Question

A fraction becomes 1/6 when 4 is subtracted from its numerator and 1 is added to its denominator. If 2 and 1 are respectively added to its numerator and the denominator, it becomes 1/3. Then, the lcm of the numerator and denominator of the said fraction, must be

Answer 1

hey friend there is your answer.

Answer 2

The LCM of the fraction $\frac{10}{35}$ is 70.

Step-by-step explanation:

Let the numerator be 'x'.

Also Let denominator be 'y'.

Then the fraction will become $\frac{x}{y}$.

Now Given:

A fraction becomes 1/6 when 4 is subtracted from its numerator and 1 is added to its denominator.

framing in equation form we get;

$\frac{x-4}{y+1}=\frac{1}{6}$

On Solving we get:

By Using Cross  Multiplication we get;

$6(x-4))=1(y+1)$

Applying Distributive Property we get;

$6x-24=y+1\\\\6x-y=1+24\\\\6x-y=25 \ \ \ \ \ equation \ 1$

Also Given:

If 2 and 1 are respectively added to its numerator and the denominator, it becomes 1/3.

framing in equation form we get;

$\frac{x+2}{y+1}=\frac{1}{3}$

On Solving we get:

By Using Cross  Multiplication we get;

$3(x+2))=1(y+1)$

Applying Distributive Property we get;

$3x+6=y+1\\\\3x-y=1-6\\\\3x-y=-5 \ \ \ \ \ equation \ 2$

Now Subtracting equation 2 from equation 1 we get;

$(6x-y)-(3x-y)=25-(-5)\\\\6x-y-3x+y= 30\\\\3x= 30$

Using Division Property dividing both side by 3 we get;

$\frac{3x}{3}= \frac{30}{3}\\\\x=10$

Now Substituting the value of x in equation 1 we get;

$6x-y=25\\\\6\times10-y=25\\\\60-y=25\\\\60-25=y\\\\y=35$

Hence the fraction becomes $\frac{10}{35}$

Now factors of 10 = $2\times 5$

Also factors of 35 = $5\times7$

So the LCM of 10 and 35 = $2\times5\times7=70$

Hence the LCM of the fraction $\frac{10}{35}$ is 70.