Variables

Background

It's one thing to figure things out when we know what all the numbers are that are involved, say like 1 + 2 = 3. But what if we don't know what all the numbers are? Like 1 + "something" = 3?

Question

What is a variable? What is a constant?

Answer

A variable is a place holder - it tells us that a number (or a whole bunch of numbers) can go into that spot.

A constant is a number that doesn't change. Any stated number is a constant. 

Analysis

Up to this point, when entries have gone over different kinds of numbers, we've known what those numbers are. There are entries that show how to work with these different kinds of numbers: how to deal with addition between counting numbers, for instance, or exponential expressions using integers. But what if we don't know what some of the numbers are? What do we do?

What we can do is to set up a place holder for the numbers we don't know. We can do that using a letter symbolizing that number. For instance, if I don't know what 1 + 2 equals, I can write this:

1 + 2 = x

We can figure out that 1 + 2 = 3, and so we can say that x = 3.

But what if we know the 1 and the 3 but don't know the 2?

1 + x = 3

We can look at this and figure out that x = 2.

What if all we know is that we want two unknown numbers to add up to 3?

x + y = 3

Then x and y could be all sorts of pairs of numbers. x can be 2 and y = 1. x can be 1 and y = 2. In fact, there is an infinite number of pairs we can work out for this - we'll do that in a later entry.

And so a variable is a symbol that tells us that a number (or numbers) goes in there and we don't know what it is (yet). 

A constant is a stated number, such as 3, 0, and -34. 

While any letter or symbol can be used to indicate a place holder, there are some variables that are more common:

x is probably the most used variable of all. It's commonly the "default" variable - or in other words, if you want to indicate a variable and you don't have a variable that makes more sense, x is the one often used.

y is another commonly used variable and often used along with x.

n is a common variable when looking to talk about the nth term

t is a commonly used when solving problems involving time

d is a commonly used when solving for distance or displacement

v is commonly used when solving for velocity

a is commonly used when solving for acceleration

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:

• Counting/Natural Numbers
• Whole Numbers
• Integers
• Rational Numbers
• Real Numbers
• Complex Numbers

Where might we go?

Operations with different kinds of numbers:

• Addition, Subtraction, and Variables
• Multiplication, Division, and Variables
• Exponentials and Variables

Relations:

• Inequality

Graphing:

• X, Y Axes