Multiply or divide as indicated. Write answers in lowest terms as needed. (6/11)/(5/4)

Verified step by step guidance

1. Identify the operation: This problem involves division of two fractions, \( \frac{6}{11} \div \frac{5}{4} \).
2. Recall the rule for dividing fractions: To divide by a fraction, multiply by its reciprocal.
3. Find the reciprocal of the second fraction: The reciprocal of \( \frac{5}{4} \) is \( \frac{4}{5} \).
4. Rewrite the division as multiplication: \( \frac{6}{11} \times \frac{4}{5} \).
5. Multiply the numerators and the denominators: \( \frac{6 \times 4}{11 \times 5} \).

Key Concepts

Division of Fractions

Dividing fractions involves multiplying by the reciprocal of the divisor. For example, to divide (6/11) by (5/4), you multiply (6/11) by (4/5). This process simplifies the operation and allows for easier calculation.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms, where the numerator and denominator have no common factors other than 1. This is done by dividing both the numerator and denominator by their greatest common divisor (GCD).

Multiplication of Fractions

When multiplying fractions, you multiply the numerators together and the denominators together. For instance, in the expression (6/11) * (4/5), you calculate 6 * 4 for the numerator and 11 * 5 for the denominator, resulting in a new fraction that may need simplification.