Question

The numerator of a fraction is 5 less than its denominator. If 1 is added to the numerator and to the denominator, the new fraction is 2/3. Find the fraction.​

Answer 1

9/14

Step-by-step explanation:

Let the original denominator be 'x'. So, numerator is 5 less than x = x - 5.

Fraction is (x - 5)/x

When 1 is added to the numerator and to the denominator. Denominator is (x + 1) and numerator is (x - 5) + 1 = (x - 4).

Fraction is 2/3 :

=> (x - 4)/(x + 1) = 2/3

=> 3(x - 4) = 2(x + 1)

=> 3x - 12 = 2x + 2

=> 3x - 2x = 12 + 2

=> x = 14

Original fraction = (x - 5)/x = (14 - 5)/14

Original fraction is 9/14

Answer 2

${\large{\pmb{\sf{\underline{Required \; Solution...}}}}}$

Given that:

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

⋆ 1 is added to the numerator and to the denominator.

⋆ The new fraction is 2/3

To find: The original fraction.

Solution: The original fraction = 9/14

Assumption: Let denominator be a

Full Solution:

• As we already take a as the denominator. As it is given that the numerator of a fraction is 5 less than its denominator henceforth, let us assume numerator as a-5. Henceforth, as we know that a fraction is consists of a numerator and denominator. Henceforth, fraction be (a-5)/a

• Also given that 1 is added to the numerator and to the denominator henceforth, now it be the following:

• Numerator = (a-5)+1 = a-4
• Denominator = a+1 = (a+1)

• Now given that the new fraction is 2/3. Now let's put the values.

→ 2/3 = (a-4)/(a+1)

◕ Cross multiplying we get,

→ 3(a-4) = 2(a+1)

→ 3a - 12 = 2a + 2

→ 3a-2a = 2+12

→ 1a = 14

→ a = 14

• We get denominator as 14.

• Henceforth, original fraction be

→ (a-5)/a

→ (14-5)/14

→ 9/14

• Original fraction is 9/14