Question

The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes 3/4 Find the fraction. ​

Answer 1

Answer:

Step-by-step explanation:

Let the denominator be x. Then the fraction becomes $\frac{x-2}{x}$.

Case given: 3 is added to both num and den

Then$\frac{x-2}{x}$ becomes $\frac{(x-2)+3}{x+3}$. It is given that  $\frac{(x-2)+3}{x+3}$=3/4

=>$\frac{x+1}{x+3}$=3/4

Cross multiplying,

4x+4=3x+9

=>4x-3x=9-4

=>x=5

=> Fraction is 3/5

Answer 2

➤ Answer

• The fraction = $\bf{\green{\cfrac{3}{5}}}$

➤ Given

• The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes 3/4.

➤ To Find

• The fraction.

➤ Step By Step Explanation

Given that the numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes 3/4. We need to find the fraction.

So let's do it !!

➠ Assumption

Let the denominator of the fraction be x then the numerator will be x - 2. Now, If we add 3 to both the numerator and denominator the fraction will become 3/4.

➠ Equation

$\maltese\underline{\boxed{ \bf{ \red{\cfrac{x - 2 + 3}{x + 3} = \cfrac{3}{4}}}}}$

➠ Solution of equation

$\longmapsto\tt\cfrac{x - 2 + 3}{x + 3} = \cfrac{3}{4} \\ \\ \longmapsto\tt\cfrac{x + 1}{x + 3} = \cfrac{3}{4} \\ \\\longmapsto\tt 4(x + 1) = 3(x + 3) \\ \\ \longmapsto\tt4x + 4 = 3x + 9 \\ \\\longmapsto\tt 4x - 3x = 9 - 4 \\ \\\longmapsto\tt x = 5$

Therefore, the fraction = $\bf{\green{\cfrac{3}{5}}}$

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➤ Check

➠ By substituting the values of x.

L.H.S. ⤵

$\longmapsto\tt\cfrac{x - 2 + 3}{x + 3} \\ \\\longmapsto\tt\cfrac{x + 1}{x + 3} \\ \\ \longmapsto\tt \cfrac{5 + 1}{5 + 3} \\ \\\longmapsto\tt \cfrac{ \not6}{ \not8} \\ \\\longmapsto\bf\cfrac{3}{4}$

R.H.S. ⤵

$\longmapsto\bf\cfrac{3}{4}$

Hence, L.H.S. = R.H.S.

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