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What is an Algebraic Expression?

Algebraic expressions are essential for making calculations in algebra and other math subjects. Learn the basics of algebraic expressions, how to use them, and how they can help you make more accurate calculations.
Algebra
7 minutes
What is an Algebraic Expression?
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Algebra is a mathematics discipline that helps us understand and solve equations. An algebraic expression is an equation that contains one or more variables. Letters, numbers, or other symbols can represent these variables.

By solving an algebraic expression, we can find the value of the variable(s) in the equation.

In this blog post, we'll take a closer look at the meaning and use of algebraic expressions and answer the question, "What is an algebraic expression?" Time for a quick algebra refresher!

What is Algebra?

Algebra is a fascinating part of math that helps you understand and work with numbers in a more abstract way.

It operates by taking the relationships between two or more variables and employing those relationships to solve equations, describe patterns, and make connections between different pieces of information.

Algebraic formulas let us take complicated problems from the real world and turn them into questions that can be answered logically, giving us satisfying answers in both the classroom and the real world.

Algebra can be used to model real-world problems and help us analyze data, such as predicting future trends. It is also used in areas such as physics and engineering to understand the behavior of systems under different conditions.

By learning algebra, we learn to appreciate how math can be used to explain complicated ideas and solve hard problems. It also helps us think of new ways to solve problems and improves our ability to think logically and abstractly, which are skills that are useful in many fields.

Algebraic equations let us break down hard problems into parts that are easier to solve with basic math operations like adding, subtracting, multiplying, dividing, and exponentiating. This makes it easy to solve problems quickly, accurately, and without needing a calculator. Algebra teaches us how to read graphs and other visual data sets, which helps us understand trends in many different fields of study.

When used properly, algebra can open up entirely new ways of looking at problems and help drive solutions far beyond what was previously possible.

Four Basic Operations

Algebra is a branch of mathematics that focuses on studying variables and constants and their relationships to one another.

At its foundation, algebra comprises four basic operations: addition, subtraction, multiplication, and division. Addition seeks to find the sum of two or more numbers; subtraction looks for the difference between two or more numbers; multiplication multiplies two or more numbers together; and division divides one number by another in order to find out a quotient.

When it comes to understanding algebraic equations and fundamentals, these four operations are required.

Numbers, Variables, and Operations

Algebraic expressions are often used in math because they let us show mathematical equations and relationships in a short way.

An expression can be anything from a single number or variable to a group of terms put together using operators like add or multiply.

When making algebraic expressions, it is important to remember the order of operations. To solve an expression, you must work in a certain order, usually starting with parentheses, then exponents, then multiplication or division, and finally addition or subtraction.

By adhering to this rule, one can easily solve complex equations without becoming confused. Algebraic expressions are thus immensely useful for quickly representing and calculating mathematical values.

Let's look at an example. Consider the equation 5x + 7. Here, the x is known as a variable and can represent any integer value; thus, this equation could also be written as 5(1) + 7 = 12 or 5(-3) + 7 = -8, and so on. In this case, the parentheses show that 5 should be multiplied by 1 (or -3), and then 7 should be added, giving a total of 12 (or -8).

If you know how to solve algebraic expressions, it's easy to change equations to get what you want. An example would be solving for x in the expression 5x + 7 = 12. By taking 7 away from both sides of the equation, we can easily figure out what x is, giving us the answer 5x = 5. Dividing both sides by 5 yields x = 1; thus, the solution to this expression is x = 1.

As you can see, algebraic expressions are a shorthand way of representing equations and calculations. They can save you a lot of time because you can write a bunch of calculations in one expression. Using the order of operations, we can solve these expressions without getting confused and get the right answer quickly.

How to read Algebraic Expressions

Understanding algebraic expressions and equations is a vital piece of mathematics. Every expression comprises terms, separated by either addition (+) or subtraction (-) signs.

The first step in solving more complicated algebra problems is to learn how to recognize and write basic expressions. From seemingly simple operations like "2x + 5y" to algebraic formulas that define the circumference of a circle, knowing how to combine terms with a combination of these operators is an important part of math knowledge.

Getting good at working with expressions can help you understand more advanced math, which can open up new ways to study geometry and other subjects.

A good example of an algebraic expression is the equation for calculating the area of a rectangle. The formula is A=LxW, which stands for "area equals length times width." In this expression, the letter L represents the rectangle's length, while W represents its width. By multiplying these two terms together, one can arrive at the answer to the problem: the area of the rectangle.

One of the most important aspects of algebraic expressions is learning how to simplify them. This requires knowledge of various algebraic operators, such as addition, subtraction, multiplication, and division. By manipulating these operators in a specific order (known as the "order of operations"), one can reduce equations to their simplest form.

This can be very helpful when working with complicated expressions with multiple variables, because simplifying the expression can help you see how the different terms relate to each other. Additionally, it can often make solving for a particular variable much easier.

What is the Order of Operations?

The order of operations, also known as the standard order of operations, is an important concept to understand in mathematics. It specifies the order in which operations are done when evaluating expressions, so that a different answer can be found if an expression isn't evaluated correctly.

Generally, most mathematicians refer to the acronym PEMDAS (Parenthesis, Exponents, Multiplication and Division from left to right within parentheses only, Addition and Subtraction from left to right) when following the rules for this order.

For example, if you were evaluating the expression 2 + 3 x 7 =, according to PEMDAS, you would start with multiplication (3 x 7), then addition (2 + 21), resulting in 23 as your answer. Understanding this system gives us a reliable method for correctly solving complex mathematical equations with accuracy and assurance.

Using the order of operations can also help you solve equations with more than one step without getting confused or making mistakes. If the order is not followed, it can result in a different answer than intended. This concept is important for both students of mathematics and professional mathematicians alike, as it ensures accuracy when completing calculations.

It is important to remember that all operations should be done from left to right. This includes addition, subtraction, multiplication, division, exponentiation, and grouping symbols like parentheses. 

Additionally, the order of operations should be followed closely when working with fractions and decimals, as these can be more complicated to solve than whole numbers.

Using Parentheses

It's important to know how to use parentheses correctly in math equations if you want to understand and do math. When parentheses are used correctly, they can be used to group terms that come before, after, or both before and after other terms within an equation.

This lets you change the order in which operations are done. Operations that are inside parentheses must be done first.

When doing math, using parentheses incorrectly can have a big effect on how an equation works out in the end, so it's important to get used to using them.

Get expert help with algebra today

Algebra can be a tricky subject and is often overlooked when it comes to math fundamentals. By taking the time to explore algebraic principles, you’ll be able to better understand how to apply them in everyday life.

Your child can learn the math skills they need to do well in the future with the help of an experienced tutor. Learner has a large number of experienced mathematicians who want to help students learn algebra and other math topics. 

With their help, it's easy to get a better grasp of the basics and try out more advanced ideas.

Contact us today to get started on improving your mathematics skill set!

About the author:

Mike developed his passion for education as a math instructor at Penn State University. He expanded his educational experience launching and running an Executive Education business - training over 100,000 students per year. As the CEO of Learner, Mike focuses on accelerating learning and unleashing the potential of students. 

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