What are Variables? | An Intro to Variables

Welcome to Math with Mr. J. In this video, I'm going to go through an introduction to variables. We'll go through what a variable is and then some different situations where we will use variables. Now simply put, a variable is a symbol, usually a letter, used to represent a number. Variables can represent one specific number or a variable can represent a number that changes, a number that varies. Let's jump into number one, where let's picture a group of friends going to the movies. They all plan on buying some snacks and their ticket. So they'll each have the cost of snacks plus a $10 movie ticket. We can figure out how much each person will have to pay using this expression right here. We have a fill-in-the-blank box for the cost of snacks plus $10 for the movie ticket. Now again, the cost of snacks will go in the fill-in-the-blank box since that cost will change or vary depending on the person. So if someone spent $5 on snacks, we would put $5 in that box. Now you've probably seen something like this before where we have a box, a circle, or something where we need to fill in a missing number. And you'll notice for number two, we have a fill-in-the-blank box as well. Now instead of using boxes that we need to fill in, in algebra we use letters. For example, we can use a letter here to represent the cost of snacks. Let's use x. So x plus 10. x is a very common letter used as a variable. But keep in mind, we can use any letter for a variable. So the expression right here, x plus 10, we can use this to figure out the total cost for anyone going to the movies. Let's say someone buys $8 worth of snacks. So x equals 8. Well, we can plug in 8 for x then. So we have 8 plus 10. And that gives us a total of 18. So that person's total cost is $18. $8 for the snacks plus $10 for the movie ticket. Or maybe someone buys $15 worth of snacks. We'd plug in 15 for x. Or if someone didn't buy any snacks at all, we would plug in 0 for x. So our variable here can change. It can vary. It all depends on how much someone spends on snacks. Now to go off of this, let's move on to number two. We have a similar situation, but it's more specific. Olivia buys snacks plus a $10 movie ticket. The total cost is $23. Here we have more information. And our variable represents one specific unknown number. It represents how much Olivia spent on snacks. This number can't vary because we know the total that Olivia spent. We have the snacks plus the $10 ticket equals $23. Notice we have that blank box again here. But we don't want to use this. We want to use a variable. And we'll stick with x. So we have x plus 10 equals 23. Here we have an equation rather than just an expression like number one. We have an equal sign and enough information to figure out what x equals. So what plus 10 equals 23? Well, 13. x equals 13 here. That means Olivia spent $13 on snacks. So our variable represents one specific number in this situation. For example, could x equal 5 here, 11, 15, 20, or any other number besides 13? No, x has to equal 13. It's the only number that will work here. So right now we should know that a variable is a symbol, usually a letter used to represent a number. Now depending on the situation, a variable can represent one specific number, like number two, or a number that can change, like number one. Let's move on to a few more examples. Taking a look at number three now, we have Jackson rides his bike five miles each day. Let's write an expression using a variable that we can use to find the number of miles he rides depending on the number of days he rides. So we need five miles times the number of days he rides. Let's use d for our variable here to represent the number of days. So five times d, and we're going to write this as 5d. Now keep in mind, when a number is written directly next to a variable, that means multiplication. So again, whenever we see a number and a variable written next to each other, it's multiplication. So we can write this as 5d. Now we can use this expression to figure out how many miles Jackson rides for a certain number of days, and the number of days can vary. We can figure out how many miles he rides in five days, 12 days, 25 days, or whatever the case may be. Let's say we want to figure out how many miles Jackson rides in 12 days. So d equals 12. We can plug in 12 for d and go from there. So 5 times 12. So when we plug in 12 here for d, do not put a number next to a number. So 5 next to 12. We can only put a number next to a letter. We can't do a number next to a number. So we need something to show multiplication here. I used a dot to show multiplication and separate those numbers. Now 5 times 12 gives us 60. So Jackson will ride 60 miles in 12 days. Again, for this situation, the variable can vary. It can change depending on the number of days. Let's move on to number four where we have how many days will it take him to reach 50 miles. Here our variable will represent one specific number. 5 times a certain number of days equals 50 miles. So what does d equal here? So we have 5d equals 50. So 5 times what equals 50? Well, d is going to equal 10 here. 10 days. So it will take Jackson 10 days to reach 50 miles. Can d equal any other number? No, only 10 in this situation. Lastly, let's move on to number 5 where we have an area problem. I included this to show that variables are used within formulas and area is something we are already familiar with. We have a rectangle here and the formula for the area of a rectangle is area equals length times width. Let's rewrite this formula using variables. So area equals length times width. I used a cursive L here for length, by the way, so it wouldn't look like a one. Now when using a formula like this, we may already know what some of the variables will be and others we may need to figure out. Now the area, length, and width can all vary depending on the rectangle. But here we have a specific rectangle and measurements. So our variables represent specific numbers. Here we know the length and width. We'll use 8 feet for the length and 4 feet for the width. So let's plug these in here. We have area equals 8 feet times 4 feet. The area is unknown here, so we need to figure out what a equals. And this is going to be one specific number. Now 8 times 4 gives us 32. So area equals 32. And this is square feet. So area equals 32 square feet. And that's it. That's our area for number 5. So there you have it. There's an introduction to variables. Just remember, variables are symbols, usually letters used to represent numbers. And depending on the situation, variables can represent specific numbers or numbers that can vary. I hope that helped. Thanks so much for watching. Until next time, peace.