To simplify the fraction \( \frac{14c}{49c} \), you can follow these steps:

1. **Cancel out common factors**: 
   - Both the numerator (14c) and the denominator (49c) share a common factor of \( c \), so you can cancel \( c \) from both, which gives us:

\[
\frac{14c}{49c} = \frac{14}{49}
\]

2. **Simplify the fraction \( \frac{14}{49} \)**:
   - Find the greatest common divisor (GCD) of 14 and 49, which is 7.
   - Divide both the numerator and the denominator by 7:

\[
\frac{14 \div 7}{49 \div 7} = \frac{2}{7}
\]

Thus, the simplified form of \( \frac{14c}{49c} \) is:

\[
\boxed{\frac{2}{7}}
\]

Would you like further details or have any questions?

Here are some related questions you might explore:

1. How do you find the greatest common divisor (GCD)?
2. What is the process to simplify fractions with variables?
3. How can you simplify expressions involving multiple variables?
4. How do you multiply and divide algebraic fractions?
5. What happens if the variable \( c \) in the fraction is zero?

**Tip**: Always look for common factors between the numerator and denominator when simplifying fractions.

This guide explains how to simplify the algebraic fraction 14c/49c. Learn the step-by-step process to cancel common factors and reduce fractions using the GCD theorem. Ideal for students in Grades 6-8, this problem covers key concepts such as simplifying fractions with variables and the use of the greatest common divisor.

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