Question

1. $2\frac{1}{2} \div \frac{2}{5}$

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \( 2\frac{1}{2} \) can be converted to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). For \( 2\frac{1}{2} \), \( a = 2 \), \( b = 1 \), \( c = 2 \), so we have \( \frac{2\times2 + 1}{2}=\frac{4 + 1}{2}=\frac{5}{2} \).

Step2: Divide by multiplying by reciprocal

To divide by a fraction, we multiply by its reciprocal. So \( \frac{5}{2}\div\frac{2}{5} \) is equivalent to \( \frac{5}{2}\times\frac{5}{2} \) (since the reciprocal of \( \frac{2}{5} \) is \( \frac{5}{2} \)).

Step3: Multiply the numerators and denominators

When multiplying fractions \( \frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d} \). Here, \( a = 5 \), \( b = 2 \), \( c = 5 \), \( d = 2 \), so \( \frac{5\times5}{2\times2}=\frac{25}{4} \).

Step4: Convert improper fraction to mixed number (optional)

\( \frac{25}{4} = 6\frac{1}{4} \) or as a decimal \( 6.25 \). But if we leave it as an improper fraction, it's \( \frac{25}{4} \).

Answer:

\( \frac{25}{4} \) (or \( 6\frac{1}{4} \) or \( 6.25 \))