Question

how to form the linear equations
give step by step explanation ​

Answer 1

Question:

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Answer:

$\large\boxed{\sf{\dfrac{5}{12}}}$

Step-by-step explanation:

Let the numerator and denominator be "x" and "y" respectively.

Therefore, the fraction is x/y

Now, according to question

$= > \frac{x - 1}{y} = \frac{1}{3} \\ \\ = > 3(x - 1) = y \times 1 \\ \\ = > 3x - 3 = y$

And, we get

$= > \frac{x}{y + 8} = \frac{1}{4} \\ \\ = > 4x = y + 8 \\ \\ = > 4x = 3x - 3 + 8 \\ \\ = > x = 5$

Therefore, we get

$= > y = 3 \times 5 - 3 \\ \\ = > y = 15 - 3 \\ \\ = > y = 12$

Hence, the required fraction is 5/12

Answer 2

$\huge{\boxed{\boxed{\tt{Answer:}}}}$

Given:

• A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to it's denominator.

Find:

• Find the fraction.

Calculations:

• Let "n" be numerator and "d" be denominator.

• The fraction = (n/d) respectively.

$\sf\rightarrow\: \frac{n - 1}{d} = \frac{1}{3} \\ \sf\rightarrow\:3(n - 1) = d \times 1 \\ \sf\rightarrow\:3n - 3 = n \\ \sf\rightarrow\: \frac{n}{d + 8} = \frac{1}{4} \\ \sf\rightarrow\:4n = d + 8 \\ \sf\rightarrow\:n = 5$

We get our answer with few more steps;

$\sf\rightarrow\:d = 3 \times 5 - 3 \\ \sf\rightarrow\:d = 15 - 3 \\ \sf\rightarrow\:d = 12$

Therefore, 5/12 is the required fraction.