English, asked by Anonymous, 5 months ago

the denominator of a rational number is less than its ne numerator than 5 if the five is added to the numerator the new number become 11 by 6 find the original rational number​

Answers

Answered by ItzCaptonMack
0

\huge\mathtt{\fbox{\red{Answer✍︎}}}

\large\underline\red{GIVEN,}

\sf\dashrightarrow \blue{THE\:GIVEN\:FRACTION\:IS\:A\:RATIONAL\:NUMBER.}

\sf\dashrightarrow {\blue{\mathbb{\text{ denominator is less than its numerator by 5.}}}}

\sf\therefore \blue{let\:the\:numerator\:be\:x}

\sf\dashrightarrow \blue{denominator= x-5}

\sf\dashrightarrow \blue{\dfrac{x}{x-5}}

\sf\dashrightarrow \bold\pink{if \:5 \:is \:added\: to \:the \:numerator, \:numerator \:becomes\: ; \dfrac{11}{6}}

\sf\dashrightarrow \red{numerator= x+5}

THE EQUATION FORM IS,

\rm{\boxed{\sf{\green{ \circ\:\: \dfrac{x+5}{x-5} = \dfrac{11}{6}\:\: \circ}}}}

\large\underline\purple{TO\:FIND,}

\sf\dashrightarrow \red{\:THE\:ORIGINAL\:RATIONAL\:NUMBER}

\sf\implies \green{\dfrac{x  + 5}{x - 5}  =  \dfrac{11}{6}}

\sf\implies \green{6 \times (x+5)= 11 \times (x-5)}

\sf\implies \green{6x+30= 11x-55}

\sf\implies \green{30+55=11x-6x}

\sf\implies \green{85= 5x}

\sf\implies \green{x= \dfrac{85}{5}}

\sf\implies \green{x= \cancel  \dfrac{85}{5}}

 \sf\implies  \orange{x = 17}

\rm{\boxed{\sf{ \circ\:\: x= 17 \:\: \circ}}}

THE ORIGINAL NUMBERS ARE,

\sf\implies \red{numerator=x =17}

\sf\implies \red{d enominator= x-5}

\sf\implies \red{denominator=17-5}

\sf\implies \pink{denominator=12}

\large\underline\orange{FRACTION,}

\sf\dashrightarrow \purple{\dfrac{x}{x-5}= \dfrac{17}{12}}

\sf\dashrightarrow \purple{\dfrac{NUMERATOR}{DENOMINATOR}= \dfrac{17}{12}}

\rm\underline\blue{NUMERATOR\:IS\:17\:AND\: DENOMINATOR\:IS\:12}

\rm{\boxed{\sf{ \circ\:\: \dfrac{NUMERATOR}{DENOMINATOR}= \dfrac{17}{12} \:\: \circ}}}

Answered by Rajeshwari8025
3

Answer:

The denominator of a rational number is less than the numerator by 5. If 5 is added to the numerator, the new number becomes 11/6.

D = N - 5

(N + 5)/D = 11/6

(N + 5)/(N - 5) = 11/6

6N + 30 = 11N - 55

5N = 85

N = 17

D = 12

Hence, the fraction is \dfrac{17}{12}

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