The denominator of additional number is greater than its numerator by 6 if we subtract new number number become 1​ by 4 the find original number

Let's denote the original number as \( \frac{x}{x+6} \), where:

- The numerator is \( x \),
- The denominator is 6 more than the numerator, so it's \( x + 6 \).

According to the problem, subtracting the number from \( 1 \) gives \( \frac{1}{4} \), so we can set up the equation:

\[
1 - \frac{x}{x+6} = \frac{1}{4}
\]

### Step 1: Solve for \( \frac{x}{x+6} \)
Subtract \( \frac{x}{x+6} \) from 1:

\[
\frac{(x+6) - x}{x+6} = \frac{1}{x+6}
\]

This simplifies to:

\[
\frac{1}{x+6}
\]

So, the equation becomes:

\[
\frac{1}{x+6} = \frac{1}{4}
\]

### Step 2: Solve for \( x \)
Now, set the denominators equal to each other:

\[
x + 6 = 4
\]

Solve for \( x \):

\[
x = 4 - 6 = -2
\]

### Step 3: Verify the solution
The original number is \( \frac{-2}{-2 + 6} = \frac{-2}{4} = -\frac{1}{2} \).

Let's check if the condition holds:
\[
1 - \left(-\frac{1}{2}\right) = 1 + \frac{1}{2} = \frac{3}{2}
\]
And:
\[
\frac{3}{2} \neq \frac{1}{4}
\]

It appears there was an error, let me rework the steps and find the correct result.

### Reattempt

Let the original number be \( x \). Then we are told:

\[
1 - x = \frac{1}{4}
\]

So, subtracting \( x \) from 1 gives \( \frac{1}{4} \), which leads to:

\[
x = 1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4}
\]

Thus, the original number is \( \frac{3}{4} \). 

Would you like more details or clarifications on any step? Here are some related questions for further practice:

1. If the denominator is 8 more than the numerator, and the difference from 1 is \( \frac{1}{5} \), what is the number?
2. Solve for \( x \) if \( \frac{x}{x+5} = \frac{2}{3} \).
3. What is the value of \( x \) if the denominator is twice the numerator, and subtracting from 1 results in \( \frac{1}{6} \)?
4. Find a fraction where the denominator is 4 more than the numerator and the sum of the fraction and \( \frac{1}{3} \) is \( 1 \).
5. If subtracting a fraction from 1 gives \( \frac{2}{7} \), and the denominator is 5 more than the numerator, what is the fraction?

**Tip:** Always ensure to verify solutions by substituting the values back into the original problem.

The denominator of a fraction is greater than its numerator by 6. If we subtract the fraction from 1, the result is 1/4. Find the original number.

This problem involves solving a fraction where the denominator is 6 greater than the numerator, and subtracting the fraction from 1 results in 1/4. Explore the step-by-step algebraic approach to find the original number. Suitable for Grades 6-8 students.

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