Problem 67 - Prealgebra

Question

Over a recent five-year period, 9 hurricanes struck the mainland of the United States. Three of these hurricanes were classified as a category \(3,4\) or \(5 .\) Represent the number of major hurricanes that struck the mainland U.S. over this time period as a fraction in lowest terms.

Step-by-Step Solution

Answer

The fraction of major hurricanes is \( \frac{1}{3} \).

Step 1: Identify Total Hurricanes

The problem states that over the five-year period, 9 hurricanes struck the mainland United States. This is our total number of hurricanes, which we will use as the denominator in our fraction.

Step 2: Count Major Hurricanes

Out of the 9 total hurricanes, 3 were classified as category 3, 4, or 5 hurricanes. These are considered major hurricanes and will be our numerator in the fraction.

Step 3: Formulate the Fraction

We represent the number of major hurricanes as a fraction of the total number of hurricanes: \( \frac{3}{9} \). This fraction shows the part of the whole that comprises major hurricanes.

Step 4: Simplify the Fraction

To simplify \( \frac{3}{9} \), we find the greatest common divisor (GCD) of 3 and 9, which is 3. We divide both the numerator and the denominator by their GCD: \( \frac{3 \div 3}{9 \div 3} = \frac{1}{3} \). Thus, the simplified fraction is \( \frac{1}{3} \).

Key Concepts

Understanding Hurricanes

Hurricanes are powerful and destructive storms that form over warm ocean waters, characterized by heavy rains, strong winds, and sometimes, deadly consequences. They are categorized based on their wind speeds using the Saffir-Simpson Hurricane Wind Scale. This scale ranges from Category 1, with winds of 74-95 mph, to Category 5, with winds exceeding 157 mph. Major hurricanes, which are of Categories 3, 4, and 5, bring about the most significant damage due to their high wind speeds and torrential rains. Understanding the classification of hurricanes helps in assessing their potential impact and preparing communities for upcoming weather conditions. The categorization also allows for more accurate historical recording and reporting, which is essential for analysis and future forecasting.

Simplifying Fractions Made Easy

Simplifying fractions means reducing them to their lowest terms so they are easier to understand and compare. A fraction consists of a numerator and a denominator. In the case of the hurricane example, the fraction initially was \( \frac{3}{9} \). The goal of simplifying is to find the simplest form with the smallest whole numbers possible.
Here's how:

• Find a number that divides both numerator and denominator evenly.
• Use this number to divide both parts of the fraction.

This makes understanding ratios and proportions much simpler. Once simplified, fractions are easier to use in additional math operations, such as addition or multiplication.

Discovering the Greatest Common Divisor

The Greatest Common Divisor (GCD) is the largest positive integer that divides two numbers without leaving a remainder. To simplify fractions effectively, finding the GCD is a crucial step.
For example:

• Identify the numbers involved - here it was 3 (numerator) and 9 (denominator).
• List the divisors of each number.
• Find the largest number that appears in both lists.

For 3 and 9, the GCD is 3, because 3 divides both 3 and 9 evenly. Using the GCD simplifies the fraction by dividing both the numerator and denominator by this number. This leads to the simplest form of the fraction, making calculations more straightforward and easier to understand.