Fraction Word Problems Worksheets - Free Printable

It seems like you've described a problem involving fractions, but the image itself is not visible. However, based on your description, I can infer that the problem involves fractions and some arithmetic operations. Let me break it down step by step and solve it.

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Problem Breakdown

From your description, here are the key points of the problem:

1. Initial Fraction: A fraction is given as \( \frac{3}{7} \).
2. Doubling the Denominator: The denominator of the fraction is doubled.
3. Subtracting 2 from the Numerator: After doubling the denominator, 2 is subtracted from the numerator.
4. Final Fraction: The resulting fraction is \( \frac{1}{6} \).

We need to determine the original fraction and verify the steps.

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Solution

#### Step 1: Represent the Original Fraction
The original fraction is given as:
\[
\frac{3}{7}
\]

#### Step 2: Double the Denominator
When the denominator is doubled, the new fraction becomes:
\[
\frac{3}{2 \times 7} = \frac{3}{14}
\]

#### Step 3: Subtract 2 from the Numerator
Next, we subtract 2 from the numerator of the fraction \( \frac{3}{14} \):
\[
\frac{3 - 2}{14} = \frac{1}{14}
\]

#### Step 4: Verify the Final Fraction
According to the problem, the final fraction after these operations is \( \frac{1}{6} \). However, our calculation shows that the final fraction is \( \frac{1}{14} \), which does not match \( \frac{1}{6} \).

This suggests there might be a misunderstanding in the problem statement or an error in the initial fraction provided. Let us re-evaluate the problem with a general approach to ensure accuracy.

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General Approach

Let the original fraction be \( \frac{a}{b} \).

1. Double the Denominator: The new fraction becomes \( \frac{a}{2b} \).
2. Subtract 2 from the Numerator: The resulting fraction is \( \frac{a - 2}{2b} \).
3. Final Fraction: According to the problem, this results in \( \frac{1}{6} \).

Thus, we have the equation:
\[
\frac{a - 2}{2b} = \frac{1}{6}
\]

#### Solve for \( a \) and \( b \)
Cross-multiply to solve for \( a \) and \( b \):
\[
6(a - 2) = 2b
\]
\[
6a - 12 = 2b
\]
\[
3a - 6 = b \quad \text{(Divide both sides by 2)}
\]
\[
b = 3a - 6
\]

#### Use the Initial Fraction
The problem states that the initial fraction is \( \frac{3}{7} \). This means:
\[
a = 3 \quad \text{and} \quad b = 7
\]

Substitute \( a = 3 \) into the equation \( b = 3a - 6 \):
\[
b = 3(3) - 6 = 9 - 6 = 3
\]

This does not match the given denominator \( b = 7 \). Therefore, there seems to be a discrepancy.

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Conclusion

Based on the problem's description and the steps taken, the initial fraction \( \frac{3}{7} \) does not satisfy the conditions given in the problem. If the initial fraction were different, we could solve for it using the general approach. However, with the provided information, the solution does not align.

If you can provide additional details or clarify the problem, I can refine the solution further.

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Final Answer

\[
\boxed{\text{The problem as stated has a discrepancy; please verify the initial fraction or conditions.}}
\]