Problem 33 - Prealgebra

Question

The following problems can be solved by the same method you used in Problems \(1-24\) 65 is what percent of \(130 ?\)

Step-by-Step Solution

Answer

65 is 50% of 130.

Step 1: Understand the Problem

The exercise is asking us to find what percentage 65 is of 130. This means we are looking for a ratio of 65 to 130 expressed as a percentage.

Step 2: Set up the Percentage Equation

To find a percentage, we use the formula: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Here, the 'Part' is 65 and the 'Whole' is 130.

Step 3: Calculate the Ratio

Divide the part by the whole to find the ratio: \( \frac{65}{130} = 0.5 \).

Step 4: Convert the Ratio to a Percentage

Multiply the ratio by 100 to convert it to a percentage: \( 0.5 \times 100 = 50 \).

Key Concepts

Understanding Ratios

A ratio is a way to compare two different numbers, showing how much of one thing exists in relation to another. In our exercise, this involves comparing 65 to 130, meaning we want to find out how much 65 is "of" or in comparison to 130. Ratios can be represented in several forms:

• As fractions, such as \( \frac{65}{130} \)
• Using a colon, like 65:130
• In words, for example, "65 to 130"

In mathematics and everyday life, ratios play a crucial role because they help us make sense of relative sizes and distributions. When dealing with problems of this nature, it is vital to ensure that the quantities being compared are related in a meaningful way. Always make sure the two parts of a ratio are in the same units to make this comparison valid.

The Role of Mathematics in Percentage Calculation

Mathematics provides us with various tools and formulas to find percentages, an essential skill in many real-life scenarios. One of these tools is the percentage formula:

\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]

In our example, we use this formula to determine the percentage that 65 is of 130. Here's how it works step by step:

• Identify the 'Part' and 'Whole'—in this case, 65 and 130.
• Divide the part by the whole to get a ratio, which in this example is 0.5.
• Multiply the ratio by 100 to find the percentage: 50%.

Math isn't just numbers and equations; it's a language through which we can express and solve commonplace problems like finding a percentage. This understanding can enhance both everyday decision-making and academic performance.

Introduction to Prealgebra Concepts

Prealgebra is all about laying a sturdy foundation for future mathematics learning. It introduces students to the basic principles that underpin more advanced topics. One of these principles is understanding ratios and percentages, as demonstrated in the exercise.
Key prealgebra concepts related to our problem include:

• Recognizing relationships between numbers, such as the part-whole relationship (e.g., 65 and 130).
• Learning how to manipulate fractions and convert them into percentages.
• Understanding division as a means of comparison, critical when determining ratios and percentage values.

Developing a clear grasp of these fundamentals through prealgebra will pave the way for success in algebra and beyond. Taking time with problems like these reinforces mathematical thinking and problem-solving strategies.