Question

Identify the unknown amount as the percent, part, or whole. 4.8 is what percent of \(12 ?\)

Short answer

Answer: 4.8 is 40% of 12.

Step-by-step solution

Identify the Part, Percent, and Whole

In this problem, the part is 4.8, and the whole is 12. The unknown to be determined is the percent.

Set Up the Equation

We write the equation: Percent = (Part / Whole) × 100%

Substitute the Known Values

Replace the part with 4.8 and the whole with 12: Percent = (4.8 / 12) × 100%

Calculate the Percent

Divide 4.8 by 12 and multiply the result by 100%: Percent = (0.4) × 100%

Solve for the Percent

Multiply 0.4 by 100% to get the percent: Percent = 40% So, 4.8 is 40% of 12.

Key concepts

Part-Whole Relationship

Understanding the part-whole relationship is essential in solving percent problems. In a given scenario, the 'whole' represents the total amount or grouping you are considering, while the 'part' is a specific section or piece of that total. For example, imagine a pizza cut into 12 equal slices; the entire pizza represents the 'whole,' and each slice is a 'part.'

In mathematical problems, determining the part and whole is the first step in solving questions that involve percents. For instance, consider the problem "4.8 is what percent of 12?" Here, 12 is the total amount or whole, and 4.8 is the part of that whole. Identifying these elements correctly is crucial to setting up equations and finding accurate answers. Without a clear understanding of the parts and whole, calculations can quickly become confusing.

Percent Calculation

The next step in solving percent problems is to calculate the percentage. This involves determining what fraction the part is of the whole and then converting that fraction into a percentage. Here's how it works:

• Divide the part by the whole to find the fraction. For example, divide 4.8 by 12 to get 0.4.
• Multiply the resulting fraction by 100 to convert it to a percent. So, 0.4 multiplied by 100 gives you 40%.

Percent calculation is simply expressing a number as a fraction of 100. It helps to remember that 'percent' literally means 'per hundred.' It's often used to compare different quantities or to express a proportion in a way that is easy to understand, as people are generally comfortable with percentages.

Visualizing this can also be helpful; think of shading in 40 out of 100 squares on a grid to represent 40%. This visual aid is an excellent way to grasp what a particular percentage might look like practically.

Prealgebra Concepts

Prealgebra serves as the bridge to more advanced algebra topics. It includes foundational skills such as the ability to manipulate numbers, understand fractions, decimals, and percents—vital for navigating percent problems. Let's explore this with an example.

• Step 1: Identify the part and whole quantities in a problem.
• Step 2: Set up the appropriate equation or fraction for the situation.
• Step 3: Perform calculations carefully, following the order of operations if necessary.

For instance, using our ongoing example, you determine that 4.8 is the part and 12 is the whole. Then, setting up the fraction: \(\frac{4.8}{12}\) and calculating gives you \(0.4\). Finally, multiplying by 100 converts this to 40%.

These steps reiterate the preciseness needed in prealgebra where decimal operations play a substantial role. Practicing these steps equips you with a robust understanding that will be highly valuable in more complex math situations. Always remember, mastering the basics is the key to tackling more complicated math problems with confidence.