Problem 17 - Elementary Algebra

Question

Find \(300 \%\) of 65 .

Step-by-Step Solution

Answer

195.

Step 1: Understanding Percentages

A percentage is a fraction out of 100. So when we are asked to find 300% of 65, it means we need to calculate 3 times 100% of 65.

Step 2: Convert Percentage to Decimal

Convert the percentage to a decimal by dividing it by 100. Thus, 300% becomes \(\frac{300}{100} = 3\).

Step 3: Multiply Decimal by the Number

Multiply the decimal form of the percentage by the given number. So, multiply 3 by 65: \(. 3 \times 65 \) = 195.

Key Concepts

Converting percentages to decimals

When it comes to converting percentages to decimals, the first thing you need to remember is that a percentage is just a number out of 100. This means that to turn a percentage into a decimal, you simply divide it by 100. This is straightforward and can be done in a few simple steps.

Let's take an example to clarify this concept. If you have 300%, you want to convert it to a decimal. Here's how you do it:

• Divide the percentage number (300) by 100.
• The formula becomes \(\frac{300}{100}\).
• When you carry out the division, you get 3.

So, 300% when converted to a decimal is 3. This trick works for any percentage you need to convert. Remember, always divide by 100, and you will easily get your decimal number.

Multiplication

Once we have converted the percentage to a decimal, the next step usually involves some multiplication. Multiplication is a fundamental math operation where you add a number to itself a certain number of times. In this case, you're multiplying the decimal form of the percentage by another number (also known as the base number).

Using our example, we have the decimal 3 (converted from 300%). We want to find 300% of 65. Here's how you'll do it:

• Take your decimal (3) and the base number (65).
• Multiply them together: 3 * 65.
• The multiplication is performed as follows: \[(3 * 60) + (3 * 5) = 180 + 15 = 195\]

So, 300% of 65 is 195. Multiplication ties the conversion and the final calculation together, giving us the answer.

Understanding percentages

Before diving into calculations involving percentages, it's important to understand what a percentage actually is. A percentage is a way of expressing a number as a fraction of 100. For example, 50% means 50 out of 100 parts, essentially simplifying to half.

Percentages are useful in everyday life for various reasons, such as calculating discounts, determining interest rates, or understanding statistics. Here's what you need to keep in mind:

• Percentages can be greater than 100%. For instance, 300% means three times the whole.
• They can also be less than 1%, representing very small parts of a whole.

In our problem, finding 300% of 65 means we want to know what three whole parts (300%) look like compared to 65. By converting the percentage to a decimal and multiplying it by 65, we effectively calculate the extended ratio, making these concepts easier to apply in various real-world scenarios.