Problem 55 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

The answer of the operation \(\frac{18}{5} \div 2\) reduced to its lowest terms is \(\frac{9}{5}\).

Step 1: Understanding Division with fractions

To perform the division operation in this context, we must recall that division of a number by a second number can be transformed into multiplication by the reciprocal of the second number.

Step 2: Reciprocal of the second number

The reciprocal of a whole number is simply \(1\) divided by that number. In this specific case, the reciprocal of \(2\) is \(1/2\).

Step 3: Perform the multiplication

Now we can perform the multiplication operation, changing the division operation into the multiplication with \(1/2\) would look like this: \(\frac{18}{5} \times \frac{1}{2}\). Now multiply both numerators together \(18 \times 1 = 18\), and both denominators together \(5 \times 2 = 10\) to get the result of the operation.

Step 4: Simplify the resulting fraction

The result of the operation is now \(\frac{18}{10}\). The final step is to simplify this fraction. This fraction can be simplified by using common factors of the numerator and the denominator, in this case \(2\), and subsequently divided, yielding \(\frac{9}{5}\).