To simplify the ratio \( \frac{2 \frac{1}{3}}{1 \frac{1}{2}} \), we first convert the mixed numbers to improper fractions:

1. Convert \( 2 \frac{1}{3} \) to an improper fraction:
   \[
   2 \frac{1}{3} = \frac{3 \times 2 + 1}{3} = \frac{7}{3}
   \]

2. Convert \( 1 \frac{1}{2} \) to an improper fraction:
   \[
   1 \frac{1}{2} = \frac{2 \times 1 + 1}{2} = \frac{3}{2}
   \]

Now, the ratio becomes:
\[
\frac{\frac{7}{3}}{\frac{3}{2}}
\]

To simplify this, multiply by the reciprocal of the denominator:
\[
\frac{7}{3} \times \frac{2}{3} = \frac{7 \times 2}{3 \times 3} = \frac{14}{9}
\]

Thus, the simplest form of the ratio \( 2 \frac{1}{3}:1 \frac{1}{2} \) is \( \frac{14}{9} \), or \( 14:9 \).

Would you like any further details or clarifications?

Here are 5 related questions for practice:
1. How do you simplify the ratio \( 3 \frac{1}{4} : 2 \frac{2}{5} \)?
2. What is the simplest form of \( 5 \frac{2}{3} : 4 \frac{1}{3} \)?
3. How do you convert mixed numbers into improper fractions?
4. How do you solve a ratio where one term is a mixed number and the other is a whole number?
5. Can a ratio of fractions be simplified further using common factors?

**Tip:** When simplifying ratios with mixed numbers, always convert them to improper fractions first to make the calculations easier.

Learn how to simplify the ratio 2 1/3:1½ by converting mixed numbers to improper fractions and multiplying by the reciprocal. This guide breaks down the steps with formulas and explanations. Suitable for middle school students in Grades 6-8.

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