Question

the numerator of a fraction is 3 less than denominator. if 1 is added to both it's and denominator, it becomes 1/2. find the fraction.​

Answer 1

Answer:

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Answer 2

Given :

• The numerator of a fraction is 3 less than its denominator .
• If 1 is added to both it's numerator and denominator,it becomes 1/2 .

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To Find :

• Find the fraction .

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Solution :

~ According to the Question :

➢ The numerator of the fraction is 3 less than the denominator. Let the number be y . So ,

$\large{\bigstar \; {\underline{\overline{\boxed{\red{\sf{ \dfrac{Numerator}{Denominator} = \dfrac{y - 3}{y} }}}}}}} \; {\bigstar}$

➢ If 1 is added to both numerator and denominator the fraction becomes 1/2 . So ,

$\large{\bigstar \; {\underline{\overline{\boxed{\red{\sf{ \dfrac{(y - 3) + 1}{y + 1} = \dfrac{1}{2} }}}}}}} \; {\bigstar}$

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~ Now ,let's Cross Multiply :

$\; {\dashrightarrow {\qquad{\sf{ 2 \bigg\{ (y - 3) + 1 \bigg\} = 1(y + 1) }}}}$

$\; {\dashrightarrow {\qquad{\sf{ (2y - 6) + 2 = y + 1 }}}}$

$\; {\dashrightarrow {\qquad{\sf{ (2y - y) + 2 = 1 + 6 }}}}$

$\; {\dashrightarrow {\qquad{\sf{ (2y - y) + 2 = 7 }}}}$

$\; {\dashrightarrow {\qquad{\sf{ 2y - y = 7 - 2}}}}$

$\; {\dashrightarrow {\qquad{\sf{ 2y - y = 5}}}}$

$\; {\qquad \; \; {\therefore \; {\underline{\boxed{\green{\sf{ y = 5 }}}}}}}$

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~ Calculating the Numerator and Denominator :

• ➬ Numerator = y - 3 = 5 - 3 = 2
• ➬ Denominator = y = 5

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~ Therefore :

❛❛ The original fraction is ${\sf{\dfrac{2}{5}}}$ . ❜❜

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