Quick Homework Help

Enjoy 3,000 videos just like this one.

# ACT Pre-Algebra

Star this video

I'm planning a party after a football game. Now I know the players are going to be really, really hungry. So I figured out I need about two pies for every three players. But here is the thing there're 36 players coming, so how many pies of pizzas do I need? Well in this episode we're going to talk about propositions which can help us solve this. We're also going to talk about the other top pre-algebra concepts that you'll see on the ACT.

Okay let's take a look at proportions I've seen ACT tests where proportions will show three or four or sometimes even five times so I want you to feel really good about proportions. What are proportions? Well, proportions are an equation that states that two ratios are equal. This is kind of like a fraction and then the reduced form of the fraction and you know they're equivalent to each other, for example four eighths is the same as one half right 'cause if you reduced four eighths you'd end up with a half, the cool thing about proportion is you can cross multiply and they should be equal to each other. So four times two for example that's eight and so is eight times one and you can use this to solve ACT problems.

Let's go to the pizza problem and then we'll look at a real ACT problem testing proportions, okay if you'll remember I need two pizzas for every three football players coming to my party, so how many pizzas do I need for thirty six football players pay attention this really does help you in real life. So two pizzas for every three football players okay so we can write that out as a fraction or is it really a ratio, really same thing here, so two 'to' three right or two over three for every two pizzas well every two pizzas are going to feed three people okay and we know that we need an equivalent fraction just bigger for how many people we're going to feed, sorry for how many pizzas we're going to need to feed 36 people. Okay so if you need two pizzas for every three football players how many, we don't know so we'll call that X, do you need for 36 people so you see how we again, just have two equivalent fractions now like I said we can have two equivalent fractions. Now like I said we can cross multiply to actually solve for X so we have two times 36 equals three X let me write that down, two times 36 is equal to three X okay so two times 36 that's 72 so 72 equal to three X we're just going to divide both sides by three right, great so X is going to be equal to 24 good. So now let's take a look at this if I need two pizzas for every three football players I'm going to need 24 pizzas that's a lot of pizzas to feed 36 football players but now I know great.

Let's look at a real ACT problem testing proportions, Julie and Mike are on a carousel that rotates 30 degrees every five seconds. How many degrees will they rotate in a minute? Okay so we know we're going to have an equivalent ratio or an equivalent fraction here, we've got 30 degrees every five seconds, so 30 every five seconds and that's going to be equivalent to however many degrees they rotate in a minute right this is just going to be a simplified fraction. So how many degrees will they rotate in a minute well X degrees make sure though you've got your 60 seconds for a minute because when you do proportions your equivalent parts have to be in the same units. Okay now we can just go ahead and cross multiply so we've got 30 times 60 equals five X so 30 times 60, 1800 equals five X and therefore if you divide both sides by five to isolate your variable X is going to be equal to 360. Okay so we see if the carousal rotates 30 degrees every five seconds in an entire minute they're rotating an entire 360 degrees. And C is the correct answer choice here.

Okay let's move on to another concept taking a look at average problems these will always show up on the ACT and usually you'll see them two or three or sometimes even four times. The formula hopefully you're familiar with already but let's just go over it, sum of terms divided by the number of terms meaning adding up all the different parts you have that you want to take the average of and divided by how many different things there are. We're going to look at two example average problems because there are two types of average problems that show up, a really basic average problem and then a slightly more complicated one.

First let's look at the easier one, Tom scored an 89, 72, 54, 50, 80 and 69 on six high school biology tests. Approximately what's Tom average in the class? Hopefully this looks really familiar to you so we've got a bunch of different terms and we know that the formula is that you add up all the terms and divide by how many you have to find the average, let's do that. So we've got 89 plus 72 plus 54 plus 50 gosh this is a lot of tests this guy took, plus 80 plus 69 did I get that right, yes. So we've got everything added up divided by how many we have so let's divide by six, write six different tests that's going to equal out average which is X, okay. So let's go ahead and pick up our calculators because this is a lot to add, so we have got 89 plus 72 plus 54 plus 50, hopefully you're doing this along with me, plus 80, plus 69 okay that's equal to 414 so 414 over six is going to be our average so let's do that 414 divided by six and this guy's average is a 69, great so answer choice B.

