Adding/Subtracting Decimals

Hey everyone, today we are going to be talking about how to add and subtract decimals. Make sure you write down everything you see on the screen that's not already in your notes. Your objective for today, I will be able to add and subtract rational numbers fluently, and specifically we're focusing on decimals. So let's review. Whenever we add numbers that have the same sign, we simply add them together and just keep the sign. So that means if we're adding negatives together, we add like normal and make our answer negatives. Same thing for positives. If we're adding with a different sign, such as a positive plus a negative, or a negative plus a positive, we just subtract the numbers, find their difference and take the sign of the bigger number. And then if we subtract, we just add the opposite. Also, anytime we add or subtract with decimals, we want to make sure we line up the decimals before we actually do any solving. So let's look at our steps. Okay, the first thing we want to do is figure out what integer rules we need to follow so we can set up the problem. Then we want to line up our decimals and then we'll simply solve. All right, so let's look at some addition examples. Okay, letter a, we have negative 9.1 plus 2.34. So I have a negative plus a positive. So what I want to do is find the difference between these numbers. So if I'm looking at 9.1 and 2.34, I'm just going to do like normal subtraction. So that would be 9.1 minus 2.3 four. Notice how I lined up the decimals right here. Now in this blank space, I'm going to put a zero. All right, so now I can not do zero minus four, so I borrow. And ten minus four is 6. Again, here I have to borrow. Ten minus three is 7. Bring down the decimal and 8 minus two is 6. Now I'm going to take the sign of the bigger number. So I'm just going to look at 9.1 and 2.34. So ignoring if it's positive or negative, if they were both positive, 9.1 would be bigger. So now that I know 9.1 is negative, I have to make my answer negative. So we would have a negative 6.76. All right, let her be. Negative 5.2 plus a negative 17.23. That's a negative. Plus a negative. So we're just going to add like normal and make our answer negative. So I have 17 .23 plus 5.2. Again, notice how I lined up my decimals. And I'm going to put a zero in this empty space. And if I'm adding negatives, my answer will be negative. So three plus zero is three, two plus two is four. Bring down the decimal. 7 plus 5 is 12. And one plus one is two. So our answer is negative. 22 .43. All right, let's look at some subtraction examples. So letter a we have 6.44 minus a negative 3.2. So anytime we have subtraction, we always add the opposite. Anytime there's a negative involved. We do not subtract with negative numbers. We add the opposite. So this is really 6.44 plus the positive 3.2. So that's easy. Now it's just 6.44 plus 3.2. So I'm just going to add those together. Again, notice how I'm lining up the decimals. And I'm going to fill in the empty space with a zero. Four plus zero is four. Four plus two is 6. Keep the decimal and 6 plus three is 9. So we just have a positive 9.64. Letter B, we have negative two minus 4.8. So again, we've got a negative number involved. We do not subtract with negative numbers. We add the opposite. So that would be negative two, plus, and this is a positive 4.8, the opposite of that would be a negative. So now I really have a negative plus a negative. So I'm just going to add like normal and keep my answer negative. So that would be 4.8 plus two. Now you may be wondering, okay, we have to, and that doesn't have a decimal. Well, anytime we have a whole number, we would simply write it with a decimal and a zero behind it. Any time you have a whole number, think of it like a period at the end of the sentence. So it's just going to go on the right of the number. So I would write this as two .0. And again, I lined up my decimals. So now I just add 8 plus zero is 8, bring down the decimal and four plus two is 6. Now again, I'm adding negatives, so I would have a negative answer. So this is negative 6.8. Okay, example three, and that does not say three. This is example three. All right, zakia measured the Lake level of Lake Arlington, beginning in January. Then she monitored how much the Lake level increased or decreased each month over a 6 month period. She recorded her data in the table below. Based on the table, what is the total amount that the Lake level changed over the 6 month period? Okay, so we can see in the table that the Lake level is going up or it's going down. Okay, so we just want to figure out what all of this is in total. So we're really adding all of these together. So an easy way we can do this is we can take all of the increases, find out how much that was in total. So we're going to find the total increase, then we can find the total decrease and combine the two. Okay, and I'm going to do these in different colors just so we can see our increases and decreases separately. So in February, we had an increase of .5 feet. In April we had an increase of .32 feet again, notice how I'm lining up decimals right here. In May, we had an increase of 3.71 feet. And those are the only increases. So what I'm going to do is I'm going to add those together since they're all positive and see how much it increased in total. So I'm going to take a zero and put it in this empty space. So I have zero plus two plus one. That's three. 5 plus three is 5. Oh, sorry, 8 plus 7 is 15. Keep my decimal. And then one plus zero plus zero plus three is four. So an increased 4.53 feet, now let's see how much it decreased. So in March it decreased by 1.26 feet. In June it decreased 1.27 feet. And in July, it decreased two .40 feet. Now, if this is a decrease, I'm going to have a negative answer. And these were all negative amounts. When we add negatives, we just add like normal and make the answer negative. So 6 plus 7 is 13. One plus two is three plus two is 5 plus four is 9. Keep the decimal. One plus one is two plus two is four. So it increased by 4.53 and then decreased by 4.93. So what I want to do now is I want to add these two together. So that would be 4.53. Plus a negative four .93. So I have a positive plus a negative. So I'm going to find the different between those numbers and then I'm going to take the sign of the quote unquote bigger number. So if I'm finding the difference, that would be 4.93. -4.53. Three minus three is zero. 9 -5 is four. Keep our decimal and four minus four is zero. Now, the quote unquote bigger number here would be 4.93 because if they were both positive, that would be bigger than 4.53. Think of money if you're having trouble thinking of what's bigger. So like $4 and 93 cents would be more than $4 and 53. So since that would technically be bigger if they were both positive, we look at the sign. It's negative, so our answer is negative. So that means that the Lake level decreased by .4 feet. And this is a word problem so our answer must be in a complete sentence. So we would say the Lake level of Lake Arlington decreased by .4 feet during the 6 month period. Go ahead and pause and take a moment to write that down. All right, now it's time for you to try. Use the following information to determine how much Mandy needs to spend on soccer equipment. Once you have solved this, don't forget to rate your summary and bring your notes with you to class. All right, we'll see you next class day. Have a good day.