What you need to know

Things to remember:

  • When combing variables, we are adding, subtracting, dividing, and multiplying as usual, we just have to put our numbers in first.

Before we start, what is a variable? A variable is something that varies, it changes. So, “variable” is just a fancy word for something that changes. Here, we are going to look at combining two things that change, and how they affect each other.

x+ y = 5

Here, our variables are x and y, they can change. How do I know they can change, you ask? Well, let’s think about what it is saying. This is equation is telling us that “something plus something equals 5”. Well, that’s easy, 1+4=5.

x=1         y=4

1 + 4 = 5

But wait, 2+3=5 as well.

x=2         y=3

2 + 3 = 5

x and y are variables, they can change. There isn’t just one answer: Notice also how as x gets bigger, y gets smaller. Does this always happen? What about if we’re subtracting?

x - y = 3

What is this telling us this time? “Something minus something equals 3.” Well, 7-4=3.

x=7         y=4

7 - 4 = 3

But wait, 11-8=3 as well.

x=11       y=8

11 - 8 = 3

So, our x and y are changing, but how does one affect the other? Notice how as x gets bigger, so does the y. Why do you think that is? Think about what subtraction means.

x\times y = 36

What is this telling us this time? “Something multiply something equals 36.” Well, 3\times12=36.

x=3         y=12

3\times12 = 36

But wait, 2\times18=36 as well.

x=2         y=18

2\times18 = 36

So, our x and y are changing, but how does one affect the other? Notice how as one gets bigger, the other gets smaller. Why do you think that is?

Let’s look at division now.

x\div y = 4

What is this telling us this time? “Something divided by something equals 4.” Well, 20\div5 =4.

x=20       y=5

20\div5 =4

But wait, 24\div6 =4 as well.

x=24       y=6

24\div6 = 4

So, our x and y are changing, but how does one affect the other? Notice how as x gets bigger, y gets smaller.

Example Questions

Question 1: If x+y=6 what are some values of x and y? How do the numbers affect each other?

Answer

x              0          1          2          3          4          5          6

y              6          5          4          3          2          1          0

 

As one gets bigger, the other gets smaller

Question 2: If x\div y=6 what are some values of x and y? How do the numbers affect each other?

Answer

x              6          12        18        24        36        42        48

y              1          2          3          4          5          6          7

 

As x gets bigger, so does y[/latex