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Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

00:57

Amy J.

The model $L=4 S$ gives the total number of legs that $S$ sheep have. Using this model, we find that 12 sheep have $L=$ __________ legs.

01:56

Taylor S.

Suppose gas costs $\$ 3.50$ a gallon. We make a model for the cost $C$ of buying $x$ gallons of gas by writing the formula $C=$ _________.

0:00

Kyle I.

Using Models Use the model given to answer the questions about the object or process being modeled. The distance $d$ (in mi) driven by a car traveling at a speed of $v$ miles per hour for $t$ hours is given by $$d=v t$$ If the car is driven at 70 milh for 3.5 $\mathrm{h}$ , how far has it traveled?

01:04

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So in this section we're gonna be talking about classifying real numbers. So it's really kind of just a lot of vocabulary here. So real numbers are all the numbers that you've ever dealt with so far. Um, it's whole numbers, fractions. It's decibels. It's all of those. Well, real numbers can get broken up into two different types of numbers, as you can see in the chart that I have here. So first thing, every real number will either be considered a rational number or an irrational number. So as I put for a definition here for rational numbers, it's any number that could be written as a fraction. So the best way to think about it any fraction is a fraction because it is a fraction. So it fits the definition. Any positive, negative whole numbers of fraction or I'm sorry, irrational number, because it could be written as a fraction. And any decimal values that end or repeat are all set to. So some examples of some rational numbers would be like three fours, because it already is a fraction. So it kind of fits the definition because it could be written as a fraction because this one, Um, negative seven. This would be also an example of rational number, because to write as a fraction, we would just simply put it over one. Um, we could have 0.8 as a rational number because 0.8 would be the same thing is eight temps. So this would be fine and the same thing with the decimal like 0.3 repeating and they repeated decimal could be written as a fraction. For example, 0.3 repeating is one third, so these would be examples of rational numbers. Now let's go. The irrational numbers thes air the decimals that never repeat or end. So the most infamous irrational number is pie. Because, remember, pi is a decimal value that goes on forever. It doesn't repeat, and it's never going to end. The other most common examples of irrational numbers are when you try to take the square root of a number that is not a perfect square. So, for example, like the square with a five five is not a perfect square, and what you find is when you try and take, the square root of five is going to be a decimal value that goes on forever and doesn't repeat as opposed Teoh. A rational number would be like to square the four because the square of the four is just equal to two and two is a rational number. Now rational numbers can get broken down into sub categories, the first being integers So integers are any positive and negative whole numbers. And I realized that spelt numbers wrong here. So I'm just gonna cross this off and put numbers in here correctly. There we go. So essentially, if you wanna be thinking about integers, think about what you would set up for your basic general number line. You would always start with zero in the middle. Then you would go 123 etcetera to the right and you go negative one negative to negative three, etcetera. To your left. These are all examples of integers. Now the King doesn't remember is every integer is a rational number because we can write all these values as fractions. Now we can break up into Jersey even more into whole numbers, while whole numbers are just your positive integers, including zero. So essentially, if we thought about in terms of the number line we're going to get rid of all of the negative integers. We're going to start it zero and then we're gonna go 12 three, etcetera. So 456 and knowledge. So essentially the only difference between integers and whole numbers is whole numbers does not include the negative integers now wait of want to think about it is every whole number is an integer. All of these numbers would fit on the number line. And because every whole number is an integer that means every whole number is a rational number is well because we can write them as fractions. Now we can actually break down whole numbers, even fervor and one last category Natural numbers, which are also known as counting numbers and essentially what it is, is your positive integers. So it's almost like if we started a number line but just started at one. So we went 123 etcetera. Thes would be all you're counting numbers. The way I always like to remember it is think about If you were counting objects, you would start with one go 2 to 3, etcetera. Now, kind of like to charge says every natural numbers the whole number, So every natural numbers and integer and every number, every natural number is a rational number. So no, this it does move up so it will always fit in the category before. But it doesn't necessarily go the opposite way because there are rational numbers that are integers, for example, three fours and the next couple of examples. We'll talk about how we can actually go ahead and classify numbers into their categories.

Linear Functions

Solve Linear Inequalities

Functions

Systems of Equations and Inequalities

Graph Linear Functions

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