + 9 = 13
5/11: 5 + 1 + 1 = 7
6/13: 6 + 1 + 3 = 10
7/15: 7 + 1 + 5 = 13
8/17: 8 + 1 + 7 = 16
9/19: 9 + 1 + 9 = 19
10/21: 1 + 0 + 2 + 1 = 4
11/23: 1 + 1 + 2 + 3 = 7
3. The difference between the numerator and denominator is 7.
From the list above, let's check the fractions where the difference between the numerator and denominator is 7:
5/11, 11/23
Out of these, only 5/11 satisfies both conditions. Therefore, the fraction you are looking for is 5/11.