Question

The number of a fraction is less 5 than its deomeriator. If is added to the numerator and to the new fraction is 2/3. Find the fraction.​

Answer 1

Answer:

FOR EXAMPLE

Step-by-step explanation:

Given:-

The numerator of a fraction is 5 less than its denominator.

If 3 is added to the numerator and denominator both , the fraction becomes 4/5.

To Find:-

The Original Number

Solution:-

Let denominator of the fraction be = x  

And then numerator be x – 5

Original fraction = (x – 5)/x

According to the Question,

⇒  (x – 5 + 3)/(x + 3) = 4/5

⇒ (x – 2)/(x + 3) = 4/5

⇒ 5(x – 2) = 4x + 12

(By cross multiplication)

⇒ 5x – 10 = 4x + 12  

⇒ 5x - 4x = 12 + 10  

⇒ x = 22

Original fraction = (x – 5)/x  

Original fraction  = (22 – 5)/22  

Original fraction = 17/22

Hence, the original number is 17/22.

                                  OR

Given:

The numerator of a fraction is 5 less than its denominator. If 3 is added to the numerator and denominator both, the fraction becomes = 4/5

Step 1

Instruction:- Let the original denominator be x.

The numerator of the fraction is 5 less than its denominator. Find the original numerator.

Calculation:- Original numerator = x - 5

Step 2

Instruction :- If 3 is added, find a new numerator and new denominator.

Calculation:- New numerator = x - 5 + 3

                                                   = x - 2

                   = New numerator = x + 3

Step 3

Instruction:- Equate the new fraction with = 4/5

Calculation = x - 2 / x + 3 = 4/5

Step 4  

Instruction:- Cross multiple the obtained equation and solve for x.

Calculation:- 5 x ( x - 2) = 4 x ( x + 3)

                            5x - 10 = 4x + 12

                                      x = 22

Step 5

Instruction:- Find the original numerator and denominator.

Calculation:- Original Denominator = 22

                    = Original Numerator = 22 - 5

                    =  17

Step 6

Instruction:- Write the Original fraction

Calculation:- Original fraction = 17/22