Ordered Pair: Definition & Examples

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Lesson Transcript
Instructor: Kimberlee Davison

Kim has a Ph.D. in Education and has taught math courses at four colleges, in addition to teaching math to K-12 students in a variety of settings.

An ordered pair is a simple way of keeping track of two numbers by writing them in a specific order. Learn about ordered pairs and how they are useful.

Definition & Example

An ordered pair such as (3,-1), is a shorthand way of writing two variables, such as x = 3 and y = -1. The order of the numbers in the pair is important: x always comes before y.

Example: Teeth Brushing and Dog Kisses

Let's take a look at an example. Pretend you want to study the relationship between the number of minutes you spend brushing your teeth each morning and the number of kisses your dog tries to give you. One day you brush your teeth for 2 minutes, and your dog gives you 5 kisses. The next day you brush for 1 minute, and your dog offers you 2 kisses. Then, on the third day, you totally forget to brush your teeth, and your dog offers you only 1 kiss. On the fourth day, you brush for 5 minutes, and your dog offers you 6 kisses.

Writing all that out verbally is a hassle. It also takes a lot of space. So, there are a few shortcuts. For example, you might put all your data (numbers) in a table. It would look like this:

The table looks nice when you have a lot of data; however, if you just want to talk about one day's data, then a table is a bit cumbersome. For example, maybe you just want to refer to the second day. On that day, you brushed for 1 minute and got 2 dog kisses. Instead of using the cumbersome chart, you can call the minutes of brushing x and the dog kisses y. Then you can simply say, x = 1 and y = 2. That is a little better, but it still takes more space and time to write than necessary.

Mathematicians have found an even shorter way to write it, like this: (1,2). This format is called an ordered pair because the order of the pair of numbers matters: x always comes before y. With our teeth brushing and dog kissing example, the four days of data can be represented as four ordered pairs: (2,5), (1,2), (0,1), and (5,6). With this method, our order takes the place of labeling. You know the first number is always x, so, you don't have to write x = 2.

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