Question

Числитель дроби на 5 меньше ее знаменателя.Если числитель этой дроби уменьшить на 2 ,а знаменатель увеличить на 2,то получится дробь,равная 1/10.Чему равен знаменатель дроби? Скажите пожалуйста.

Answer 1

(х-5)/х

(х-5-2)/(х+2) = 1/10

(х-7)/(х+2) = 1/10       10(х-7) = х+2   10х-70=х+2    9х=72    х=8

 

Дробь изначальная была   3/8. Знаменатель дроби = 8

Answer 2

Problem Analysis

We are given a fraction where the numerator is 5 less than the denominator. If we decrease the numerator by 2 and increase the denominator by 2, the resulting fraction is equal to 1/10. We need to find the value of the denominator of the original fraction.

Solution

Let's assume the original fraction is x/y, where x is the numerator and y is the denominator.

From the given information, we can form the following equations:

Equation 1: x = y - 5 (The numerator is 5 less than the denominator)

Equation 2: (x - 2) / (y + 2) = 1/10 (If we decrease the numerator by 2 and increase the denominator by 2, the resulting fraction is 1/10)

To find the value of the denominator (y), we can solve these equations simultaneously.

Solving the Equations

Let's substitute Equation 1 into Equation 2:

((y - 5) - 2) / (y + 2) = 1/10

Simplifying the equation:

(y - 7) / (y + 2) = 1/10

Cross-multiplying:

10(y - 7) = y + 2

Expanding:

10y - 70 = y + 2

Simplifying:

10y - y = 2 + 70

9y = 72

Dividing both sides by 9:

y = 8

Answer

The denominator of the fraction is 8.

Explanation

By solving the given equations, we found that the denominator of the original fraction is 8.