Expert in study
alarm
Ask
English
Pavel

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: 1
Register to add an answer
The time for answering the question is over
350 cents William Fields
Answer:

\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}}}

414
William Fields
For answers need to register.
Contacts
mail@expertinstudy.com
Feedback
Expert in study
About us
For new users
For new experts
Terms and Conditions