Multiply or divide as indicated. Write answers in lowest terms as needed. (2/5)/30

Verified step by step guidance

1. Start by rewriting the division of fractions problem: \( \frac{\frac{2}{5}}{30} \).
2. Recognize that dividing by a number is the same as multiplying by its reciprocal. So, rewrite the expression as \( \frac{2}{5} \times \frac{1}{30} \).
3. Multiply the numerators together: \( 2 \times 1 = 2 \).
4. Multiply the denominators together: \( 5 \times 30 = 150 \).
5. Simplify the resulting fraction \( \frac{2}{150} \) by finding the greatest common divisor of 2 and 150, and divide both the numerator and the denominator by this number.

Key Concepts

Fraction Division

Dividing fractions involves multiplying by the reciprocal of the divisor. For example, to divide 2/5 by 30, you can rewrite it as (2/5) * (1/30). This process simplifies the operation and allows for easier calculation.

Lowest Terms

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1. To express a fraction in lowest terms, you can divide both the numerator and denominator by their greatest common divisor (GCD). This ensures the fraction is simplified as much as possible.

Multiplication of Fractions

When multiplying fractions, you multiply the numerators together and the denominators together. For instance, in the operation (2/5) * (1/30), you would calculate 2 * 1 for the numerator and 5 * 30 for the denominator, resulting in a new fraction that can then be simplified.