Answer:
To simplify the expression \( \frac{4x}{10} \div \frac{6}{20} \), you can follow these steps:
1. Rewrite the division as multiplication by the reciprocal of the second fraction:
\( \frac{4x}{10} \times \frac{20}{6} \)
2. Simplify each fraction separately:
\( \frac{4x}{10} = \frac{2x}{5} \) (dividing both numerator and denominator by 2)
\( \frac{20}{6} = \frac{10}{3} \) (dividing both numerator and denominator by 2)
3. Substitute the simplified fractions back into the expression:
\( \frac{2x}{5} \times \frac{10}{3} \)
4. Multiply the numerators together and the denominators together:
\( \frac{2x \times 10}{5 \times 3} = \frac{20x}{15} \)
5. Further simplify the fraction by dividing both the numerator and denominator by 5:
\( \frac{20x}{15} = \frac{4x}{3} \)
Therefore, the simplified form of the expression \( \frac{4x}{10} \div \frac{6}{20} \) is \( \frac{4x}{10} \div \frac{6}{20} = \frac{4x}{10} \times \frac{20}{6} = \frac{4x}{3} \).
