Addition, Subtraction, and Variables

Background

We've covered what a variable is (it's a place holder for a number). So now let's talk about how to add them.

Question

Evaluate:

1. a + b
2. a + a
3. a - b
4. a - a

Answer

1. a + b = a + b
2. a + a = 2a
3. a - b = a - b
4. a - a = 0 

Analysis


When working with variables, we have to keep in mind that each of the variables could be a different number. For instance, in Question 1, a might equal 5 and b might equal 3. And so we can't add the two together - we have to notate that we have two separate variables. And so with the expression:

a + b

we can't do anything further with it. It is in its simplest form.

Question 2

Here we have two of the same variable, a. The variable a could be the number 6 or 3.5 or a fraction - it could be anything. Let's say for the moment it's the number 6:

a = 6

which means

a + a = 6 + 6 = 12

This is the same as doing this multiplication:

6 x 2 = 12

and so we can say this:

a + a = 2a

and to check:

6 + 6 = 2 x 6 = 12

Question 3

Just like we couldn't add a and b together in question 1, so too we can't combine them in this subtraction problem. Therefore the only thing we can say is:

a - b

Question 4

We can combine the two terms together. If we take a number (such as 6) and subtract that same number, we get 0. And so:

a - a = 0

Vocabulary used:

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Where might you have come from?

Fact-orials Index

Operations:

• Addition
• Subtraction
• Multiplication
• Division
• Variables

Relations:

• Inverse Relations

Where might we go?

Operations with Different Kinds of Numbers:

• Addition, Subtraction, and Variables - Practice Problems
• Multiplication, Division, and Variables