Question

the numerator of a fraction is 4 less then its denomenator. if the numerator is decreased by 1, the fraction is equal to 2/3 , find the fraction​

Answer 1

Answer:

3/7 is a required fraction.

Step-by-step explanation:

Let the numerator be x and denominator be y.

Then,

The required fraction will be x/y.

_____________________

$\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

☯ Condition 1 :

$:\implies\sf x = y - 4:⟹x=y−4$

$\begin{gathered}\\\end{gathered}$

$: \implies \sf \: x - y = -4 \: \: \: \bigg \lgroup \bf{Equation \: 1} \bigg\rgroup:⟹x−y=−4⎩⎪⎪⎪⎧Equation1⎭⎪⎪⎪⎫$

☯ Condition 2 :

$:\implies\sf 8(x - 2) \: = \: y + 1:$

$\begin{gathered}\\\end{gathered}$

$:\implies\sf 8x - 16\: = \: y + 1:$

$\begin{gathered}\\\end{gathered}$

$:\implies\sf 8x - y \: = \: 1 \: \: \: \bigg \lgroup \bf{Equation \: 2} \bigg \rgroup:⟹8x−y=1⎩⎪⎪⎪⎧Equation2⎭⎪⎪⎪⎫$

Substracting equation (2) from (1) we get,

$:\implies\sf - 7x \: = \: - 21:$

$\begin{gathered}\\\end{gathered}$

$:\implies\sf x \: = \: \dfrac{21}{7}:⟹x=721$

$\begin{gathered}\\\end{gathered}$

$:\implies \underline{ \boxed{\sf x \: = \: 3}}:⟹x=3$

Putting the value of x in equation (2) :

$:\implies\sf x - y \: = \: - 4:$

$\begin{gathered}\\\end{gathered}$

$:\implies\sf 3 - y \: = \: - 4:$

$\begin{gathered}\\\end{gathered}$

$:\implies\sf y \: = \: 3 + 4:⟹y=3+4$

$\begin{gathered}\\\end{gathered}$

$:\implies \underline{ \boxed{\sf y \: = \: 7}}:$

$\therefore\:\underline{\textsf{The required fraction is}$

∴The required fraction is 3/7.

Answer 2

The answer is in the photo my dear friend
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