https://file.aiquickdraw.com/mathbot/file/17261089275013cii4eni.jpg

Let's go through the steps to solve the question in the image:

### Given:
- \( A = 110 \)
- \( B = 320 \)

### a. Find the ratio of A to B:
The ratio of \( A \) to \( B \) is calculated as:
\[
\text{Ratio of } A \text{ to } B = \frac{A}{B} = \frac{110}{320}
\]
Simplifying this fraction by dividing both numerator and denominator by their greatest common divisor (GCD = 10):
\[
\frac{110}{320} = \frac{11}{32}
\]
Thus, the ratio of \( A \) to \( B \) is \( \frac{11}{32} \).

### b. Find the ratio of B to A:
The ratio of \( B \) to \( A \) is the reciprocal of the previous ratio:
\[
\text{Ratio of } B \text{ to } A = \frac{B}{A} = \frac{320}{110}
\]
Simplifying this fraction by dividing both numerator and denominator by their GCD (which is 10):
\[
\frac{320}{110} = \frac{32}{11}
\]
Thus, the ratio of \( B \) to \( A \) is \( \frac{32}{11} \).

### c. Complete the sentence: A is ___ percent of B.
To find what percent \( A \) is of \( B \), we calculate:
\[
\text{Percent} = \left( \frac{A}{B} \right) \times 100 = \left( \frac{110}{320} \right) \times 100
\]
\[
= 0.34375 \times 100 = 34.375\%
\]
So, \( A \) is 34.375% of \( B \).

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Would you like more details on any of these steps or a further explanation?

Here are some additional related questions:
1. What is the greatest common divisor, and how is it used to simplify ratios?
2. How would the result change if \( B \) were smaller than \( A \)?
3. What is the importance of expressing ratios in their simplest form?
4. How would you interpret the ratio of \( B \) to \( A \) in real-world terms?
5. Can ratios be expressed as decimals, and what is the advantage of doing so?

**Tip**: Always simplify ratios by dividing both terms by their GCD for clarity and accuracy in comparisons.

Compare the following pair of numbers A and B in three ways: a. Find the ratio of A to B. b. Find the ratio of B to A. c. Complete the sentence: A is ___ percent of B. Given: A = 110 and B = 320

Learn how to compare two numbers A = 110 and B = 320 by finding their ratio, reciprocal ratio, and calculating what percentage A is of B. This problem involves key mathematical concepts such as ratios, proportions, and percentages, and is suitable for students in Grades 5-7.

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