Transcript for:
Decimal Operations: A Comprehensive Review

Welcome to Math with Mr. J. In this video I'm going to be doing a decimal review. So a refresher on how to add, subtract, multiply, and divide decimals. So hopefully if you need a little more help with one of these operations this helps you out. Now if you're looking for a little more in-depth instruction or more examples I dropped the links. to my videos on adding, subtracting, multiplying, and dividing decimals below in the description.

So let's jump right into number one here where we have addition. So 18 and 4 tenths plus 3 and 97 hundredths. So for adding and subtracting decimals, the most important part is lining the problem up correctly. And you do that by lining up your decimals. So 18. and 4 tenths plus 3 and 97 hundredths.

Now the problem looks a little offset. That's fine. We can use placeholder zeros because zeros to the right of a decimal do not change the value.

So I can put a zero here to the right of that 4 and it doesn't change the value. It's an equivalent decimal. So now it looks a little neater and more lined up. So once you have your decimals lined up and any placeholder zeros put into place, we can just add.

So 0 plus 7 is 7. 4 plus 9 is 13. Bring my 1 over here. Now decimals line up throughout the whole problem. So...

Bring it straight down. 1 plus 8 is 9, plus 3, 12. 1 plus 1 is 2. So our answer is 22 and 37 hundredths. Now let's take a look at our original problem. With decimals, it's good to always see if your answer makes sense, and we can use estimation.

So this number, 18 and 4 tenths, is around 18. And the second number, 3 and 97 hundredths, if we were to round that to the nearest whole, it would be around 4. 4. So 22 is a good estimate. So our answer, 22 and 37 hundredths, is a reasonable answer. If you put the decimal in the wrong place or forgot the decimal, it should tell you that something went wrong because that answer doesn't make sense.

So let's take a look at number two. Again, adding and subtracting the most important thing, line your decimals up. So here we have 34. and six tenths minus four and eight hundred sixty-four thousandths. Now that problem looks even more offset than the first one. That's okay because we lined our decimals up, the most important part.

And when you line your decimals up, it lines all of your places up. So now we need a couple of placeholder zeros. Now we're all lined up and we have our our placeholder zeros.

I cannot do 0 minus 4. I need to borrow. So I can't borrow from this 0, so I need to borrow from the 6. It's now a 5. This 0 turns to a 10, but I need to bring the 1 over all the way to the right, so it's going to be a 9, and then the 0 to the far right is now a 10. So 10 minus 4 is 6. 6. 9 minus 6 is 3. I cannot do 5 minus 8, so I need to borrow from the 4, which now becomes a 3. So I get 15 minus 8, which is 7. Bring my decimal straight down. I need to borrow again from the 3, which is now a 2. And that other 3 now becomes a 13. 13 minus 4 is 9. And then bring my 2 down, 2 minus 0. there would give me 2. So 29 and 736 thousandths.

So let's estimate here. Let's do an estimation. So 34 and 6 tenths would round to 35. 4 and 864 thousandths would round to 5. So 35 minus 5, our estimation would be 30. So our actual answer is reasonable.

It makes sense. Let's check number three as we move to multiplication. So for multiplication, you don't necessarily have to line that decimal up.

I find it easier, let's take out the decimals to start with. And we are going to do 52 times 45. Again, I took out the decimals. I'm going to put them in at the end.

5 times 2 is 10. 5 times 5 is 25, plus 1, 26. Done here, done here. We need our 0 here as we move to the next place. 4 times 2 is 8. 4 times 5 is 20. Now we add our partial products. 0 plus 0, 0. 6 plus 8 is 14. 1 plus 2 is 3, and we have our 2 here.

Now, we need to put our decimal back in to our answer. So we take a look back at our original problem, and we need to see how many digits are to the right or behind a decimal. Well, we have this 2 here, so that's 1. And we have this 5 here, so that is 2. 2 digits behind the decimal. so our answer needs two digits behind the decimal. So we bring it in one two and it goes right here or think of it as one two digits behind the decimal in our answer.

So for number three the product is 23 and 40 hundredths. And if we take a look at our original problem we have something around five times something around five. So our answer is should be somewhere around 25 so our answer is reasonable we know we put the decimal in the correct place so for number four we have dividing decimals so let's set it up three and two tenths is our divisor and thirteen and seventy six hundredths is our dividend so when you get to division problems the First thing we need to check is, is the divisor or outside number whole? If not, we need to make it a whole number.

Here we have 3 and 2 tenths, so it's not exactly a whole. So we need to move this decimal to the right one time to make it a whole number. This is going to make our problem much easier. Now whatever you do to the outside, you have to do to the inside. Everything needs to stay balanced.

So we moved it once to the right. the outside so we need to move it once to the right on the inside. Now we can rewrite our problem.

So we have 32 as our divisor and we have 137 and 6 tenths. Now that the divisor is whole we bring this decimal straight up. That's where it's going to be placed in the answer. So if you have a whole number on the outside side right off the bat, you can bring that decimal straight up right away.

But here, in this case, we did not. So now we can go through our long division steps. Can we do 1 divided by 32?

No. Can we do 13 divided by 2? I'm sorry, 13 divided by 32? No.

So we need to do 137 divided by 32. And 32 can be pulled out of 137 for... times. That gets us to 128. So we'll subtract. We get 9. Bring down this 6. So now we have 96 divided by 32, which happens to give us 3. We can pull 3 whole 32s out of 96. And 96 and 32 are compatible, so we hit it without any remainder. So 3 32s out of 96, 3 times 32, like we said, hits 96 exactly.

Our answer is 4 and 3 tenths. So if we take a look at our original problem, we have something around 14 here divided by 3. So 14 and 3 aren't necessarily perfectly compatible, but we can think how many whole 3s can we pull out of 14? Well, 4 whole 3s, that gets us to 12s.

And then we'll have a little left over. So this answer makes sense, right? Because we pulled 4 whole 3 and 2 tenths out of 13 and 76 hundredths with a little left over. So this answer is reasonable. Say, for example, you forgot to put the decimal and you got an answer of 43. You can look back at the original problem and think, well, that answer doesn't really make sense.

It's not reasonable. Maybe I did something incorrectly. And you can figure out.

where you need to put the decimal. So there's the quick refresher slash decimal review. Hopefully that helped. Thanks so much for watching.

Until next time, peace.