One and one-fifth plus two and one-tenth equals what.
A common mistake with problems like this is to think that when we add the fractions part, all we have to do is add the numerators, one add one equals two, and then add the denominators, five plus 10 equals 15. But we can’t just expect that one of these plus one of these equals two of these. All three fractions are different sizes. They have different denominators. So we can’t just add fifths and tenths and expect to get an answer in fifteenths. So when the time comes to add the fraction part of these mixed numbers together, we’re going to have to convert them so they have the same denominator.
Let’s partition both of our mixed numbers into a whole number and a fraction. One and one-fifth is the same as one plus one-fifth. And two and one-tenth is the same as two plus one-tenth. So really, we could write the whole addition as one plus one-fifth plus two plus one-tenth. First let’s start by adding the whole number part of our mixed numbers. One plus two equals three. Now, we can find the total of the fraction part of each mixed number. And as we spotted already, we need to convert these fractions so they have a common denominator before we add them together.
What number is a multiple of both five and 10? We could convert them both into twentieths because 20 is a multiple of both five and 10. But it’s much quicker to convert fifths into tenths. And that way, both fractions will have a common denominator of 10. We only need to convert the first one. But how do you know what the answer is going to be without writing it out? To turn fifths into tenths, we double the denominator. And to keep the fraction the same value, we do the same to the numerator. One-fifth is the same as two-tenths. And so our calculation becomes two-tenths plus one-tenth, which equals three-tenths.
So when we added the whole number part of our mixed numbers, we got an answer of three. And after adding our fraction part of our mixed numbers, we got an answer of three-tenths. So to find the overall total, all we have to do is to add the two answers. Three plus three-tenths equals three and three-tenths.
Can you think of any other ways that we could write three and three-tenths? But remember, if we use a place value grid, three and three-tenths is the same as three ones and three-tenths. And so if we write the answer 3.3, that would be just as good as three and three-tenths.
There’s another way we could write the answer and that’s as a fraction. We know that the tenths column shows us that we’ve already got three-tenths. But if we have three wholes as well, three ones, how many tenths is that all together? Well, we know that one whole or one one is the same as ten-tenths. So three wholes or three ones must be the same as three lots of ten-tenths or thirty-tenths. And so if we also add the three-tenths part of our number, we can write the answer as an improper fraction, thirty-three tenths.
All three answers are exactly the same. And you could write any one of them and still get the correct answer. First, we split up the mixed numbers so we could see the whole numbers and the fractions separately. Then, all we needed to do was to add the whole numbers then add the fraction parts. And we had to remember to convert the first fraction so that they both had common denominator and then, finally, find the total.
One and one-fifth plus two and one-tenth equals three and three-tenths or 3.3 or thirty-three tenths.