Problem 31 - Prealgebra

Question

Use the percent proportion to solve each problem. Round to the nearest tenth if necessary. $$What is \(0.3 of \)750 ?$$

Step-by-Step Solution

Answer

0.3 of 750 is 225.

Step 1: Understand the Percent Proportion

The percent proportion is a mathematical concept used to find the part, whole, or percent in a problem. It is represented by the equation \( \frac{part}{whole} = \frac{percent}{100} \). In this problem, we are given a decimal (0.3), which represents the percent in decimal form.

Step 2: Convert the Decimal to a Percent

To use the percent proportion correctly, we need to convert 0.3 to a percent. This is done by multiplying the decimal by 100. Thus, \( 0.3 \times 100 = 30\% \).

Step 3: Set Up the Proportion

Use the percent proportion \( \frac{part}{whole} = \frac{percent}{100} \). Here, the 'whole' is 750, the 'percent' is 30, and we need to find the 'part.' The equation becomes \( \frac{x}{750} = \frac{30}{100} \).

Step 4: Solve the Proportion

To solve for \(x\), cross-multiply: \(100x = 750 \times 30\). Calculate \(100x = 22500\).

Step 5: Isolate the Variable

Divide both sides by 100 to solve for \(x\): \(x = \frac{22500}{100} = 225\).

Key Concepts

Decimal to Percent Conversion

Understanding how to convert a decimal into a percent is essential, especially when dealing with various mathematical problems. A percent is simply a way to express a number as a part of 100.
To convert a decimal to a percent, you multiply the decimal by 100. The reason for this is because "percent" essentially means "per one hundred." For instance, when you have a decimal like 0.3 and you want to express it as a percent, you multiply 0.3 by 100. This calculation gives you:

• 0.3 x 100 = 30%

So, 0.3 in decimal form is equal to 30% in percentage form. This conversion is foundational for solving problems where percentages are involved.

Cross-Multiplication

Cross-multiplication is a powerful tool used in solving proportions. A proportion is an equation where two ratios are set equal to each other.
The general form of a proportion is \( \frac{a}{b} = \frac{c}{d} \). Cross-multiplying involves multiplying the numerator of one fraction by the denominator of the other fraction, and equating the products. This simplifies the equation, allowing you to solve for the unknown variable easily.Here's how you do it:

• Multiply the numerator of the first fraction by the denominator of the second: \(a imes d\).
• Multiply the numerator of the second fraction by the denominator of the first: \(b imes c\).
• Set these two products equal to each other: \(a imes d = b imes c\).

For instance, when the problem \( \frac{x}{750} = \frac{30}{100} \) is solved, you cross-multiply to obtain \(100x = 750 imes 30\). This step greatly simplifies solving the equation.

Prealgebra

Prealgebra is a branch of mathematics that acts as a foundation for all future algebraic concepts. It involves understanding basic arithmetic and the initial exploration of variables and simple equations.
In prealgebra, problems often involve real-world applications, which include topics like percentages, proportions, and basic geometry. Knowing how to solve problems that involve decimals and percentages is critical for prealgebra students. These skills are not only necessary for academic success but also for everyday scenarios like calculating discounts or understanding interest rates. Here's what you should focus on:

• Grasping the basics of fractions, decimals, and percentages.
• Using proportions to solve problems involving part-whole relationships.
• Developing the ability to transition between different forms, such as going from a percent to a decimal.

By mastering prealgebra, students build the necessary skills to advance into more complex levels of mathematics with confidence.