Question

The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator the fraction increase by unity. The fraction is

Answer 1

In the above Question , the following information is given -

The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.

To find - The Required fraction

Solution -

The denominator of a fraction exceeds the numerator by 2.

Let the numerator of the fraction be x

Therefore denominator of the fraction is x + 2 .

So , the required fraction becomes [ x ] / [ x + 2 ]

Now , 5 is added to the Numerator of the fraction ...

So , the new numerator becomes [ x + 5 ]

Thus the new Fraction becomes -

[x + 5 ] / [ x + 2 ]

This is greater than the original fraction by unity

So ,

[ x ] / [ x + 2 ] + 1 = [x + 5 ] / [ x + 2 ]

[x + x + 2 ] / [ x + 2 ] = [ x + 5 ] / [ x + 2 ]

=> [ 2x + 2 ] / [ x + 2 ] = [ x + 5 ] / [ x + 2 ]

=> 2x + 2 = x + 5

=> x = 3

Required fraction = 3/5

Answer 2

Concept:

Fractions is a mathematical way of expressing the parts of a whole object. For example: 3 / 4 means three parts out of 4.

Given:

We are given that:

The denominator exceeds the numerator by 2.

If 5 be added to the numerator, the fraction increase by 1.

Find:

We need to find the fraction.

Solution:

Let the numerator be x.

So, the denominator will be x + 2

ATQ, the fraction will become:

x / x + 2

Now, we have:

x + 5 / x + 2 = 1 + [x / x + 2]

Multiply both sides by x + 2:

x + 5 = x + 2 + x

2 x - x = 5 - 2

x = 3.

So, the fraction will be:

x / x + 2 = 3 / 3 + 2 = 3 / 5.

Therefore, the fraction is 3 / 5.

#SPJ2