Problem 73 - Elementary Algebra

Question

$$ \text { Find } 20 \% \text { of } 60 $$

Step-by-Step Solution

Answer

20% of 60 is 12.

Step 1: Understand the Problem

The goal is to find 20% of 60. This means we need to calculate what 20% of the number 60 is.

Step 2: Convert Percentage to Decimal

To work with percentages, it can be useful to convert them to decimals. To convert a percentage to a decimal, divide by 100. Therefore, \( 20\text{ %} \) as a decimal is \( \frac{20}{100} = 0.2 \).

Step 3: Multiply the Decimal by the Number

Next, multiply the decimal by the given number. So, we calculate \( 0.2 \times 60 \).

Step 4: Perform the Multiplication

Calculate \( 0.2 \times 60 \): \( 0.2 \times 60 = 12 \). Therefore, 20% of 60 is 12.

Key Concepts

Converting Percentages to Decimals

To solve percentage problems, one of the key steps is to convert the percentage to a decimal. This makes the calculations easier. To convert a percentage to a decimal, you need to divide the percentage value by 100. For example, if you have 20%, dividing 20 by 100 gives 0.2. Here's a simple breakdown:

• Start with the percentage value (e.g., 20%).
• Divide this number by 100 (dividing by 100 moves the decimal point two places to the left).
• The result is the decimal form of the percentage (e.g., 20% becomes 0.2).

This step is crucial because it sets the stage for the subsequent multiplication to find the final result. Remember, any percentage can be converted to a decimal using this method.

Multiplication

Multiplication plays a major role in solving percentage problems. Once you have converted your percentage to a decimal, the next step is to multiply the decimal by the number in question. For example, in the problem where we need to find 20% of 60:

• First, we converted 20% to 0.2.
• Next, we multiply 0.2 by 60 to find the part of the whole.

Performing the multiplication step looks like this: \(\text {0.2} \times \text {60} = \text {12}\). Multiplication is straightforward; you are scaling the number by the decimal value which represents the percentage. In our case, 0.2 times 60 equals 12. This tells us that 20% of 60 is 12.

Percentage Problems

Percentage problems often ask you to find a part of a whole number based on a given percentage. The process involves a few clear steps that, when followed correctly, simplify finding the answer:

• Identify the percentage and the whole number (like 20% and 60).
• Convert the percentage to a decimal (20% becomes 0.2).
• Multiply the decimal by the whole number (0.2 times 60).

Percentage problems are common in everyday scenarios, such as calculating discounts, taxes, or even tips. Understanding these steps ensures you can handle such calculations with ease. Remember, practice makes perfect. The more you work with percentages, the more intuitive the steps will become.