Question

the dinometer of rational number is greater than it's numerator by 6 if the numerator is decreased by 1 and denominator is increased by 1, the number obtained is 1/3. find the rational number​

Answer 1

Given :

• The denominator of rational number is greater than its numerator by 6 if the numerator is decreased by 1 and denominator is increased by 1, the number obtained is 1/3.

To find :

• The number.

Solution :

Let the numerator be x and the denominator be (x + 6).

• According to the question,

The numerator is decreased by one and the numerator is increased by one, then the number obtained is 1/3.

• Therefore,

➟ (x - 1)/(x + 6 + 1) = 1/3

➟ (x - 1)/(x + 7) = 1/3

• Cross multiply,

➟ 3x - 3 = x + 7

➟ 3x - x = 7 + 3

➟ 2x = 10

➟ x = 10/2

➟ x = 5

Hence,

• Numerator = x = 5
• Denominator = (x + 6) = 5 + 6 = 11

•°• The required rational number is 5/11.

Answer 2

❍ Let's say, that the numerator of the fraction be x and denominator of the fraction be (x + 6).

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

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$\underline{\bigstar\;\boldsymbol{According\;to\;the\;Question:}}$

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• If the numerator is decreased by 1 and denominator is increased by 1, the number obtained is 1/3.

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Therefore,

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$\begin{gathered}:\implies\sf{\dfrac{x-1}{x+6+1}=\dfrac{1}{3}}\\\\\\\\:\implies\sf{\dfrac{x-1}{x+7}=\dfrac{1}{3}}\\\\\\\\:\implies\sf{3(x-1)=1(x+7)}\\\\\\\\:\implies\sf{3x-3=x+7}\\\\\\\\:\implies\sf{3x-x=7+3}\\\\\\\\:\implies\sf{2x=10}\\\\\\\\:\implies\sf{x=\cancel{\dfrac{10}{2}}}\\\\\\\\:\implies\underline{\boxed{\frak{\pink{\pmb{x=5}}}}}\;\bigstar\end{gathered}$

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Hence,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Numerator = x = 5
• Denominator = (x + 6) = (5 + 6) = 11

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$\therefore\;{\underline{\sf{Hence,\;the\;rational\;number\;is\;{\pmb{\frak{\dfrac{5}{11}}}}}.}}$⠀⠀