Question

Calculate \(84 \%\) of 560 .

Short answer

Answer: 470.4

Step-by-step solution

Convert the percentage to a decimal

To convert 84% to a decimal, divide 84 by 100. This gives us 0.84.

Multiply the decimal by the given number

Now, multiply 0.84 by 560 to find the value that represents 84% of 560: \(0.84 \cdot 560 = 470.4\)

Interpret the result

The result, 470.4, represents 84% of the given number, 560.

Key concepts

Converting Percentages to Decimals

Understanding how to turn percentages into decimals is an essential math skill, crucial for solving many types of problems. A percentage can be easily converted into a decimal by dividing it by 100. The reason behind this is that the word 'percent' literally means 'per hundred.' So, when you are given a percentage, it implies that the number is a certain part out of 100. For example, to convert 84% to a decimal, you just divide 84 by 100, which is equivalent to moving the decimal point two places to the left.

Therefore, \[84\% = \frac{84}{100} = 0.84\].
Once you have this decimal, it can be used in further calculations, as we will see in the 'percentage of a number' concept.

Percentage of a Number

After converting a percentage to a decimal, the next step is often to find that percentage of a given number. To do this, you simply multiply the decimal form of the percentage by the number in question. This operation reflects how much of the number would be obtained if it were divided into 100 equal parts and a certain number of those parts were taken, as indicated by the initial percentage.

For instance, to find 84% of 560, you multiply the decimal form of 84% (which is 0.84) by 560: \[0.84 \times 560 = 470.4\].
This multiplication gives you the value that represents 84% of the number 560, which is 470.4. This step involves basic arithmetic, specifically multiplication, which we will cover next.

Basic Arithmetic Operations

At the heart of percentage calculations are basic arithmetic operations such as addition, subtraction, multiplication, and division. Multiplication, used in finding the percentage of a number, involves combining equal groups. When we multiplied the decimal version of the percentage (0.84) by the number 560, we were essentially adding up 560 'eighty-four times' to find out what 84% of it is.

Such operations are the building blocks for more complex mathematical problems and are performed following the rules of arithmetic, which includes the understanding of order of operations: parentheses, exponents, multiplication, division, addition, and subtraction (PEMDAS). Mastery of these operations allows for handling various mathematical challenges confidently.