Input & output tables: identifying the rule
About this video
A table has inputs 27, 15 and 6 with outputs 9, 5 and 2. The video tests each choice (subtract 18, subtract 9, divide by 3, divide by 5) on every row and shows that only divide by 3 works for all of them.
You'll be able to
- test a rule on every row of an input-output table.
- rule out a rule that fails for even one row.
- identify a division rule from a table.
Key words
- input
- The number you put into a rule.
- output
- The number that comes out after you use the rule.
- rule
- One step that must work for every input to give its output.
Transcript
- [Instructor] The table shows the relationship between input and output numbers. So they're saying that when I put 27 in, I guess you could say to this table, or we're going to be doing something with it, so this is a number we're gonna do something with. And after we do that something, we output nine, interesting, we input 15, we output five, when we input six, we output two.
Which rule can we use to find the output when given the input? Pause this video and have a go at that. All right, now let's work through this right over here. There's a bunch of ways we could think about it, but the same rule's gotta work for all of these inputs and outputs.
So this first one says we subtract 18, so when we look at this first choice, if we take 27, and if we were to subtract 18, it does indeed look like that, well, that would be equal to nine, so that one works. But if I took 15 and I were to subtract 18, I definitely don't get five.
So I don't even have to go to that third row here, I can rule out choice A, so let me rule that one out. Let's see subtracting nine. Well, that one doesn't work even on the first one right over here, if I do 27 minus nine, it doesn't equal nine, it equals 18. It actually doesn't work for any of these, so we could rule that one out as well.
Divide by three, this one's interesting. 27 divided by three is equal to nine. 15 divided by three is equal to five, it's looking good. Six divided by three is equal to two, yep. You give me any input, I divide by three, it looks like that's the output you're going to get.
So I like this choice. Five, this last one's not going to work, but we can verify that, 27 divided by five is definitely not nine, 15 divided by five is definitely not five, and six divided by five is definitely not two, so that one's definitely not right.
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