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Lesson 3: Parts of algebraic expressions

# What is a variable?

Variables in math are symbols, often letters, that represent different values in various situations. They help us understand and solve problems with changing values. For example, when calculating total earnings at a job with an hourly wage plus tips, a variable can represent the fluctuating tips, making it easier to determine total income. Created by Sal Khan.

## Want to join the conversation?

• Can you use a ! for a variable? • Where did they come up with the name variable? •   If something varies, it changes from time to time. A variable is so named because it is capable of changing, as opposed to a numerical value, which must remain constant. Let me explain.

x could be anything. 1, 5, 273, 50 trillion--anything. Thus, it can vary in its actual value. This potential variability gives it the name variable. In contrast, the number 5 cannot change its value. It always will be 5. If it held a value of something other than 5, it simply wouldn't be 5. In this way, its value is constant. Hence, it is named a constant.
• How do you graph functions? •  you need the table of points or the coordinates themselves. make the x and y axes on a piece of graph paper. You need an equation to plug in numbers for x and y variables too
• I know that x and y are the most common variables, but are you allowed to use other variables to? Like O?
Wondering,
Allie • Yes. At , Sal uses "Tips" as the variable. At , he uses T to represent time.
• So, the only reason we use lowercase letters for variables is to keep things simple? So that means we can still use words, but letters is easier, right? • and what is tips
what is a variable
why do we use them
who created them • In this case, tips are the sum of money given to someone as a reward for a service. For exemple: give a tip for a good waiter.
Now, a variable can be anything, it depends of the statement. In Math, when you make a statement, then it can be false or true. But, if you put a variable in a statement, so the proposition can be false and true either for different values. Therefore, a variable works how a question. For exemple:
x + 2 = 4 . I have a statement and x is a variable because it can be any real number, but in truth it is a question: what numbers i can put in place the x and the results will be true? The answer how you know is 2. More one: y - 5 = 2 + x. Now, you have 2 variables and several responses. Thats why we use them: to work when we dont know the answer yet. In a function, for exemple, we have two variables: one is independent and other is dependent for the first one which means that when you change intentionally the independent then the dependent changes too. The speed is a exemple: if you have a constant speed, then the distance is the dependent variable and the time is the independent variable. How much more time pass, the distance you traveled increase in a same speed.
François Viète introduced at the end of 16th century the idea of representing known and unknown numbers by letters, nowadays called variables, and of computing with them as if they were numbers, in order to obtain, at the end, the result by a simple replacement. François Viète's convention was to use consonants for known values and vowels for unknowns.
In 1637, René Descartes "invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c". Contrarily to Viète's convention, Descartes' is still commonly in use. I hope to have could help you. Good luck!
• Why are x and y the most common variables? • René Descartes used letters from the end of the alphabet as variables, and letters from the beginning of the alphabet as constants. In particular, he used x for an independent variable and y for the dependent variable, the letters we use for the standard coordinates of the plane, along with z.
• Are variables hard and do they get harder in every grade you go in? • Variables are hard at first. Variables themselves get easier to use the more you use them, as with any concept. Math classes tend to get harder because they will expect you to use more variables in different ways. Yet the harder the math you do, the easier it becomes to use variables, and other ideas, to solve problems in your life. For example, what score do you need on your next test to get an A? This is a question that is much easier to answer using variables than without them.  • 