Question

6. The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the fraction becomes 1/8. Find the fraction.​

Answer 1

✬ Fraction = 3/7 ✬

Step-by-step explanation:

Given:

• Numerator of a fraction is 4 less than its denominator.
• Fraction becomes 1/8 after increasing denominator by 1 and decreasing numerator by 2.

To Find:

• What is the original fraction ?

Solution: Let the numerator be x and denominator be y. Therefore fraction will be x/y.

➟ Numerator = 4 less than x

➟ x = (y – 4)

Now, decreasing numerator by 2

• New numerator = (x – 2)

Increasing denominator by 1.

• New denominator = (y + 1)

A/q

• New (numerator/denominator) = 1/8

$\implies{\rm }$ (x – 2)/(y + 1) = 1/8

$\implies{\rm }$ 8(x – 2) = (y + 1)

$\implies{\rm }$ 8x – 16 = y + 1

$\implies{\rm }$ 8(y – 4) – 16 = y + 1

$\implies{\rm }$ 8y – 32 – 16 = y + 1

$\implies{\rm }$ 8y – y – 48 = 1

$\implies{\rm }$ 7y = 49

$\implies{\rm }$ y = 7

So,

• Denominator is 7.
• Numerator is (7 – 4) = 3.

Hemce, fraction was 3/7.

Answer 2

Answer:

✭ Given :-

• The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, then the fraction become $\dfrac{1}{8}$

✭ To Find :-

• What is the fraction.

✭ Solution :-

» Let, the denominator be x

» And, the numerator be x - 4

» Then, the fraction will be $\dfrac{x - 4}{x}$.

➣ According to the question,

⇒8(x - 4) - 2 = x + 1

⇒ (x - 4) - 2 = $\dfrac{x + 1}{8}$

⇒ x - 6 = $\dfrac{x + 1}{8}$

⇒ 8x - 48 = x + 1

⇒ 8x - x = 48 + 1

⇒ 7x = 49

⇒x = $\sf\dfrac{\cancel{49}}{\cancel{7}}$

➠ x = 7

➙ Fraction = $\dfrac{x - 4}{x}$

➣ Putting the value of x we get,

$\implies$ Fraction = $\dfrac{7 - 4}{7}$

$\mapsto$ Fraction = $\dfrac{3}{7}$

✰ $\therefore$ The fraction is $\dfrac{3}{7}$ ✰

Hence Solved

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