Certainly! Here's the transcription of the image for an educational website:---**18. Write equations that use rules about operating with fractions and possibly also properties of arithmetic to show why it is valid to cancel to evaluate the expression**\[\frac{22 \cdot 3}{77}\]**as follows:**\[\frac{\cancel{2}\,^{22} \cdot 3}{\cancel{7}\,^{77}} = \frac{2 \cdot 3}{7} = \frac{6}{7}\]---**Explanation:**The problem involves simplifying the fraction $\frac{22 \cdot 3}{77}$ by canceling common factors in the numerator and denominator.1. **Factorization**: - The numerator $22$ is factored as $2 \cdot 11$. - The denominator $77$ is factored as $7 \cdot 11$.2. **Cancellation**: - The common factor of $11$ is canceled from both the numerator and the denominator.3. **Resulting Expression**: - After canceling, the simplified expression becomes $\frac{2 \cdot 3}{7} = \frac{6}{7}$.This method uses the property of fractions where you can cancel common factors, leading to a simplified and equivalent expression.

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Answered: 18. Write equations that use rules…

18. Write equations that use rules about operating with fractions and possibly also properties of arithmetic to show why it is valid to cancel to evaluate the expression 22 3 77 ●

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Certainly! Here's the transcription of the image for an educational website:

---

**18. Write equations that use rules about operating with fractions and possibly also properties of arithmetic to show why it is valid to cancel to evaluate the expression**

\[
\frac{22 \cdot 3}{77}
\]

**as follows:**

\[
\frac{\cancel{2}\,^{22} \cdot 3}{\cancel{7}\,^{77}} = \frac{2 \cdot 3}{7} = \frac{6}{7}
\]

---

**Explanation:**

The problem involves simplifying the fraction $\frac{22 \cdot 3}{77}$ by canceling common factors in the numerator and denominator.

1. **Factorization**:
- The numerator $22$ is factored as $2 \cdot 11$.
- The denominator $77$ is factored as $7 \cdot 11$.

2. **Cancellation**:
- The common factor of $11$ is canceled from both the numerator and the denominator.

3. **Resulting Expression**:
- After canceling, the simplified expression becomes $\frac{2 \cdot 3}{7} = \frac{6}{7}$.

This method uses the property of fractions where you can cancel common factors, leading to a simplified and equivalent expression.

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