Problem 43 - Prealgebra

Question

Forty-six percent of the world's water is in the Pacific Ocean. What fraction is this?

Step-by-Step Solution

Answer

The fraction is \( \frac{23}{50} \).

Step 1: Understanding the Percentage

We are given that 46% of the world's water is in the Pacific Ocean. To convert this percentage to a fraction, understand that the percentage represents 46 parts out of 100.

Step 2: Converting Percentage to Fraction

To convert 46% into a fraction, place the percentage over 100. This gives us the fraction \( \frac{46}{100} \).

Step 3: Simplifying the Fraction

We can simplify the fraction \( \frac{46}{100} \) by finding the greatest common divisor (GCD) of 46 and 100, which is 2. Divide both the numerator and the denominator by 2 to simplify: \( \frac{46 \div 2}{100 \div 2} = \frac{23}{50} \).

Step 4: Conclusion of the Fraction

The simplified fraction representation of 46% is \( \frac{23}{50} \). Thus, 46% can be expressed as \( \frac{23}{50} \).

Key Concepts

Percentage to Fraction Conversion

Converting percentages to fractions is a crucial mathematical skill which helps us understand proportions more intuitively. When you see a percentage, it means a certain number of parts out of 100. For instance, 46% simply represents 46 out of 100 parts. To convert a percentage to a fraction, follow these steps:

• Write the percentage number over 100. So, 46% becomes \( \frac{46}{100} \).
• This fraction shows the exact same relationship as the percentage but expressed in a different form.

By understanding this conversion, you can easily transform any percentage into a fraction. This is helpful in many areas of mathematics and real-life scenarios where fractions are more useful than percentages.

Simplifying Fractions

Simplifying fractions is all about making a fraction easier to read or work with. It involves reducing the fraction to its smallest possible equivalent form. This often makes calculations simpler and more efficient.Here’s how you simplify a fraction:

• Find the greatest common divisor (GCD) of both the numerator and the denominator. The GCD is the largest number that divides both numbers without any remainder.
• Divide both the numerator and the denominator by their GCD.

In our example with the fraction \( \frac{46}{100} \), the GCD of 46 and 100 is 2. By dividing both the numerator and the denominator by 2, we simplify the fraction to \( \frac{23}{50} \). Simplifying is important because it makes fractions easier to work with and compare.

Mathematics Education

Mathematics education equips students with tools to explore and understand the world through numbers and calculations. Understanding concepts like fractions and percentages is foundational in learning math. Teaching methods often aim to:

• Build a strong foundational skill set for solving real-world problems.
• Improve mental math skills, enhancing cognitive abilities.
• Promote logical and analytical thinking, essential for academic success.

Mathematics education can be made more effective by using step-by-step approaches, hands-on examples, and relatable contexts like the percentage of water distribution in the world's oceans. It’s about making the abstract tangible, thereby nurturing a student's ability to think critically and solve problems.