https://file.aiquickdraw.com/mathbot/file/1726146830621by8ul82r.jpg

The fraction given in the image is:

\[
\frac{4p + 12}{7p + 21}
\]

To simplify this fraction, we can factor both the numerator and the denominator.

1. Factor the numerator \( 4p + 12 \). The common factor is 4:
\[
4p + 12 = 4(p + 3)
\]

2. Factor the denominator \( 7p + 21 \). The common factor is 7:
\[
7p + 21 = 7(p + 3)
\]

Now the fraction becomes:
\[
\frac{4(p + 3)}{7(p + 3)}
\]

Since \( (p + 3) \) appears in both the numerator and the denominator, we can cancel it out, leaving:

\[
\frac{4}{7}
\]

Thus, the fraction in its simplest form is:
\[
\frac{4}{7}
\]

Would you like more details or have any questions?

Here are 5 related questions to practice:
1. How do you factor a quadratic expression?
2. What are the steps to simplify a fraction with variables?
3. Can all algebraic fractions be simplified by canceling terms?
4. How do you know when you can cancel terms in a fraction?
5. What is the difference between factoring and simplifying?

**Tip:** Always check for common factors in both the numerator and the denominator before canceling terms in a fraction.

Write the following fraction in its simplest form: (4p + 12) / (7p + 21)

Learn how to simplify the algebraic fraction (4p + 12) / (7p + 21) by factoring both the numerator and denominator. This problem covers key algebraic concepts such as factoring linear expressions and simplifying fractions, suitable for students in Grades 7-9.

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