Problem 57 - Introductory Algebra for College Students

Question

Perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$2 \div \frac{18}{5}$$

Step-by-Step Solution

Answer

The answer is \(\frac{5}{9}\).

Step 1: Write the Division as Multiplication

Rewrite the division problem as a multiplication problem by flipping (finding the reciprocal of) the fraction. So the original problem, \(2 \div \frac{18}{5}\), becomes \(2 \times \frac{5}{18}\).

Step 2: Perform the Multiplication

Multiply the number by the reciprocal of the fraction. \nWhich is: \(2 \times \frac{5}{18} = \frac{2 \times 5}{18} = \frac{10}{18}\).

Step 3: Simplify the Result

Reduce the resulting fraction to its lowest terms. The highest number that both 10 and 18 can be divided evenly by is 2. When we divide both top and bottom by 2, we'll get \(\frac{10}{18} = \frac{5}{9}\).