Question

The denominator of a fraction exceeds the numerator by 5 if the numerator is increased by 9 then the fraction is increased by 1 find the fraction.​

Answer 1

Given that:

• The denominator of a fraction exceeds the numerator by 5.
• If the numerator be increased by 9, then the fraction gets increased by 1.

To Find:

• The required fraction.

Let us assume:

• The numerator of the fraction be x.
• Denominator = x + 5
• Fraction = x/(x + 5)

According to the question.

ㅤ↠ㅤ(x + 9)/(x + 5) = x/(x + 5) + 1

ㅤ↠ㅤ(x + 9)/(x + 5) = (x + x + 5)/(x + 5)

Cancelling the denominator (x + 5).

ㅤ↠ㅤx + 9 = x + x + 5

ㅤ↠ㅤx + 9 = 2x + 5

ㅤ↠ㅤ2x - x = 9 - 5

ㅤ↠ㅤx = 4

Hence,

• The required fraction = x/(x + 5) = 4/(4 + 5) = 4/9