Question

6. The numerator of a fraction is 2 less than the demoninator is one is added to its denominator, it becomes 1/2 find the fraction​

Answer 1

⅗

Step-by-step explanation:

Given:

The numerator of a fraction is 2 less than the demoninator is one is added to its denominator, it becomes 1/2

To Find:

The fraction

Solution:

Let Numerator be x

Denominator=x+2

$\sf \: Original \: fraction = \tt{ \frac{x}{x + 2}}$

New denominator = x+2+1=x+3

$\sf \: New \: fraction = \tt{ \frac{x}{x + 3}}$

Now x/x+3 is equal to 1/2 so,

ACQ

$\therefore \tt \frac{x}{x + 3} = \frac{1}{2} \\ \tt \leadsto \: 2(x) = x + 3 \\ \tt \leadsto \: 2x = x + 3 \\ \tt \leadsto \: 2x - x = 3 \\ \tt \leadsto \: x = 3$

Now Numerator=3

Denominator=x+2=3+2=5

$\sf \: Original \: fraction = \red {\underline{\boxed{</strong><strong>\frac{3}{5}}}}$

Answer 2

Given in Question: The numerator of the fraction is 2 less than the denominator of the fraction. & If 1 is added to the denominator, fraction becomes ½.

Need to Calculate: The fraction?

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀

❍ Let the Denominator of the fraction be 'x'. Then, the Numerator of the fraction be (x – 2).

$\bigstar\;\underline{\boxed{\pmb{\sf{Fraction = \dfrac{x - 2}{x}}}}}$

⠀⠀⠀

$\underline{\bigstar\:\textsf{According to the Given Question :}}$

• Now, when 1 is added to the denominator 'x' of the fraction. Then, the fraction becomes ½. On Substituting values in the fraction we get:

⠀

$\dashrightarrow\sf \Bigg\{\dfrac{x - 2}{x + 1}\Bigg\} = \Bigg\{\dfrac{1}{2}\Bigg\}$

On Cross – Multiplication we get:

$\dashrightarrow\sf 2\Big\{x - 2\Big\} = x + 1$

$\dashrightarrow\sf 2x - 4 = x + 1$

On transposing the term of 'x' from the RHS to the LHS we get:

⠀⠀

$\dashrightarrow\sf 2x - x = 1 + 4$

${\purple{\dashrightarrow{\pmb{\sf{x = 5}}}}}$

∴ The value of 'x' is 5. Now we'll substitute this value in the numerator given to find the numerator of the fraction.

⠀⠀

$\dashrightarrow\sf Numerator = \Big\{x - 2\Big\}$

$\dashrightarrow\sf Numerator = 5 - 2$

${\purple{\dashrightarrow{\pmb{\sf{Numerator = 3}}}}}$

⠀

Hence,

• Numerator of the fraction is 3
• Denominator to the fraction is 5

⠀

∴ Therefore, the required fraction is ⅗.