In our last few videos we looked at simplifying expressions with addition and subtraction, multiplication and division parentheses, and even with exponents. But with all of our examples, we worked with whole numbers, or maybe a few integers, but we haven't seen any with decimals and fractions. So in this lesson we're going to put together all those skills that we learned in our last few lessons, and we're going to use examples that have decimals and fractions just to get a little practice with those. Here's our first example. Let's simplify this expression. It looks like there's a lot going on here and it kind of is. But as long as we follow the order of operations properly, we can do this problem with ease. So we have 7.1 being multiplied by something in parentheses. We have twelve minus nine in parentheses, and then we have a plus ten point 52. So let's take note on our order of operations chart. There we'll keep track of what steps we need to complete. We mentioned that we have multiplication, we have parentheses. Now keep in mind that even though there's some subtraction going on in those parentheses, we still count that as the parentheses step. Whatever goes on inside the parentheses is done during the parentheses step. It's not a separate step by itself. So we're going to count that as just parentheses. And then we also have addition. So where do we begin? Our first step is simplifying what's in the parentheses. So our twelve minus nine gives us three. Now we're going to bring down everything else that was written around it. We're just going to copy and paste it right on down. There we go. Now we have multiplication and addition left. Well, multiplication gets done before addition, so let's focus on that. And remember, we're looking at just the number that's to the left and right of the multiplication sign. So we're focusing just on the 7.1 times three. Now it's been a little while since we've multiplied with decimals. So let's use a little extra workspace to make sure that we don't make any mistakes. So we get 7.1 times three. Now remember, when you do the multiplication, you ignore the decimal point. We don't place that back in until the end. So three times one gives us three, three times seven, we have 21. Now we figure out where the decimal point goes. Since we only have one digit after the decimal point in our numbers that we started with, that means our answer has to have one digit after the decimal point. So we're going to place it right there. So now our answer is 21.3. Now we bring down everything else from that problem that we didn't complete yet. So we bring down the plus ten point 52. Now we have just the addition step left, but it is with decimals. And remember, with decimals we have to be careful with how we line up our digits. So we want to line up the digits so that the decimal points are right on top of each other. Everything should line up with the correct place value within the numbers. Once we line it up, we just add them. We get 31.82 and that's our final answer. So that whole big long expression that we started off with simplifies to just 31.82. Let's look at one more example. When you first look at a problem like this, it might seem a little intimidating and that's understandable, it's okay. But when we start looking at each piece of the problem, we'll see that it's not too bad. So first thing that we might notice is that we have some parentheses and inside the parentheses we have one minus two thirds. So we know that that will need to be done first because parentheses is our first step. And then the other thing that we have is an exponent. Notice that we have a two written outside of the parentheses. It's written a little bit smaller and a little bit higher than the rest of the problem. So we can recognize that it is an exponent. We can also call it a superscript when a number is written up higher than the rest of the numbers. Okay, so we know we need to start within the parentheses first, we need to do the one minus two thirds. Let's get a little workspace so that we can do that. So we have one minus two thirds. Now if you go back and recall how to do subtraction and addition when we have whole numbers and fractions all mixed up together, you can review that video. But one of the tricks that we learned is that when we have a whole number, it's helpful to write it over as a fraction using the same denominator as our other fraction. So one written as a fraction can be three thirds. That way it has the same denominator as our two thirds, which will make the subtraction a lot easier to work with. So when we subtract our numerators, three minus two will give us one. Keep the denominator the same, which is three. Final answer is one third. So now all that stuff in parentheses, now just becomes one third. Now notice I'm keeping the parentheses there. But that's just because I need to write that exponent. I need to bring that exponent down. And by keeping it in parentheses, it just helps me to see that the exponent is separate from the rest of the fraction. So that's just one of those tips to use, just to help keep your work nice and neat so that you don't get confused with which number is supposed to be where. Okay, so now we just have to perform our exponent step. And since our exponent is two, that means that we're going to multiply that one third by itself. We're going to multiply two of those together. So it'll be one third times one third and we can use our workspace to help us keep track of what we're doing. And when we're multiplying fractions, you just multiply the numerators together and multiply the denominators. So one times one will give us one up top. Three times three gives us nine at the bottom, which becomes one 9th. So all of that simplifies to just one 9th. So remember, when you see these expressions that have a lot going on with them, they might have lots of steps and it might look a little scary at first. Just take your time, figure out what types of operations you have to do and then use your order of operations to keep track of your steps.