Question

The numerator of a rational number is 3 less than the denominator. If the numerator is increased

by 2 and the denominator by 5, we get the rational number ½. Find the rational number.
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Answer 1

Given :

• Numerator of a rational Number is 3 less than the denominator.
• If the numerator is increased by 2 and the denominator by 5, we get the rational number ½.

To Find :

• Rational Numbers .

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that Numerator is 3 less than the Denominator . So ,

$\longmapsto\tt{Numerator=x-3}$

Now ,

• If the numerator is increased by 2 and the denominator by 5, we get the rational number ½.

$\longmapsto\tt{Numerator=x-3+2=x-1}$

$\longmapsto\tt{Denominator=x+5}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-1}{x+5}=\dfrac{1}{2}}$

$\longmapsto\tt{2(x-1)=1(x+5)}$

$\longmapsto\tt{2x-2=1x+5}$

$\longmapsto\tt{2x-1x=5+2}$

$\longmapsto\tt{1x=7}$

$\longmapsto\tt\bf{x=7}$

Value of x is 7 ..

Therefore :

$\longmapsto\tt{Numerator=7-3}$

$\longmapsto\tt\bf{4}$

$\longmapsto\tt\bf{Denominator=7}$

So , The Rational Number is 4/7 ..

Answer 2

Answer:

4/7

Step-by-step explanation:

its the answer I'm done