Multiply or divide as indicated. Write answers in lowest terms as needed. $\frac{6}{11}÷\frac{5}{4}$

Verified step by step guidance

1. Identify the problem as a division of two fractions: \(\frac{6}{11} \div \frac{5}{4}\).
2. Recall that dividing by a fraction is the same as multiplying by its reciprocal. So rewrite the expression as \(\frac{6}{11} \times \frac{4}{5}\).
3. Multiply the numerators together and the denominators together: numerator = \(6 \times 4\), denominator = \(11 \times 5\).
4. Write the product as a single fraction: \(\frac{6 \times 4}{11 \times 5}\).
5. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it to write the answer in lowest terms.

Key Concepts

Dividing Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. The reciprocal of a fraction is obtained by swapping its numerator and denominator. For example, dividing by 5/4 is the same as multiplying by 4/5.

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. For instance, (6/11) × (4/5) equals (6×4)/(11×5) = 24/55. This process combines the fractions into a single fraction.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor (GCD). For example, if the fraction is 24/55, since 24 and 55 share no common factors other than 1, it is already in simplest form.