Problem 45 - Prealgebra

Question

Thirty percent of high school freshman chose apples as their favorite fruit in a survey. Strawberries were chosen by 0.03 of students, and onethird chose watermelon. Which group is the largest? Explain.

Step-by-Step Solution

Answer

Watermelon is the largest group with approximately 33.3% of students choosing it.

Step 1: Understand and Organize Data

We have three groups of students who chose different fruits as their favorites. The survey indicates 30% for apples, 0.03 (or 3%) for strawberries, and one-third for watermelon.

Step 2: Convert Percentages to Decimals for Comparison

Convert 30% into a decimal: \[ 30\% = \frac{30}{100} = 0.30 \]Strawberries are already given in decimal as 0.03. For watermelon, convert the fraction: \[ \frac{1}{3} \approx 0.333\ldots \].

Step 3: Compare the Decimal Values

With decimals of apples as 0.30, strawberries as 0.03, and watermelon as approximately 0.333, we can compare these values directly to determine which is the largest.

Step 4: Determine Which Group is the Largest

Compare 0.30 (apples), 0.03 (strawberries), and 0.333 (watermelon). Watermelon, with 0.333, represents the largest group.

Key Concepts

Percentages

When we talk about percentages, we often refer to how much out of 100 something represents. For students who prefer apples, it's mentioned that 30% chose apples. This 30% is a simple way to express a part of a whole as out of 100 parts.

The formula to convert a percentage into a decimal is straightforward:

• Divide the percentage by 100.

For example:

• 30% becomes \( \frac{30}{100} = 0.30 \).

Using percentages can offer an intuitive grasp of proportions in a population, making it easier to compare segments like the favorite fruits among students.

Fractions to Decimals

Converting fractions into decimals is a common task that helps in comparing different values more easily. A fraction is essentially a division operation waiting to be resolved.

For the watermelon preference, expressed as one-third, you convert this fraction as follows:

• Divide the numerator (top number) by the denominator (bottom number).
• \( \frac{1}{3} \,\approx\, 0.333\ldots \)
• The repeating decimal represents a continuous division that doesn't resolve neatly.

Being comfortable with fractions and their decimal equivalents helps bridge the gap between understanding abstract concepts and applying them to practical scenarios, such as determining preference ratios in a survey.

Comparison of Values

Understanding how to compare values is a basic skill essential for making informed decisions. In this context, comparing the number of students favoring different fruits is straightforward once all values are in decimal form.

Here's how you do it:

• Align the decimal values: Apples at 0.30, Strawberries at 0.03, and Watermelon at approximately 0.333.
• Simply observe which decimal is the largest.

Comparing decimals is akin to alphabetizing words; you start from the left and move to the right, prioritizing the largest number.

Understanding and comparing values with different formats—like fractions, percentages, and decimals—becomes much easier with practice. This skill is not only useful in math but also in everyday decision-making scenarios.