Calculate after r $$ 2.1 \quad 1 \frac{1}{2} \div 3 \frac{1}{3} $$ $$ 2.4 \quad 7 \frac{4}{5} \div 3 \frac{5}{6} $$

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**Step 1. Evaluate $$1 \frac{1}{2} \div 3 \frac{1}{3}$$**

1. Convert each mixed number to an improper fraction:
   - $$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$$
   - $$3 \frac{1}{3} = \frac{(3 \times 3) + 1}{3} = \frac{10}{3}$$

2. Perform the division by multiplying by the reciprocal:
   $$
   \frac{3}{2} \div \frac{10}{3} = \frac{3}{2} \times \frac{3}{10}
   $$

3. Multiply numerators and denominators:
   $$
   \frac{3 \times 3}{2 \times 10} = \frac{9}{20}
   $$

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**Step 2. Evaluate $$7 \frac{4}{5} \div 3 \frac{5}{6}$$**

1. Convert each mixed number to an improper fraction:
   - $$7 \frac{4}{5} = \frac{(7 \times 5) + 4}{5} = \frac{35 + 4}{5} = \frac{39}{5}$$
   - $$3 \frac{5}{6} = \frac{(3 \times 6) + 5}{6} = \frac{18 + 5}{6} = \frac{23}{6}$$

2. Perform the division by multiplying by the reciprocal:
   $$
   \frac{39}{5} \div \frac{23}{6} = \frac{39}{5} \times \frac{6}{23}
   $$

3. Multiply numerators and denominators:
   $$
   \frac{39 \times 6}{5 \times 23} = \frac{234}{115}
   $$

4. Convert $$\frac{234}{115}$$ to a mixed number:
   - Divide: $$234 \div 115 = 2$$ remainder $$234 - 2 \times 115 = 234 - 230 = 4$$
   - Thus, the result is $$2 \frac{4}{115}$$

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**Final Answers:**

$$
1 \frac{1}{2} \div 3 \frac{1}{3} = \frac{9}{20}
$$

$$
7 \frac{4}{5} \div 3 \frac{5}{6} = \frac{234}{115} \quad \text{or} \quad 2 \frac{4}{115}
$$
$$ 1 \frac{1}{2} \div 3 \frac{1}{3} = \frac{9}{20} $$ $$ 7 \frac{4}{5} \div 3 \frac{5}{6} = \frac{234}{115} \quad \text{or} \quad 2 \frac{4}{115} $$

Calculate after r \( 2.1 \quad 1 \frac{1}{2} \div 3 \frac{1}{3} \) \( 2.4 \quad 7 \frac{4}{5} \div 3 \frac{5}{6} \)

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