Multiply or divide as indicated. Write answers in lowest terms as needed. $\frac{2}{5}÷30$

Verified step by step guidance

1. Identify the problem as a division of fractions: \( \frac{2}{5} \div 30 \). Remember that dividing by a whole number is the same as dividing by a fraction with denominator 1, so rewrite 30 as \( \frac{30}{1} \).
2. Rewrite the division of fractions as multiplication by the reciprocal: \( \frac{2}{5} \div \frac{30}{1} = \frac{2}{5} \times \frac{1}{30} \).
3. Multiply the numerators together and the denominators together: \( \frac{2 \times 1}{5 \times 30} = \frac{2}{150} \).
4. Simplify the fraction \( \frac{2}{150} \) by finding the greatest common divisor (GCD) of 2 and 150, then divide both numerator and denominator by the GCD.
5. Write the simplified fraction as the final answer in lowest terms.

Key Concepts

Division of Fractions

Dividing fractions involves multiplying the first fraction by the reciprocal of the second. For example, dividing by 30 is the same as multiplying by 1/30. This method simplifies complex fraction division problems.

Simplifying Fractions

After performing operations, fractions should be simplified to their lowest terms by dividing numerator and denominator by their greatest common divisor (GCD). This makes the answer clearer and easier to interpret.

Multiplication of Fractions

Multiplying fractions requires multiplying the numerators together and the denominators together. This operation is straightforward and essential when converting division problems into multiplication by reciprocals.