Fill in the blanks. Eight-tenths plus twenty-two hundredths equals what hundredths plus twenty-two hundredths equals what hundredths?
This problem is all about adding together two fractions, eight-tenths and twenty-two hundredths. And by working through the calculation from left to right, we can see how to work out the answer, what method we should use. And along the way, there are two missing numbers that we need to fill in. So let’s think about how to add eight-tenths and twenty-two hundredths together. And hopefully, along the way, we’ll consider how to fill in the blanks.
First of all, what do we notice about eight-tenths and twenty-two hundredths? What’s going to make it difficult to add them together at the moment? Well, we know that, in order to be able to add fractions together, they need to have the same denominator. And at the moment, they don’t. We have a fraction in tenths and another fraction in hundredths. So we’re going to have to change one of the fractions so that the denominator is the same as the other.
If we were to convert one hundredths into tenths, we’d need to divide by 10. But as the numerator or the top number in this fraction is 22, we can’t actually divide it by 10 and get a whole number. So we can’t write twenty-two hundredths as a number of tenths. What we can do, however, is to convert eight-tenths into hundredths. So let’s start off by doing that.
To convert a number of tenths into a number of hundredths, we need to multiply the denominator by 10. 10 times 10 equals 100. And for our new fraction to be equivalent to eight-tenths, we need to do the same to the numerator. Eight multiplied by 10 equals 80. So we can say that eight-tenths is the same as eighty hundredths. The fraction still represents the same amount. We’ve converted eight-tenths into eighty hundredths.
And now we can write our addition with two fractions that now have the same denominator: eighty hundredths plus twenty-two hundredths. So we can see that our first missing number, which was this numerator here, is 80.
Now that our fractions have the same denominator, we simply need to add them together. Remember, we don’t to add the denominators together. We just add the numerators. Eighty hundredths plus twenty-two hundredths equals how many hundredths? The answer to this will be our final missing number. We just need to add 80 and 22 together.
Well, to do this quickly in our heads, we can partition 22 into 20 and two. Why would we do this? Well, we know straightaway that 80 plus 20 equals 100. So 80 plus two more than 20 equals two more than 100, or 102. Eighty hundredths plus twenty-two hundredths equals one hundred two hundredths. But is this the right answer? How can we have one hundred two hundredths? The numerator is bigger than the denominator.
Well, we can’t have a numerator larger than 100. It just means that it represents a number that’s more than one. And these sorts of fractions are improper fractions. Here’s what one hundred two hundredths would look like. It’s the same as one and two hundredths.
So in this problem, we wanted to add together a number of tenths and a number of one hundredths. We couldn’t do this. So we knew that we needed to convert the number of tenths into a fraction that was exactly the same but with a denominator of 100. So eight-tenths became eighty hundredths. 80 was our first missing number.
Because our two fractions then have the same denominator, we could add eighty hundredths and twenty-two hundredths quickly together. And the answer was one hundred two hundredths. 102 was our second missing number. The two blanks should be filled in with the numbers 80 and 102.