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Chapter 3: Problem 68

In the following exercises, translate and solve. What number is \(65 \%\) of \(100 ?\)

Short Answer

Expert verified
The number is 65.

Step by step solution

01

- Understand the Question

The question is asking to find a number that represents 65% of 100. This can be translated into a mathematical expression.
02

- Set Up the Equation

We can translate the question into the equation: \[ x = 0.65 \times 100 \] Here, \(x\) represents the number we are looking for.
03

- Perform the Multiplication

Now, multiply the numbers: \[ x = 0.65 \times 100 \] This simplifies to: \[ x = 65 \]
04

- Conclusion

Therefore, the number that is 65% of 100 is 65.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Basic Algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In the problem provided, we use algebra to find an unknown number, represented by the variable \(x\), which is 65% of 100.
To set this up, we first understand that percentages can be converted to decimals. The percentage 65% can be written as the decimal 0.65. Then, we create an equation using multiplication to find the value of \(x\). The equation is:
\[x = 0.65 \times 100\]
This is a simple algebraic expression where \(x\) is isolated on one side of the equation. Using basic multiplication, we can solve for \(x\) and find our answer.
Percentage
Understanding percentages is crucial for solving many real-world problems. A percentage is a way of expressing a number as a fraction of 100. For example, 65% is equivalent to the fraction 65/100 or the decimal 0.65.
In our exercise, we need to determine 65% of 100. To do this, we convert 65% into a decimal (0.65) and then multiply by 100. This makes our calculation straightforward:
\[x = 0.65 \times 100\]
Performing this multiplication gives us:
\[x = 65\]
Therefore, 65% of 100 is 65. This kind of calculation is common in both academics and everyday life, helping us make sense of data, offers, and statistics.
Problem-Solving
Approaching mathematical problems systematically helps in understanding and solving them efficiently. Let's break down the steps applied in our exercise to find the number that is 65% of 100:
  • Step 1: Understand the Question
    Identify what the problem is asking. Here, we need to find a number that represents 65% of 100.

  • Step 2: Set Up the Equation
    Translate the problem into a mathematical equation. We use the formula:\(x = 0.65 \times 100\).

  • Step 3: Perform the Multiplication
    Calculate the result by multiplying the decimal form of the percentage by the given number. This results in the equation: \(x = 65\).

  • Step 4: Conclusion
    State the answer clearly. The number that is 65% of 100 is 65.

Practicing these steps can improve mathematical problem-solving skills, making it easier to handle various types of questions in exams and daily activities. Breaking problems into smaller, manageable steps can simplify complex calculations and improve accuracy.

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