For a simplest fraction, the numerator is 15 less than the denominator. If 16 is added to the denominator and 7 is subtracted from the numerator, what is the fraction? Do it with formulas, not equations

For a simplest fraction, the numerator is 15 less than the denominator. If 16 is added to the denominator and 7 is subtracted from the numerator, what is the fraction? Do it with formulas, not equations

41/26

(1) The simplest true fraction with denominator 16 is () (2) the simplest true fraction with numerator 8 is ()

1/16,3/16,5/16,7/16,9/16,11/16,13/16,15/16
1/8,3/8,4/5,7/8

(1) The numerator of a fraction is 13 smaller than the denominator. If 18 is added to the numerator and 21 is added to the denominator, and the score value remains unchanged, what is the original fraction?
(2) The sum of the numerator and denominator of the simplest fraction is 62. If the numerator subtracts 1 and the denominator subtracts 7, the new fraction will be 2 / 7. What is the original fraction?

(1) Method:
The denominator is: 13 × [21 / (21-18)] = 91
The molecular weight is 91-13 = 78
So the original score was 78 / 91
(2) Method:
（62-8）[2/（7+2）]=54×（2/9）=12
The original fraction molecule should be 12 + 1 = 13
The original denominator should be 62-13 = 49
So, the original score should be 13 / 49
In fact, this type of problem can be very simple to do with the equation
(1) Let the numerator be a and the denominator be a + 13
According to the title, it can be listed as follows:
a/（a+13）=（a+18）/（a+13+21）
a（a+13+21）=（a+13）（a+18）
Square of a + 34a = square of a + 31a + 234
3a=234
A = 78, denominator 78 + 13 = 91
So, the original score was 78 / 91
(2) Let the numerator be a and the denominator be 62-a
According to the title, it can be listed as follows:
（a-1）/（62-a-7）=2/7
7（a-1）=2（55-a）
7a-7=110-2a
9a=117
A = 13, denominator 62-13 = 49
So the original score was 13 / 49

The sum of the numerator and denominator of a fraction is 32. When the denominator is increased by 4, a new fraction is obtained. The fraction is reduced to the simplest fraction, which is one third of the original fraction

(32+4)÷(3+1)=9
32-9=23
The original score was 9 out of 23