Question

6. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the fraction becomes 1/8. Find the fraction.​

Answer 1

$\underline{\red{Given:}}$

• The numerator of a fraction is 4 less than its denominator.
• If the numerator is decreased by 2 and the denominator is increased by 1, then the fraction becomes 1/8.

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$\underline{ \red{To \: find:}}$

• The fraction = ?

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$\underline{ \red{Solution:}}$

Hence, The numerator of a fraction is 4 less than its denominator.......[Given]

∴ Let the denominator be ‘x’, and let the

numerator be (x - 4),

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Hence, If the numerator is decreased by 2 and the denominator is increased by 1, then the fraction becomes 1/8.....[Given]

$∴ \frac{x - 4 - 2}{x + 1} = \frac{1}{8} \\ \\ = > \frac{x - 6}{x + 1} = \frac{1}{8} \\ \\ = > 8(x - 6) = 1(x + 1) \\ \\ = > 8x - 48 = x + 1 \\ \\ = > 8x - x = 1 + 48 \\ \\ = > 7x = 49 \\ \\ = > x = \frac{ \cancel{(49})^{7} }{ \cancel{(7 })^{1} } \\ \\ = > x = \frac{7}{1} \\ \\ = > x = 7 \\ \\ ∴ The \: denominator =x= 7 \\ \\ ∴The \: numerator =x-4 \\= 7 - 4\\ = 3 \\ \\ \\ ∴ \:The \: fraction = \green{\boxed{\frac{3}{7}}}$

Answer 2

Given :

• Numerator of a rational number is less than its Denominator by 4.
• If 2 is subtracted from the numerator and 1 is added to its denominator, the new number becomes 1/8 .

To Find :

• The Rational Number .

Solution :

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

As Given that Numerator of a rational number is less than its Denominator by 4. So ,

$\longmapsto\tt{Numerator=x-4}$

Now ,

• If 2 is subtracted from the numerator and 1 is added to its denominator, the new number becomes 1/8 .

$\longmapsto\tt{Numerator=x-4-2=x-6}$

$\longmapsto\tt{Denominator=x+1}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-6}{x+1}=\dfrac{1}{8}}$

$\longmapsto\tt{8(x-6)=1(x+1)}$

$\longmapsto\tt{8x-48=x+1}$

$\longmapsto\tt{8x-x=1+48}$

$\longmapsto\tt{7x=49}$

$\longmapsto\tt{x=\cancel\dfrac{49}{7}}$

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

Value of x is 7 ..

Therefore :

$\longmapsto\tt{Numerator=7-4}$

$\longmapsto\tt\bf{3}$

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

So , The Rational Number is 3/7 ..