Multiply or divide as indicated. Write answers in lowest terms as needed. $\frac{24}{7}÷\frac{6}{21}$

Verified step by step guidance

1. Rewrite the division of fractions as multiplication by the reciprocal. So, \( \frac{24}{7} \div \frac{6}{21} \) becomes \( \frac{24}{7} \times \frac{21}{6} \).
2. Multiply the numerators together and the denominators together: \( \frac{24 \times 21}{7 \times 6} \).
3. Simplify the numerator and denominator by factoring and canceling common factors. For example, factor numbers to find common divisors.
4. After canceling common factors, multiply the remaining numbers in the numerator and denominator to get a simplified fraction.
5. If possible, reduce the fraction further to its lowest terms by dividing numerator and denominator by their greatest common divisor (GCD).

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 (24/7) by (6/21) is the same as multiplying (24/7) by (21/6).

Multiplying Fractions

To multiply fractions, multiply the numerators together and the denominators together. For instance, multiplying (24/7) by (21/6) means calculating (24 × 21) in the numerator and (7 × 6) in the denominator before simplifying.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing numerator and denominator by their greatest common divisor (GCD). This makes the fraction easier to understand and work with, ensuring the answer is in simplest form.