Addition with Decimals

[One speaker] 

[Any necessary descriptions.]

Narrator: Welcome to the video on the steps for addition with decimals. The steps for addition with decimals are exactly the same as the steps with addition with whole numbers, except that we have to keep track of the decimal point. For example, one point three plus two point eight. Well we start with one point three, which is somewhere about here on number line, and we add two point eight. So, one, two, and then point eight, one, two, three, four, five, six, seven, eight. Right here, which gives us the answer four point one. When we did the addition algorithm, we would simply stack the numbers on top of each other according to place value. One point three plus two point eight, add each one in columns, three plus eight is eleven, so we bring one up to the column on the left, we have one on the column on the right, and then one plus one plus two is four. The only step that’s different when we have decimal numbers is that we bring this decimal down. When we put our numbers into their columns according to place value our decimals automatically lined up. Now we just bring it down. So our answer is four point one. So, here are the steps for addition all written out. Notice the black steps are the ones we already had, and the ones in pink are the new steps that we’ve added for decimals. It’s important to note that these new steps were always there, we just didn’t have decimals so we didn’t need them. So once again, the first step, stack the numbers according to place value. If we do this, they will automatically line up the decimals. The decimal will between the ones place and the tenths place. For example, three point five plus four point nine. Here we have stacked our numbers according to place value. The ones are in the ones column, and the tenths are right over each other in the tenths column. Notice this automatically puts our decimal between the ones and the tenths, stacked in their own nice little column. Next, add the numbers in the columns starting with the column on the right. Five plus nine is fourteen, but remember, this is fourteen tenths. Fourteen tenths can be changed into one whole, one ones, and four tenths. So we carry our one ones up to the ones column, and we leave our four tenths in the tenths column. Now we go onto the next column, one plus three is four plus four is eight. This brings us to our final step, bring the decimal down. All this means is that we bring the decimal down in the same column as the other decimals, right between the ones place and the tenths place, and you’re done. Our answer is eight point four. Let’s do an example with negative numbers. Negative twelve point nine one, plus a negative three point eight two, I’m going to put this in parenthesis just so we can see that we’re adding a negative number, we don’t get our signs mixed up. Remember, when adding two negative numbers, since they’re both negative our answer if just going to be more negative on the number line to the left, so we actually use addition, but again, that’s only because both numbers are negative. If one of these was positive and the other was negative, we would use subtraction. So step one, stack the numbers according to place value. Twelve point nine one, three point eight two starts in the ones column. So three, our decimal point automatically line up if we’re keeping our place values in the right columns, eight two. Next, add the numbers in the columns starting with the column on the right. One plus two is three, there’s nothing to carry so we can go onto the next column, and repeat this pattern, nine plus eight is seventeen. Well seventeen tenths is one ones, and seven tenths. Next we go onto the ones column, one plus two is three plus three is six, and finally in the tens column we only have a one, so we bring that down, one. Then we come to our final step, bring the decimal down, this is very important, if we forgot to do that this would be a very different answers, one thousand six hundred and seventy three is very different than sixteen point seven three. Then, finally, don’t because both of these numbers were negative, we can even put a little negative sign in front of each of them to remind us that our answers actually negative. Negative sixteen point seven three.

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