Question

8. The numerator of a fraction is 7 less than the
denominator. If 3 is added to the numerator and
2 is added to the denominator, the value of the
2.
fraction becomes . Find the original fraction.
3​

Answer 1

Answer:

let num =x

let den=y

fraction =x/y

given x=y-7

condition 1 =x+3/x+7+2=2

x=-15

y=-8

Answer 2

Appropriate Question :

• the numerator of a fraction is 7 less than the denominator.if 3 is added to the numerator and 2 is added to the denominator the value of the fraction becomes 2/3 .find the required fraction.

Given Parameters :

• The numerator of a fraction is 7 less than the denominator.
• if 3 is added to the numerator and 2 is added to the denominator the value of the fraction becomes 2/3.

Unknown :

• The required fraction = ?

Solution :

• Let the denomintaor be 'x'. Then,the numerator will be 'x - 7'.

• Required Fraction = Numerator/Denomintaor = x - 7/x ....[Equation (i)]

★ According to Question now :

• if 3 is added to the numerator and 2 is added to the denominator the value of the fraction becomes 2/3.

→ (x - 7 + 3)/(x + 2) = 2/3

→ (x - 4)/(x + 2) = 2/3

Cross multiplying both the sides we get :

→ 3(x - 4) = 2(x + 2)

→ 3x - 12 = 2x + 4

Combining like terms we get :

→ 3x - 2x = 4 + 12

→ x = 16

• Hence,the required fraction is denomintaor is 16.

★ Finding the required fraction :

→ Required Fraction = x - 7/x

By substituting the value of x = 16 in equation (i) we get :

→ Required Fraction = 16 - 7/16

→ Required Fraction = 9/16

• Hence,the required fraction is 9/16.