Now let's take a look at a slightly more difficult average problem that you'll see, be on the lookout for this you will definitely see this problem or this problem type and you can totally nail it if you know what to do. Tom scored an 89, a 72, 54, 50, 80 and 69 same as before and six high school biology tests tomorrow he's going to take a seventh biology test if Tom needs an average of 65 to pass the class what's the lowest possible score he can get on the test and still pass the class. Okay so let's think about this for a second, we've got the scores for six things right, but we're missing a score we need the score for the seventh, this is like I said there is something you're going to see the ACT loves to test average problems where what you're missing is actually something at the top of your equation remember what our equation is everything added up divided by how many you have that gives you your average right. Here we know what we want the average to be we want him to get a 65 we also know how many tests there are, there are seven let's write that down so we've got our typical formula everything added up is going to go here divided by how many terms okay I mean there are going to be seven, seven total tests and we know his average needs to be a 65 so you see how interesting right, we actually have two of the parts but we're going to miss, we're missing part of the top. But we've got the rest of the test we know he got an 89 plus a 72 plus that 54 plus that what else 50 plus the 80 plus the 69, okay guys plus X.

Alright so just watch up for this trail over here, this is our whole top so you see how we're missing that seventh right but we know everything else added plus that seventh test whatever it is I'm calling X divided by seven the amount we have it can give you 65. A lot of students look at this and they think, "Oh my gosh what do I do", don't worry about this all you're going to do is treat it like you would a typical algebra problem remember if you have something going on in the bottom you have division and you have an equal sign with something on the other side you can multiply the seven to the other side you remember this if you think about algebra if I had multiplied both sides by the same thing which is allowed, multiply both sides by seven I can cross of my sevens here and this becomes 65 times seven.

Okay so now this whole chunk here is going to be equal to 65 times seven let me just figure out what 65 times seven which will make things a little bit clearer here. So 65 times seven is 455, okay so this whole chunk over here is going to equal 455 I don't want to rewrite this whole chunk because remember on the last problem we added this all up and they're equal to 414 right we did that for the last problem. So now we know 414 plus X is equal to 455 okay so you see what we did we just added up all the test scores for leaving our X our missing score, but it just turned into a really straight forward algebra problem all of this you move this to the other side so 414 plus X is 455 now we can just subtract to figure out what is, X is going to be 455 minus 414 that is 414 okay, let's use our calculators for that minus 414 and wow a 41. So lucky Tom just a pass if that's all he wants to do all he needs is a 41 on this test great and that looks like answer choice A.

Now i wanted to do it this way so you guys see how I set this equation but remember our pacing strategies and our back door strategies that we talked about keep in mind when you do these problems sometimes there's a shorter way to do it, you still need to know basically how the equation is going to be set up but remember you can also work backwards from the answer choices in a problem like this. So I wanted to do it straight through so you can see what it looks but another thing you could have done is once you realize it was everything added up divided by the seven gives you that 65 that you need, you could have played in through from the answer choices and said okay is X 41 there's this all added up you know with the 41 here divided by seven give you that 65 and so on and picking from the answers.

So it's just a cool thing to remember sometimes or actually pretty often there are a couple of different ways to solve a problem which is a really powerful feeling to have kind of a bunch of tools that you can pull out and use on a problem. Great so that's it for the top pre-algebra problems that you're going to see repeatedly on the ACT and I want you to feel great about these because pre-algebra shows up 14 times on the math that's almost a quarter, 60 questions on the math 14 out of the 60 questions are going to be pre-algebra. If you need some more practice then really make sure to head to your bonus materials and then with some practice I think you're going to do a great job.