Problem 42 - Prealgebra

Question

The Arctic Ocean contains \(3.7 \%\) of the world's water. What fraction is this?

Step-by-Step Solution

Answer

The fraction of the world's water in the Arctic Ocean is \(\frac{37}{1000}\).

Step 1: Understand the Problem

We know that the Arctic Ocean contains \(3.7\%\) of the world's water. We need to convert this percentage into a fraction.

Step 2: Convert Percentage to Fraction

A percentage is essentially a fraction with a denominator of 100. Therefore, \(3.7\%\) can be written as \(\frac{3.7}{100}\).

Step 3: Simplify the Fraction

Since \(3.7\) is already in decimal form, we convert it to a fraction \(\frac{37}{10}\). So \(\frac{3.7}{100}\) becomes \(\frac{37}{10 \times 100} = \frac{37}{1000}\). This fraction is in its simplest form.

Key Concepts

Understanding Fraction Conversion

Converting percentages to fractions is a fundamental concept in prealgebra. It helps you understand proportions in a different form, making calculations easier in some cases. A percentage is fundamentally a fraction with a denominator of 100. This means that when you have a value in percentage, you're essentially looking at how much out of 100 that value represents. This simplification allows us to easily convert percentages to fractions.

For example, if you have 25% of something, it implies you have 25 parts out of 100, or mathematically, \(\frac{25}{100}\). This principle holds true for both whole numbers and decimal percentages, such as 3.7%. Always remember:

• The percentage value becomes the numerator.
• 100 is always the denominator initially.

So, for 3.7%, the fractional form starts as \(\frac{3.7}{100}\). This is the foundational step before simplifying the fraction for easier use.

Grasping Percentages

Percentages are a way to express a number as a part of a whole, which is always represented as 100%. This method of representation is ubiquitous in many real-life scenarios where understanding proportions is essential, like discounts, grades, and statistics.

When working with percentages, remember:

• 100% represents the whole, or entirety, of something.
• Percentages less than 100% indicate a portion of the whole.
• Percentages more than 100% suggest an amount greater than the whole.

To convert a percentage like 3.7% into a mathematical format, remember it simply expresses 3.7 per 100. Moving from this representation to fractions or decimals helps in various calculations where further simplification or operations are necessary.

The ease of converting percentages to other forms helps provide clarity and flexibility when dealing with numbers in everyday contexts.

Mastering Simplifying Fractions

Simplifying fractions is like tidying up your math equations. It makes them cleaner and easier to handle. A simplified fraction is one in which the numerator and the denominator have no common factors other than 1. This often involves reducing both parts of the fraction by their greatest common divisor (GCD).

For the fraction obtained from 3.7%, which is \(\frac{37}{1000}\), there are no common factors between 37 and 1000, making it already in its simplest form. Here are the steps you generally follow:

• Check for common factors between the numerator and the denominator.
• Divide both by their greatest common factor, if any.

Understanding how to simplify fractions ensures that you present your answer in the most succinct form possible. This process is invaluable in any mathematical setting, as it aids in clearer communication and simpler further operations.