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## Explanation

- When the numerator of a fraction increased by 4 the fraction increases by 2/3.
- The denominator of the fraction can be find out in this way.

Let suppose y shows numerator and z shows denominator in a fraction.

Fraction increases by 2/3, when y (numerator) increased by 4

(y + 4)/z = y/z + 2/3 ________ (i)

By solving this equation, we can easily find out the denominator (z = 6).

## To Find

Denominator = ?

## Solution

Let suppose

Let suppose y shows numerator and z shows denominator in a fraction.

According to given condition

(y + 4)/z = y/z + 2/3

(y + 4)/z = (3y + 2z)/3z

3z(y + 4) = z(3y + 2z)

3yz + 12z = 3yz + 2z^{2}

2z^{2} – 12z = 0

z^{2} – 6z = 0

z(z – 6) = 0

z = 0 & z – 6 = 0

z = 0 (not possible) & z = 6 (possible)

**Denominator = 6 answer**

## Conclusion

When the numerator of a fraction increased by 4 the fraction increases by 2/3. The denominator of the fraction is 6.