"If there are four equations and only three variables, and no one of the equations is derivable from the others by algebraic manipulation than there is another variable missing." -Talcott Parsons
Constant. Equation. Exponent. Expression. Factor. Operation. Term. Variable. Operations. Division. Multiplication.
Whether you are still in school or not, the previously mentioned words remind individuals of a famous academic discipline that either made you cringe or rejoice.
Which subject are we talking about?
Algebra. One of the most notorious school subjects on the face of the planet, algebra is a layered discipline that has much to offer and analyse. In today's article, we will examine what variables are and how they are used in algebraic expressions.
Ready for a wild ride through the world of algebra?
What is a Variable?
Since mathematics comes from the Greek word máthēma meaning "knowledge, study, and learning" and encompasses the topics of quantity, structure, space, and change, that each has their own subtopics, there are many definitions things to consider.
For example, algebra is a vast subject, yet it can be understood as the study of mathematical symbols and the rules for changing these symbols. It is often placed by educators and mathematicians into the structure category of mathematics and has many regulations that make it a unique branch of maths.
Without further ado, we will consider one of the algebra's most essential aspects: variables. Familiarising yourself with variables is necessary before solving any algebraic equation. Also, to effectively translate and evaluate algebraic expressions, knowledge of variables is a must.
But what exactly is a variable?
A variable can be defined as a letter that is used to replace a number. The most commonly used variables are x, y, z, a, b, c, m, and n. Other letters may sometimes be used as well; however, the only exception is for the letters i and e since they have unique values in algebra and are typically not used as variables. Also, the letter o is rarely used since many people might mistake it for a 0.
It is essential to mention that variables are used to change verbal expressions into algebraic expressions: equations that are made up of letters which stand for numbers.
There are specific terms that help all translate words into letters and numbers; they change depending on if it is, for addition, subtraction, multiplication, and division. The following are variable terms divided into sections:
- Addition: sum, greater than increase.
- Subtraction: minus, less than decrease.
- Multiplication: times, product, multiplied by.
- Division: halve, divided by, ratio.
When the previously mentioned words are seen in a mathematics problem, they are closely linked with variables. Also, to effectively complete or evaluate an algebraic expression, inserting the value of each variable needs to be done.
The PEMDAS order of operation needs to be respected and followed to avoid any confusion on how to approach an equation.
There is no denying it, understanding algebra is no piece of cake, yet after reading this subheading, you have enlightened as to what is a variable. Keep reading to analyse specific examples of algebraic expressions with variables.
Why Isn't the Multiplication Sign Used for a Variable?
In the previous subheading, we learnt that variables could practically be any symbol; from letters to other characters, everything goes. Nevertheless, it is essential to state that one sign is always absent from variables.
Which sign is that?
The multiplication symbol. The variable of x is used quite often for variables; therefore, to use the multiplication sign could be an issue and cause unnecessary confusion for the student trying to tackle the algebraic expression.
For example, if I want to write "2 times x" and use a multiplication symbol it would be "2 x x", and some could think when reading the problem that the expression could be "two times times something." Therefore, since this is exceptionally baffling for all parties involved (student, teacher, exam corrector, etc.), other terms or symbols to represent multiplication are used.
Many mathematicians may use a dot to replace the multiplication sign, and others use written terms such as times, multiplied by, and product.
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Examples of Algebraic Expressions or Equations Using a Variable
Explaining distinct characteristics of algebra can be done verbally or by reading the rules and definitions that have been provided; however, it is essential to state that there is nothing better than examples when analysing any mathematical subject, especially for those who struggle to comprehend from the outset.
Therefore, without further ado, we will examine a brilliant algebraic expression example that can originally be found on Khan Academy's website or app and another one located on another trusted online resource.
You are working at a restaurant in London's West End, making £10 an hour; however, on top of this, you also make plenty of tips. Therefore, the equation can be as follows:
10 + t = hourly wage
Since the number of tips changes from hour to hour, a variable is necessary for this algebraic expression and t is our variable. Also, we used the letter t to help us remember that it stands for tips.
For example, one hour the tips may equal £30, so the formula would be 10 + 30 to find the hourly wage, which would be £40. However, due to an impressive sale at the restaurant next door, your tips dramatically decrease the next hour, and you only make £5; your total wage would be 10 + 5 = £15.
This first example of variables is quite simple since there is only one; nevertheless, it is easier to start this way to get a general idea. We could have used another symbol or letter as the variable; however, it is better to use a variable that will help your memory and not always cause you to question what you are varying.
We all go to the grocery store on a regular basis to buy necessary food items. Did you know that algebra can be used to calculate daily expenses?
For example, you make a grocery list and recognise that you need two dozen eggs priced at £6, three loaves of bread (each roll costs £3), and five bottles of juice (each bottle costs £2). How much quid do you need to take to the grocery store to purchase all the necessary items?
Using algebra will help us solve the problem more efficiently. The prices are:
- a = Price of two dozen eggs = £6
- b = Price of one bread = £3
- c = Price of one bottle of juice= £2
Therefore, the expression to find the answer would be a +3b +5c = total money needed for expenses.
Where are the variables?
In this equation, a, b, and c are the variables since the prices of food can increase or decrease without previous notice.
All aspects have to be put into the right place, and it should look like this: £6 +3(£3) +5(£2) = £6 +£9 +£10 = £25.
Tips to Successfully Ace Algebra
Successfully acing algebra to become a pro will definitely have its ups and downs. There will be times when you are completely discouraged and want to give up; however, on the other hand, during some moments, you will understand the subject matter and want to do more.
Even though each student is unique with his or her distinctive learning curbs, there are helpful tips that can aid anyone in acquiring the rules, expressions, and equations of algebra like a boss!
The following are specific strategies for success in mastering algebra:
- Master Numeracy Skills: since algebra is complex, mastering equations and effectively translating expressions requires a fundamental knowledge of numeric skills like addition and multiplication; if you've struggled with this since primary school, it's time to focus your attention on getting better. When numeracy skills are healthy, you won't have as many struggles with algebra.
- Memorise Algebraic Formulas: when coming across new formulas, it is essential to learn them by heart to increase understanding and general knowledge. How to memorise? Write them down and practise saying them out loud.
- Do Your Homework: we cannot stress the importance of doing your homework enough. We know that after a long day of classes the last time most students want to do is their homework; watching Netflix on the couch sounds so much more appealing! Nevertheless, by completing homework assignments, you build a stronger foundation for learning more complex algebraic formulas later on in life.
- Tutor Another Classmate: while the idea of providing academic assistance to other classmates may seem slightly bizarre when struggling through algebra, it helps build confidence and cements the concepts that you do comprehend; you're not failing in everything am I right?
By applying the four previously mentioned pieces of advice when exploring the intricate world of algebra, students are setting themselves to finally comprehending algebraic expressions; who knows; you might even fall in love with maths all over again!