Problem 11 - Prealgebra

Question

Solve each problem using the percent equation. What is \(37.5 \%\) of \(89 ?\)

Step-by-Step Solution

Answer

37.5% of 89 is 33.375.

Step 1: Understand the Percent Equation

The percent equation is given by the formula \( \, \text{Part} = \frac{\text{Percent}}{100} \times \text{Whole} \, \). We want to find what 37.5% of 89 is.

Step 2: Substitute in the Values

Substitute the given values into the percent equation. Here, the whole is 89 and the percent is 37.5. The equation becomes \( \, \text{Part} = \frac{37.5}{100} \times 89 \, \).

Step 3: Simplify the Fraction

Convert the percent to a decimal by dividing by 100: \( \, 37.5\% = 0.375 \, \). Substitute this into the equation to get \( \, \text{Part} = 0.375 \times 89 \, \).

Step 4: Perform the Multiplication

Multiply 0.375 by 89: \( \, 0.375 \times 89 = 33.375 \, \).

Step 5: Interpret the Result

The result of the calculation is 33.375. Thus, 37.5% of 89 is equal to 33.375.

Key Concepts

Percentage Calculation

Percentage calculation is a fundamental concept in mathematics that allows us to find the proportional part of a number in relation to 100. This process is often used to determine discounts, interest rates, and statistical data.

The main idea behind percentage calculation is to express a number as an amount out of 100. For example, if we say 37.5% of a number, it means 37.5 parts out of 100 parts of that number. This is usually a three-step process:

• Convert the percentage to a decimal: To do this, divide the percentage by 100.
• Multiply by the whole number: Use the decimal obtained to multiply with the whole to find the part.
• Interpret the result: The final product will be the percentage of the whole number.

In the exercise, we calculated 37.5% of 89. By converting 37.5% to the decimal 0.375 and multiplying it by 89, we found that 37.5% of 89 is 33.375.

Mathematical Equations

Mathematical equations are expressions that involve numbers and operations, structured to represent a relationship between quantities. They can solve a wide array of problems, from simple arithmetic to complex calculus.

In the context of percentage calculations, equations are vital as they provide a clear method to find the desired percentage of any number. The general form of a percent equation is:

\[\text{Part} = \frac{\text{Percent}}{100} \times \text{Whole}\]
This equation is manipulated by substituting given values, allowing you to calculate the 'Part' quickly:

• The "Part" represents the portion of the "Whole" that corresponds to the given percentage.
• The "Whole" is the total number or quantity from which the "Part" is derived.
• The "Percent" is the given percentage value, which must be converted to a fraction of 100.

Once the values are substituted, simplifying and solving the equation gives us the desired result.

Multiplication in Mathematics

Multiplication is one of the four basic operations in mathematics. It is a method of finding the total number of objects in groups of equal size.

Understanding multiplication is crucial, especially in percentage calculations, because once a percentage is converted to a decimal, multiplication allows us to calculate the correct "Part" of the "Whole".

Here's how multiplication fits into our process:

• After the percentage is converted into a decimal, we use it to multiply by the whole number.
• This operation shows how many parts we have when scaling the whole down to the percentage.
• Accurate multiplication is essential as any errors can lead to incorrect results, affecting financial calculations, measurements, and more.

In this exercise, multiplying 0.375 by 89 used the rules of multiplication effectively to achieve the result: 33.375. This exemplifies how basic math operations underpin more complex mathematical concepts.