$$ 2 \frac{2}{5} \div 1 \frac{1}{4} $$ 3) $$ 1 \frac{3}{5} \div \frac{1}{15} $$ $$ 3 \frac{3}{10} \div 1 \frac{3}{8} $$

Question

UpStudy AI · Accepted Answer

Let's solve each of the division problems step by step.

### Problem 1: $$ 2 \frac{2}{5} \div 1 \frac{1}{4} $$

1. **Convert mixed numbers to improper fractions:**
   - $$ 2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} $$
   - $$ 1 \frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{4 + 1}{4} = \frac{5}{4} $$

2. **Set up the division of fractions:**
   $$
   \frac{12}{5} \div \frac{5}{4} = \frac{12}{5} \times \frac{4}{5}
   $$

3. **Multiply the fractions:**
   $$
   = \frac{12 \times 4}{5 \times 5} = \frac{48}{25}
   $$

4. **Convert back to a mixed number:**
   $$
   48 \div 25 = 1 \quad \text{remainder } 23 \quad \Rightarrow \quad 1 \frac{23}{25}
   $$

### Problem 2: $$ 1 \frac{3}{5} \div \frac{1}{15} $$

1. **Convert mixed number to improper fraction:**
   - $$ 1 \frac{3}{5} = \frac{1 \times 5 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5} $$

2. **Set up the division of fractions:**
   $$
   \frac{8}{5} \div \frac{1}{15} = \frac{8}{5} \times 15
   $$

3. **Multiply the fractions:**
   $$
   = \frac{8 \times 15}{5} = \frac{120}{5} = 24
   $$

### Problem 3: $$ 3 \frac{3}{10} \div 1 \frac{3}{8} $$

1. **Convert mixed numbers to improper fractions:**
   - $$ 3 \frac{3}{10} = \frac{3 \times 10 + 3}{10} = \frac{30 + 3}{10} = \frac{33}{10} $$
   - $$ 1 \frac{3}{8} = \frac{1 \times 8 + 3}{8} = \frac{8 + 3}{8} = \frac{11}{8} $$

2. **Set up the division of fractions:**
   $$
   \frac{33}{10} \div \frac{11}{8} = \frac{33}{10} \times \frac{8}{11}
   $$

3. **Multiply the fractions:**
   $$
   = \frac{33 \times 8}{10 \times 11} = \frac{264}{110}
   $$

4. **Simplify the fraction:**
   $$
   = \frac{264 \div 22}{110 \div 22} = \frac{12}{5}
   $$

5. **Convert back to a mixed number:**
   $$
   12 \div 5 = 2 \quad \text{remainder } 2 \quad \Rightarrow \quad 2 \frac{2}{5}
   $$

### Summary of Results:
1. $$ 2 \frac{2}{5} \div 1 \frac{1}{4} = 1 \frac{23}{25} $$
2. $$ 1 \frac{3}{5} \div \frac{1}{15} = 24 $$
3. $$ 3 \frac{3}{10} \div 1 \frac{3}{8} = 2 \frac{2}{5} $$
1. $$ 2 \frac{2}{5} \div 1 \frac{1}{4} = 1 \frac{23}{25} $$ 2. $$ 1 \frac{3}{5} \div \frac{1}{15} = 24 $$ 3. $$ 3 \frac{3}{10} \div 1 \frac{3}{8} = 2 \frac{2}{5} $$

3)

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Answer

Solution

Problem 1:

Problem 2:

Problem 3:

Summary of Results:

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