Question

no of a fraction is 5 more than it's denominator if 4 is added to the numerator and denominator the fraction obtained is 6upon5 find the fraction​

Answer 1

Given : Numerator of the fraction is 5 more than the denominator . If 4 is added to numerator and denominator we get 6/5 .

To Find : Find the Rational Number

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SolutioN : For Solving this question we'll form the Equation first and can get the Answer . Let's Solve :

$\maltese$ Calculating the Unknown Number :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{Numerator}{Denominator} \bigg\} = \bigg\{ \dfrac{y + 5}{y} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{(y + 5) + 4}{y + 4} \bigg\} = \bigg\{ \dfrac{6}{5} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{(y + 5) + 4}{y + 4} \bigg\} = \bigg\{ \dfrac{6}{5} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{y + 9}{y + 4} \bigg\} = \bigg\{ \dfrac{6}{5} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 6 \bigg( y + 4 \bigg) = 5 \bigg( y + 9 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 6y + 24 = 5y + 45 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 6y - 5y = 45 - 24 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 6y - 5y = 21 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\frak{ y = 21 }}}}} \; {\green{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\maltese$ Calculating the Rational Number :

• Numerator = y + 5 = 21 + 5 = 26
• Denominator = y = 21

$\therefore \;$ The Rational Number is 26/21 .

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