Question

If one is subtracted from the numerator of a fraction, it becomes 1/2. If one is added to both numerator and denominator of the fraction it becomes 2/3. What is the fraction?

Answer 1

The fraction is (5/8).

Step-by-step explanation:

We are given that if one is subtracted from the numerator of a fraction, it becomes 1/2. If one is added to both numerator and denominator of the fraction it becomes 2/3.

Let the original fraction be $\frac{x}{y}$  where numerator = $x$ and denominator = $y$ .

We are given with the following conditions;

• First condition states that if one is subtracted from the numerator of a fraction, it becomes 1/2, that means;

                                $\frac{x-1}{y} =\frac{1}{2}$

                                $y = 2(x-1)$

                                $y=2x-2$  ------------ [Equation 1]

• Second condition states that if one is added to both numerator and denominator of the fraction it becomes 2/3, that means;

                                 $\frac{x+1}{y+1}=\frac{2}{3}$

                          $3(x+1) =2(y+1)$

                             $3x+3 =2y+2$

                             $3x+3 =2(2x-2)+2$         {using equation 1}

                             $3x+3 =4x-4+2$

                              $3x+3 =4x-2$

                                 $3+2 =4x-3x$

                                  $x=5$

Now, putting value of $x$ in equation 1, we get;

                         $y=(2\times 5)-2$

                            = 10 - 2 = 8

Therefore, the original fraction is $\frac{x}{y} =\frac{5}{8}$ .