Question

The numerator of a fraction is 2 less than the denominator. If one is added to its denominator,it becomes 1/2 find the fraction

Answer 1

✬ Fraction = 3/5 ✬

Step-by-step explanation:

Given:

• Numerator of a fraction is 2 less than the denominator.
• If 1 is added to its denominator the fraction becomes 1/2.

To Find:

• What is the fraction ?

Solution: Let the numerator be x and denominator be y. Therefore, fraction will be x/y

Now, according to first condition

➟ Numerator = 2 less than denominator

➟ Numerator = (y – 2)

➟ x = (y – 2)...........(1)

According to the second condition

• When we add 1 to the denominator fraction becomes 1/2

$\implies{\rm }$ N / ( D+ 1 ) = 1/2

$\implies{\rm }$ (x) / (y + 1) = 1/2

[ From equation 1 ] → x = (y – 2)

$\implies{\rm }$ (y – 2) / (y + 1) = 1/2

$\implies{\rm }$ 2(y – 2) = 1(y + 1)

$\implies{\rm }$ 2y – 4 = y + 1

$\implies{\rm }$ 2y – y = 1 + 4

$\implies{\rm }$ y = 5

So,

➙ Denominator of fraction is y = 5 &

➙ Numerator of fraction = x = (y – 2)

➙ Numerator = x = (5–2) = 3

∴ Fraction will be x/y = 3/5

Hence, the required fraction is 3/5.

Answer 2

AnsWer :

3 / 5.

SolutioN :

Let,

• The Numerator be D - 2.
• Denominator be D.

☛ Case 1.

• The numerator of a fraction is 2 less than the denominator.

→ D - 2 / D _____ ( 1 )

$\rule{100}3$

☛ Case 2.

• If one is added to its denominator,it becomes 1/2.

→ D - 2 / D + 1 = 1 / 2.

→ 2( D - 2 ) = D + 1.

→ 2D - 4 = D + 1.

→ D - 4 = 1.

→ D = 5.

$\rule{50}1$

→ N = 5 - 2 = 3.

✡ Now, Fraction become → N / D = 3 / 5.

$\rule{200}3$

VerificatioN :

D - 2 / D + 1 = 1 / 2.

→ 5 - 2 / 5 + 1 = 1 / 2.

→ 3 / 6 = 1 / 2.

→ 1 / 2 = 1 / 2.

≛ Hence Verify.