Let's solve each of the mixed fraction problems step by step.

(c) $2 \frac{2}{5} \times 1 \frac{7}{8}$

1. Convert the mixed fractions to improper fractions:

   • $2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5}$
   • $1 \frac{7}{8} = \frac{1 \times 8 + 7}{8} = \frac{15}{8}$

2. Multiply the improper fractions: $\frac{12}{5} \times \frac{15}{8} = \frac{12 \times 15}{5 \times 8} = \frac{180}{40}$

3. Simplify the result: $\frac{180}{40} = \frac{9}{2}$ This can also be written as: $4 \frac{1}{2}$

(d) $2 \frac{1}{5} \div 1 \frac{1}{2}$

1. Convert the mixed fractions to improper fractions:

   • $2 \frac{1}{5} = \frac{2 \times 5 + 1}{5} = \frac{11}{5}$
   • $1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$

2. Divide the improper fractions by multiplying with the reciprocal of the divisor: $\frac{11}{5} \div \frac{3}{2} = \frac{11}{5} \times \frac{2}{3} = \frac{11 \times 2}{5 \times 3} = \frac{22}{15}$

3. Simplify or convert to a mixed fraction: $\frac{22}{15} = 1 \frac{7}{15}$

Final answers:

• (c) $4 \frac{1}{2}$
• (d) $1 \frac{7}{15}$

Would you like further details on any step, or have any questions?

Related Questions:

1. How do you convert improper fractions back to mixed fractions?
2. What is the general method for multiplying two fractions?
3. How do you simplify a fraction after multiplication?
4. Why do we multiply by the reciprocal when dividing fractions?
5. Can mixed fractions be directly divided without converting to improper fractions?

Tip:

Always simplify the fractions before performing operations to make calculations easier.