Question

1. If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is 1/2. What is the rational number? *

Answer 1

GIVEN :–

• Numerator is 2 less than denominator of a rational number.

• when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is 1/2.

TO FIND :–

• Rational number = ?

SOLUTION :–

• Let the denominator = x

• So the rational number –

$\\ \implies \bf \:Rational \: \: number = \dfrac{x - 2}{x}$

• According to the question –

$\\ \implies \bf \dfrac{(x - 2) - 1}{(x) - 1} = \dfrac{1}{2}$

$\\ \implies \bf \dfrac{x - 2 - 1}{x- 1} = \dfrac{1}{2}$

$\\ \implies \bf \dfrac{x -3}{x- 1} = \dfrac{1}{2}$

$\\ \implies \bf 2(x - 3) = 1(x - 1)$

$\\ \implies \bf 2x - 6= x - 1$

$\\ \implies \bf 2x - x= 6 - 1$

$\\ \implies \large{ \boxed{ \bf x = 5}}$

$\\ \implies \bf Denominator = 5$

• So that –

$\\ \implies \bf Numerator = 5 - 2$

$\\ \implies \bf Numerator =3$

▪︎ Hence , The Rational number is ⅗.

Answer 2

Let the denominator be x

Numerator = x-2

Rational no. = x-2/x

A.T.Q

$x-2-1/x-1 =>1/2$

$x-3/x-1 =>1/2$

$2(x-3) =>1( x-1)$

$2x - 6 =>x -1$

$2x-x =>-1 +6$

$x =>5$

$Rational$ $no. =>5-2/5 = 3/5$ ANSWER

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