Question

Question Strip
If 3 is subtracted from the numerator of a fraction, the fraction is reduced to ⅔
Instead, if we add 2 to the numerator and 3 to
the denominator, the new fraction becomes ⅚
Find the fraction.
​

Answer 1

Answer:

• The fraction is 13/15.

Step-by-step explanation:

Let us assume:

• Numerator = x
• Denominator = y
• Fraction = x/y

Given that:

3 is subtracted from the numerator of a fraction, the fraction is reduced to ⅔.

⟶ (x - 3)/y = 2/3

Cross multiplication.

⟶ 3(x - 3) = 2y

⟶ 3x - 9 = 2y

⟶ 3x - 2y = 9 ______(i)

We add 2 to the numerator and 3 to the denominator, the new fraction becomes ⅚.

⟶ (x + 2)/(y + 3) = 5/6

Cross multiplication.

⟶ 6(x + 2) = 5(y + 3)

⟶ 6x + 12 = 5y + 15

⟶ 6x - 5y = 15 - 12

⟶ 6x - 5y = 3 ______(ii)

Finding the fraction:

Subtracting eqⁿ(i) × 2 from eqⁿ(ii).

⇒ 6x - 5y - 2(3x - 2y) = 3 - 2(9)

⇒ 6x - 5y - 6x + 4y = 3 - 18

⇒ - y = - 15

Cancelling minus sign.

⇒ y = 15

∴ Denominator = y = 15

In equation (i).

⇒ 3x - 2y = 9

Substituting the value of y.

⇒ 3x - 2(15) = 9

⇒ 3x - 30 = 9

⇒ 3x = 9 + 30

⇒ 3x = 39

⇒ x = 39/3

⇒ x = 13

∴ Numerator = x = 13

∴ Fraction = x/y = 13/15

Answer 2

Required Answer : -

Given ,

If 3 is subtracted from the numerator of a fraction, the fraction is reduced to ⅔

Solution

3x - 2 y = 9 (i)

6x - 5y = 30 (ii)

let's solve the this problem with first equation = 3x - 2 y = 9 (i)

$3 \times - 2(15) = 15$

$3 \times - 30 = 9$

$3 \times = 9 + 30$

$3 \times = 39$

$x = 13$

➠ hence , the numerator is 13 fraction

$\frac{x}{y}$

$= \frac{13}{15}$