Problem 13 - Prealgebra

Question

Use the percent proportion to solve each problem. Round to the nearest tenth. What percent of 36 is \(19.8 ?\)

Step-by-Step Solution

Answer

55% of 36 is 19.8.

Step 1: Understanding Percent Proportion

The percent proportion is used to solve problems involving percentages. It is based on the formula: \( \frac{part}{whole} = \frac{percent}{100} \). In this problem, the 'part' is 19.8, the 'whole' is 36, and we need to find the 'percent'.

Step 2: Setting Up the Proportion

Plug the known values into the percent proportion formula: \( \frac{19.8}{36} = \frac{x}{100} \), where \( x \) is the unknown percent we need to find.

Step 3: Cross-Multiplying to Solve for x

Cross-multiply to solve for \( x \). This results in the equation: \( 19.8 \times 100 = 36 \times x \). Simplifying the left side gives \( 1980 = 36x \).

Step 4: Solving for the Percent

Solve for \( x \) by dividing both sides of the equation by 36: \( x = \frac{1980}{36} \). Calculate the division to find \( x = 55 \).

Step 5: Rounding the Result

The result is already a whole number, so no rounding is needed. If it weren't, you'd round to the nearest tenth. Therefore, the answer is \( 55 \).

Key Concepts

Understanding Prealgebra

Prealgebra is a foundational branch of mathematics that prepares students for algebra. It includes basic mathematical concepts that help in understanding more advanced topics. In prealgebra, students are introduced to

• basic arithmetic operations like addition, subtraction, multiplication, and division.
• variables and simple equations.
• concepts involving fractions, decimals, and negative numbers.

These fundamentals serve as building blocks. For example, in dealing with percent proportions, you need to be comfortable with fractions and cross-multiplication—a skill honed through prealgebra. By mastering these basics, you pave the way for tackling more intricate algebraic problems in the future.

Tackling Percentage Problems

Percentage problems are common in math, and the percent proportion method is a reliable way to solve them. A percentage represents a number as a fraction of 100. Understanding how to manipulate this concept is useful in everyday situations like calculating discounts or interest rates. To approach percentage problems:

• Identify the 'part' and 'whole' of the problem.
• Set up a proportion based on the formula: \( \frac{part}{whole} = \frac{percent}{100} \).
• Solve for the unknown variable using basic algebraic techniques like cross-multiplication.

In our example, 19.8 is the 'part,' 36 is the 'whole,' and finding the percentage requires solving the equation using these values. This approach simplifies what might otherwise seem like an intimidating problem.

Using Mathematical Formulas

In prealgebra and beyond, mathematical formulas act as tools to solve problems more efficiently. One essential formula here is the percent proportion: \[ \frac{part}{whole} = \frac{percent}{100} \]. Applying formulas requires understanding their components, correctly substituting the known values, and performing the necessary operations to find the unknown. For example, in our exercise, the formula helps to calculate what percent of 36 is 19.8, leading us to set up the equation: \( \frac{19.8}{36} = \frac{x}{100} \). Using cross-multiplication—a method where you multiply diagonally across the equal sign—you solve for the unknown percent (\(x\)) and obtain the answer after performing simple division, which is not only time-saving but also systematic in yielding correct results.