Multiply or divide as indicated. Write answers in lowest terms as needed. $8÷\frac{4}{9}$

Verified step by step guidance

1. Identify the operation: You need to divide 8 by the fraction \( \frac{4}{9} \). This can be written as \( 8 \div \frac{4}{9} \).
2. Recall the rule for dividing by a fraction: Dividing by a fraction is the same as multiplying by its reciprocal. So, \( 8 \div \frac{4}{9} = 8 \times \frac{9}{4} \).
3. Rewrite the multiplication: Express 8 as a fraction to make multiplication easier, \( \frac{8}{1} \times \frac{9}{4} \).
4. Multiply the numerators together and the denominators together: \( \frac{8 \times 9}{1 \times 4} = \frac{72}{4} \).
5. Simplify the fraction \( \frac{72}{4} \) by dividing numerator and denominator by their greatest common divisor to write the answer in lowest terms.

Key Concepts

Dividing Fractions

Dividing by a fraction involves multiplying by its reciprocal. For example, dividing by 4/9 is the same as multiplying by 9/4. This simplifies the division process and helps in finding the correct answer.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. This straightforward process is essential after converting division into multiplication by the reciprocal.

Simplifying Fractions

After performing multiplication or division, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor. This ensures the answer is in lowest terms, making it easier to interpret.