The sum of the numerator and denominator of a simplest fraction is 62. If the numerator is reduced to 1 and the denominator is subtracted by 7, the new fraction will be reduced to 2 / 7. What is the original fraction?

The sum of the numerator and denominator of a simplest fraction is 62. If the numerator is reduced to 1 and the denominator is subtracted by 7, the new fraction will be reduced to 2 / 7. What is the original fraction?

Let the original molecule be x and the denominator be 62-x
Present numerator: X-1 present denominator: 62-x-7 = 55-x
The equation X-1 / 55-x is 2 / 7
Cross multiply to get 110-2x = 7x-7
117 = 9x
x=13
The root of the original fractional equation is x = 13
So the original score was 13 / 49
I think the equation of one variable is relatively simple

The sum of numerator and denominator is 23. After the denominator is increased by 19, a new fraction is obtained. This fraction is reduced to the simplest fraction, which is 15. What is the original fraction?

A fraction can be reduced to 12 if its denominator plus 1, and 23 if its denominator minus 1
A. 23B. 35C. 47D. 59

Let the fraction be AB, AB + 1 = 12, ab − 1 = 23, and the solution is a = 4, B = 7, that is, the fraction is 47

If the numerator plus 5, a fraction can be reduced to 1 / 2; if the denominator minus 3, it can be reduced to 1 / 3

Let the denominator of this fraction be x, and the molecule be y. The first condition is equivalent to 2 (y + 5) = x, and the second condition is equivalent to x-3 = 3Y. Two equations are solved simultaneously, and the fraction x = 24, y = 7 is 7 out of 24
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