Multiply or divide as indicated. Write answers in lowest terms as needed. (24/7)/(6/21)

Verified step by step guidance

1. Step 1: Recognize that dividing by a fraction is the same as multiplying by its reciprocal.
2. Step 2: Rewrite the expression \( \frac{24}{7} \div \frac{6}{21} \) as \( \frac{24}{7} \times \frac{21}{6} \).
3. Step 3: Multiply the numerators: \( 24 \times 21 \).
4. Step 4: Multiply the denominators: \( 7 \times 6 \).
5. Step 5: Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator, and divide both by the GCD to write the fraction in its lowest terms.

Key Concepts

Fraction Division

Dividing fractions involves multiplying by the reciprocal of the divisor. To divide the fraction (24/7) by (6/21), you first flip the second fraction to get (21/6) and then multiply: (24/7) * (21/6). This process simplifies the operation and allows for easier calculation.

Simplifying Fractions

Simplifying fractions means reducing them to their lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). For example, after performing the multiplication in the previous step, you may need to simplify the resulting fraction to ensure it is expressed in its simplest form.

Multiplication of Fractions

When multiplying fractions, you multiply the numerators together and the denominators together. For instance, in the operation (24/7) * (21/6), you calculate 24 * 21 for the numerator and 7 * 6 for the denominator, resulting in a new fraction that can then be simplified if necessary.