15.98 plus 26.314 equals what?
There are lots of different digits in these numbers. They both have a different amounts of digits and different number of decimal places. So rather than try to juggle all those digits in our heads, we can use column addition to find the answer. It’s really important that we line up the digits so that they’re in the correct columns. A good way to do this is to make sure that we draw the decimal points before we start.
Let’s start with the larger number. It won’t change the total at all, 26.314 plus 15.98. We can see that our second number doesn’t have anything in their thousandths column. We don’t have to, but just to make things neater, we can write a zero as a placeholder. Something that’s easy to forget and something that would really affect our answer is a decimal point. So let’s put that in before we start, make sure it lines up with the other decimal points. This will mean that all of our digits will be in the correct columns.
Start by adding the thousandths. Four thousandths plus zero thousandths equals four thousandths. One hundredth plus eight hundredths equals nine hundredths. Three tenths plus nine tenths equals 12 tenths. We know that 10 tenths make one whole. So this is the same as saying one whole and two tenths. So we can write a two in our tenths column and then exchange 10 of those tenths for one one or one whole.
Let’s add the digits now that have a whole value to the left of the decimal point. Six ones plus five ones equals 11 ones. Don’t forget we’ve got one one underneath. That makes 12 ones. So we can write a two in the ones place and exchange 10 of those ones for one 10. Finally, we can add the digits in the tens column. Two tens plus one ten equals three tens. And don’t forget the one underneath, four tens, 42.294.
This was quite a quick and efficient way that we could find the answer. But there is another method that we could use. What do we notice about the number 15.98 that might make it easy to add? Well, the number 15.98 is only two hundredths away from 16. A nice whole number that we could add very quickly. What if we started with 26.314 but then added 16 instead? And then, of course, we’d have to adjust the answer to make up for it.
Let’s try this method. Start with 26.314. And then instead of adding 15.98, we’ll round it to 16; we’ll add 16. 26 plus 16 equals 42. So this doesn’t affect the decimal part. 26.314 plus 16 equals 42.314. But remember, we weren’t asked to add 16. We were asked to add 15.98, two hundredths less than 16. We’ve added two hundredths too many. So we need to adjust our answer by subtracting two hundredths or 0.02.
At the moment, our number has three tenths and one hundredth. We can say this as 31 hundredths. 31 take away two leaves us with 29. So we can write the same number but with 29 hundredths or two tenths, nine hundredths. Can you see how those 31 hundredths have turned into 29 hundredths? And so our answer is exactly the same.
How did we calculate the total of 15.98 and 26.314? The first method that we used which worked well was to recognize that both numbers had different amount of digits. And rather than hold all those digits in our head, we could write them out and use column addition to find the answer. Adding decimals is just the same as adding whole numbers. We just needed to be very careful that we lined the numbers up correctly. And so we made sure that the decimals were all in the same place. And then we went through and added each column, just like we would do a whole number.
Our second method was to recognize that 15.98 is very near to 16. And so we added 16 to give us a quick answer of 42.314. But then we had to adjust our answer and take away two hundredths, which left us with 42.294. 15.98 plus 26.314 equals 42.294.