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!