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Magazine Chapter 6: Problem 11
Solve each problem using the percent equation. What is \(37.5 \%\) of \(89 ?\)
Short Answer
Expert verified
37.5% of 89 is 33.375.
Step by step solution
01
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.
02
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 \( \, \text{Part} = \frac{37.5}{100} \times 89 \, \).
03
Simplify the Fraction
Convert the percent to a decimal by dividing by 100: \( \, 37.5\% = 0.375 \, \). Substitute this into the equation to get \( \, \text{Part} = 0.375 \times 89 \, \).
04
Perform the Multiplication
Multiply 0.375 by 89: \( \, 0.375 \times 89 = 33.375 \, \).
05
Interpret the Result
The result of the calculation is 33.375. Thus, 37.5% of 89 is equal to 33.375.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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:
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.
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:
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.
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:
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.
