Question

The denominator of a fraction is 3 less than the thrice the numerator. If the numerator is decreased by 3, the fraction becomes 1/4. Find the original fraction.​

Answer 1

Answer:

• The fraction is 9/24.

Step-by-step explanation:

Given that:

• The denominator of a fraction is 3 less than the thrice the numerator.
• If the numerator is decreased by 3, the fraction becomes 1/4.

To Find:

• The original fraction.

Let us assume:

• The numerator of the fraction x.

Then,

• The denominator of the fraction will be (3x - 3).

If numerator is decreased by 3:

• The numerator will be (x - 3).

According tot he question:

$\sf{\implies\dfrac{x-3}{3x-3}=\dfrac{1}{4}}$

By cross-multiplication:

$\sf{\implies3x-3=4(x-3)}$

Opening the bracket,

$\sf{\implies3x-3=4x-12}$

Transposing variables to LHS, constants to RHS and changing their sign,

$\sf{\implies3x-4x=-12+3}$

Solving further,

$\sf{\implies-x=-9}$

$\sf{\implies\not\!{-}x=\not\!{-}9}$

$\bf{\implies x=9}$

Hence,

• x = 9

Therefore,

• Numerator = x = 9
• Denominator = 3x - 3 = (3 × 9) - 3 = 27 - 3 = 24

And,

• The fraction is 9/24.

Answer 2

Answer:

hope this answer will help you