Multiply or divide as indicated. Write answers in lowest terms as needed. 8/(4/9)

Verified step by step guidance

1. Identify the operation: We need to divide 8 by \( \frac{4}{9} \).
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal.
3. Find the reciprocal of \( \frac{4}{9} \), which is \( \frac{9}{4} \).
4. Rewrite the expression as a multiplication: \( 8 \times \frac{9}{4} \).
5. Multiply the whole number by the fraction: \( 8 \times \frac{9}{4} = \frac{8 \times 9}{4} \). Simplify the fraction if possible.

Key Concepts

Division of Fractions

Dividing by a fraction is equivalent to multiplying by its reciprocal. For example, dividing by 4/9 means multiplying by 9/4. This concept is essential for simplifying expressions involving fractions and is a fundamental operation in algebra.

Simplifying Fractions

Simplifying fractions involves reducing them to their lowest terms, which means expressing them in a form where the numerator and denominator have no common factors other than 1. This process is crucial for presenting answers clearly and concisely in algebra.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order, which is vital when solving complex expressions.