Question

Calculate \(220 \%\) of \(-75\).

Short answer

Answer: -165

Step-by-step solution

Convert the percentage to a decimal

To convert 220% to a decimal, divide 220 by 100: $$ \frac{220}{100} = 2.20 $$ Now we have the decimal, 2.20, which we will use to find 220% of -75.

Multiply the decimal by -75

Now, multiply 2.20 (the decimal equivalent of 220%) by -75: $$ 2.20 \times -75 = -165 $$

Final Answer

So, \(220\%\) of \(-75\) is equal to \(-165\).

Key concepts

Converting Percentages to Decimals

Converting a percentage to a decimal is a necessary first step in many mathematical calculations. It is very simple to do. Think of a percentage as 'out of 100.' For example, 220% literally means 220 out of 100.

To convert a percentage into a decimal, you just need to divide by 100. This works because percentages are based on 100. So, to convert 220% to a decimal, you do the following calculation:

• 220% ÷ 100 = 2.20

By dividing by 100, you move the decimal point two places to the left. This is why 220% becomes 2.20 as a decimal. Understanding this conversion will help you in a variety of situations and is foundational in working with percentages effectively.

Multiplication with Negative Numbers

Multiplying with negative numbers can be confusing at first, but it follows a simple rule. If you multiply a positive number by a negative number, the result is always negative. This rule is crucial to get correct results in calculations.

Let's take our example: You want to multiply 2.20 (the decimal form of 220%) by -75. Here's how it works:

• 2.20 (positive) × -75 (negative) = -165

As you can see, because one of the numbers is negative, the result of the multiplication is negative (-165). Multiplier or multiplicand should have opposite signs for the product to be negative. If both were negative, the product would be positive.

Basic Arithmetic Operations

Arithmetic operations are the foundation of mathematics, allowing us to perform calculations critical to solving real-world problems. The core arithmetic operations are addition, subtraction, multiplication, and division.

Here we are focusing on multiplication, one of the most common and powerful operations. Multiplication is essentially repeated addition. In our context, using decimals and percentages, the operation becomes slightly more detailed due to conversion and sometimes signs need careful consideration.

For example, when you multiply the decimal 2.20 by -75, what you're doing is adding the number -75 to itself 220 times or rather three times in this simplified case. This results in -165. Understanding these basic operations helps you create and follow steps to find solutions to complex problems successfully. Remember, practice is key to getting comfortable with them!