To divide the mixed fractions \(2 \frac{5}{8} \div 1 \frac{7}{8}\), follow these steps:

### Step 1: Convert mixed numbers to improper fractions
- \(2 \frac{5}{8} = \frac{2 \times 8 + 5}{8} = \frac{21}{8}\)
- \(1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{15}{8}\)

### Step 2: Division of fractions is the same as multiplying by the reciprocal
\[
\frac{21}{8} \div \frac{15}{8} = \frac{21}{8} \times \frac{8}{15}
\]

### Step 3: Multiply the fractions
\[
\frac{21 \times 8}{8 \times 15} = \frac{168}{120}
\]

### Step 4: Simplify the fraction
Find the greatest common divisor (GCD) of 168 and 120, which is 24.

\[
\frac{168}{120} = \frac{168 \div 24}{120 \div 24} = \frac{7}{5}
\]

### Step 5: Convert the improper fraction back to a mixed number
\[
\frac{7}{5} = 1 \frac{2}{5}
\]

So, \(2 \frac{5}{8} \div 1 \frac{7}{8} = 1 \frac{2}{5}\).

Would you like more details or have any questions?

Here are five related questions for practice:
1. What is \(3 \frac{1}{4} \div 1 \frac{2}{3}\)?
2. How do you multiply mixed numbers like \(4 \frac{2}{5} \times 2 \frac{3}{7}\)?
3. What is the result of dividing \(5 \frac{3}{6} \div 2 \frac{1}{4}\)?
4. How do you simplify fractions in division problems?
5. How can you convert a division of improper fractions into a multiplication problem?

**Tip**: Always simplify the fractions before converting them back into mixed numbers for easier calculations!

Learn how to divide mixed fractions, like 2 5/8 ÷ 1 7/8, with a detailed step-by-step solution. This problem covers converting mixed numbers to improper fractions, multiplying by the reciprocal, and simplifying the result. Ideal for students in Grades 6-8.

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