Question

Solve the percent problem. What number is \(25 \%\) of \(80 ?\)

Short answer

The number which is 25% of 80 is 20.

Step-by-step solution

Understand the problem

We need to calculate what number is 25% of 80.

Convert the percentage into decimal

To calculate this, you need to convert the percentage into a decimal. You do this by dividing the percentage by 100. So, \(25 / 100 = 0.25\).

Perform the multiplication

Next, you multiply the decimal you obtained from the previous step with the given number. So, \(0.25 * 80 = 20\).

Key concepts

Converting Percentages to Decimals

Understanding how to convert percentages to decimals is essential when solving percent problems, like finding what one number is of another as a percentage. It's actually quite simple once you get the hang of it. The word 'percent' literally means 'per hundred,' which is the key to the conversion. To convert a percentage to a decimal, divide the percentage by 100. This is effectively shifting the decimal point two places to the left.

For example, to convert 25% to a decimal, divide 25 by 100 to get 0.25. It’s helpful to remember that 1% is equal to 0.01 in decimal form. This knowledge is particularly useful in various applications, from calculating discounts on sales to adjusting recipes in the kitchen.

Percentages in Algebra

In algebra, percentages are often used to represent parts of a whole in an equation or expression. To work with percentages in algebra, it's important to understand how they relate to decimals and fractions. When you're given a percent in an algebra problem, remember that you're dealing with a portion of 100.

For instance, when we say '25% of a number', we mean 25 per 100 parts of that number. This concept is vital when setting up equations to solve percent problems in algebra. Being comfortable with converting percentages to fractions or decimals can greatly simplify these problems and make them more approachable. Always translate percentages into a more 'algebra-friendly' form like decimals or fractions before performing any operations.

Basic Algebraic Operations

Algebra involves a variety of basic operations, including addition, subtraction, multiplication, and division, which are also used when working with percentages. After converting percentages to decimals, as we've discussed, you then use these basic algebraic operations to solve problems.

For example, to find '25% of 80', you firstly convert the 25% to its decimal form (0.25), and then multiply this decimal by 80. It’s the same operation as if you were multiplying any two numbers together. The use of these operations forms the foundations of algebra and helps to solve more complex equations building up from these principles. Remember the order of operations (often referred to as PEMDAS/BODMAS) to perform calculations correctly and you'll be able to handle most algebraic expressions involving percentages.