Problem 67 - Elementary Algebra

Question

In the following exercises, translate and solve. What number is \(45 \%\) of \(120 ?\)

Step-by-Step Solution

Answer

54

Step 1: Understand the percentage

The task is to find a number that represents 45% of 120. We need to convert the percentage to its decimal form.

Step 2: Convert percentage to decimal

To convert a percentage to a decimal, divide by 100. So, 45% becomes \( \frac{45}{100} = 0.45 \).

Step 3: Multiply the decimal by the number

Next, multiply the decimal form of the percentage by 120. That is, \( 0.45 \times 120 = 54 \).

Step 4: Write the final answer

Thus, the number that is 45% of 120 is 54.

Key Concepts

Converting Percentages

In percentage calculations, you often need to convert a percentage to a decimal form in order to solve the problem.
To do this, you simply divide the percentage by 100. This conversion makes it easier to work with percentages in mathematical calculations.

For example, converting 45% to its decimal form involves the following steps:

• Take the percentage value, which is 45.
• Divide it by 100: \( \frac{45}{100} = 0.45 \).

Now, you've successfully converted the percentage to a decimal. This decimal form is what you will use in further calculations.

Understanding this step is crucial because percentages are often used in various fields, including finance, science, and everyday problem-solving.

Multiplication

Once you have converted the percentage to a decimal, the next step is to multiply. This step allows you to find out what portion of a whole corresponds to the given percentage.

In our example, you need to multiply the decimal 0.45 by 120. Here is how to do it:

• First, write the equation: \( 0.45 \times 120 \).
• Now, perform the multiplication: \( 0.45 \times 120 = 54 \).

Multiplication is a fundamental mathematical operation that combines quantities. It's not just limited to percentage calculations but is widely used in various areas like measuring areas, finding quantities in recipes, and more.

By mastering multiplication, you expand your problem-solving toolkit, making it easier to handle different types of mathematical problems.

Basic Algebra

Basic algebra involves using variables and numbers to solve equations. In this case, it helps you translate verbal statements into mathematical expressions.

To find 45% of 120, you can set up an algebraic equation where the unknown number is represented by a variable, say \( x \). The equation would look like this:

• Write the statement as an equation: \( x = 0.45 \times 120 \).

By solving this simple equation, you find \( x = 54 \).
Algebra is a powerful tool that simplifies complex problems into manageable steps, enabling you to handle a wide range of mathematical challenges. Through practice, you can become proficient in setting up and solving equations, which is a valuable skill for both academic and real-world applications.