Problem 20 - Basic College Mathematics

Question

Divide and simplify. \(\frac{18}{5} \div 2\)

Step-by-Step Solution

Answer

The simplified result is \(\frac{9}{5} \).

Step 1: Understand the division of fractions

Division of fractions can be performed by multiplying by the reciprocal of the divisor. So, we need to change the division problem into a multiplication problem first.

Step 2: Rewrite the problem

Rewrite \(\frac{18}{5} \div 2\) as \(\frac{18}{5} \cdot \frac{1}{2}\).

Step 3: Multiply the fractions

To multiply fractions, multiply the numerators and then the denominators. So, \(\frac{18}{5} \cdot \frac{1}{2} \) becomes \(\frac{18 \cdot 1}{5 \cdot 2} \) which simplifies to \(\frac{18}{10} \).

Step 4: Simplify the result

Simplify \(\frac{18}{10} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2. Therefore, \(\frac{18}{10} \div 2 = \frac{9}{5} \).

Key Concepts

Reciprocals

To divide fractions, you use the concept of reciprocals. A reciprocal is simply flipping the numerator and the denominator. For example, the reciprocal of \(\frac{2}{1}\) is \(\frac{1}{2}\).
When you divide by a fraction, you multiply by its reciprocal.
In the exercise, dividing by 2 (\