Question

the denominator of a fraction is 4 more than it's numerator on subtracting 1 from each other numerator and denominator the fraction become 1/2 find the original fraction​

Answer 1

Answer:

5/9

Step-by-step explanation:

x/x+4 is the fraction.

x-1/x+3=1/2

2x-2=x+3

x=5

x+4=9

Answer 2

$\huge\sf\pink{Answer}$

☞ Original fraction is 5/9

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$\huge\sf\blue{Given}$

✭ Denominator of a fraction is 4 more than it's numerator

✭ Subtracting 1 from each numerator and denominator the fraction becomes ½

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$\huge\sf\gray{To \:Find}$

◈ The original fraction?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

• Numerator be x
• Denominator be y
• Fraction becomes x/y

☯ $\sf \underline{\boldsymbol{According \ to \ the \ Question}}$

Denominator is 4 more than the numerator so the fraction becomes,

➝ $\sf \underline{\underline{\sf \dfrac{x}{x+4}}} \:\:\:\ \{ y = x+4\}$

Now when we subtract both the numerator and the denominator with 1

➳ $\sf \dfrac{x-1}{x+4-1}$

Now Equating it with ½

➳ $\sf \dfrac{x-1}{x+3} = \dfrac{1}{2}$

«« Cross Multiply »»

➳ $\sf 2(x-1) = 1(x+3)$

➳ $\sf 2x-2 = x+3$

➳ $\sf 2x-x = 3+2$

➳ $\sf \red{x=5}$

So now in the fraction,

⪼ $\sf \dfrac{x}{x+4}$

⪼ $\sf \dfrac{5}{5+4}$

⪼ $\sf \orange{Fraction = \dfrac{5}{9}}$

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