Question

if we add 1 to the numerator and subtract 1 from the denominator a fraction becomes 1 its akso becomes 1/2 we only add 1 to the denominator find the fraction​

Answer 1

Correct Question:

if we add 1 to the numerator and subtract 1 from the denominator a fraction becomes 1. it becomes 1/2 if we only add 1 to the denominator, find the fraction.

Answer:

The Fraction is -> 3/5

Step-by-step explanation:

Let us assume the fraction to be x/y.

The question says that if we add 1 to the numerator and subtract 1 from the denominator a fraction becomes 1. This means that-

$\sf \implies \dfrac{x +1}{y - 1}$ gives you 1.

Solving this equation further,

cross multiplication:-

$\sf \implies 1(x+1) = 1(y-1)$

$\sf \implies x +1 = y - 1$

(variables to the left side of the equations and constants on the right)

$\sf \implies x - y = - 1 - 1$

$\sf \implies x - y = - 2$ → (1)

Now, the question says that it becomes 1/2 if we only add 1 to the denominator. This gives us the following equation:-

$\sf \implies \dfrac{x}{ y + 1} = \dfrac{1}{2}$

Further simplifying by cross multiplication.

$\sf \implies 2x = y + 1$

$\implies \sf 2x - y = 1$ → (2)

Now, we subtract equation number one from two. So, here is what we get:

2x - y = 1

-( x - y = - 2)

-------------------

x = 3

We get the value of x as 3.

From equation 1 -

x - y = - 2

so now that we know the value of x is 3, let's plugin here.

3 - y = - 2

- y = -3 -2

- y = - 5 (minus sign gets cancelled)

we get-

y = 5,x = 3

fraction is 3/5

Answer 2

Answer:

Correct Question :-

• If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1 then it becomes 1/2. If we only add 1 to the denominator. What is the fraction.

Given :-

• If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1 then it becomes 1/2.
• If we only add 1 to the denominator.

To Find :-

• What is the fraction.

Solution :-

Let,

$\leadsto$ $\sf\bold{Numerator =\: x}$

And,

$\leadsto$ $\sf\bold{Denominator =\: y}$

Then,

$\leadsto$ $\sf\bold{\purple{Fraction =\: \dfrac{x}{y}}}$

$\longmapsto$ If we add 1 to the numerator and subtract 1 from the denominator a fraction :

$\implies \sf \dfrac{x + 1}{y - 1} =\: 1$

By doing cross multiplication we get,

$\implies \sf x + 1 =\: y - 1$

$\implies \sf x - y =\: - 1 - 1$

$\implies \sf\bold{\green{x - y =\: - 2\: ------\: (Equation\: No\: 1)}}$

Again,

$\longmapsto$ If we only add 1 to the denominator, then it's become 1/2 :

$\implies \sf \dfrac{x}{y + 1} =\: \dfrac{1}{2}$

By doing cross multiplication we get,

$\implies \sf 2x =\: y + 1$

$\implies \sf\bold{\green{2x - y = 1\: ------\: (Equation\: No\: 2)}}$

Now, by subtracting the equation no 1 from the equation no 2 we get,

$\implies \sf 2x - y - x - y =\: 1 - (- 2)$

$\implies \sf 2x - x = 1 + 2$

$\implies \sf\bold{\pink{x =\: 3}}$

Now, by putting the value of x = 3 in the equation no 2 we get,

$\implies \sf 2x - y =\: 1$

$\implies \sf 2(3) - y =\: 1$

$\implies \sf 6 - y =\: 1$

$\implies\sf - y =\: 1 - 6$

$\implies \sf {\cancel{-}} y =\: {\cancel{-}} 5$

$\implies\sf\bold{\pink{y =\: 5}}$

Hence, the required fraction will be :

$\dashrightarrow \sf \dfrac{x}{y}$

By putting the value of x = 3 and y = 5 we get,

$\dashrightarrow \sf\bold{\red{\dfrac{3}{5}}}$

${\large{\bold{\green{\underline{\therefore\: The\: fraction\: is\: \dfrac{3}{5}\: .}}}}}$