One-fifth plus three-quarters equals what.
Now, the tricky thing about adding these fractions as they are is that they have different denominators. If the denominators were the same, for example, if they were both fifths, we could add them quickly. But instead, we’re gonna have to do some work to convert them first so that they both have a common denominator, in other words, so that the bottom number is the same.
A common denominator is a denominator that two or more fractions have in common. At the moment, we’ve got denominators of five and four. How could we convert fifths and quarters so that they become the same denominator?
A quick way to do this is just to multiply five by four. And of course, this gives us the answer 20. 20 is a common denominator of fifths and quarters because it’s a common multiple of five and four. So we can convert our fifths fraction into twentieths. And we can convert our quarters fraction into twentieths. And then, we’ll be able to add them together.
So how many twentieths are the same as one-fifth? Well, to convert the denominator from five into 20, we’ve multiplied it by four. So to keep the fraction the same value, we need to do exactly the same to the numerator or the top number. One times four equals four. And so one-fifth written as twentieths is four twentieths.
Now, let’s convert our second fraction. How many twentieths are the same as three-quarters? To convert the denominator from quarters into twentieths, we’ve multiplied it by five. You know what to do with the numerator this time. Three multiplied by five equals 15. And so three-quarters written as twentieths is the same as fifteen twentieths.
So instead of writing one-fifth plus three-quarters, we can now use our twentieths fractions. We said one-fifth was the same as four twentieths. And three-quarters is exactly the same as fifteen twentieths. So now we’ve converted the fractions in the calculation, we can work it out. Four twentieths plus fifteen twentieths equals how many twentieths? Well, four plus 15 equals 19. So the answer is nineteen twentieths.
Sometimes, it’s easy to look at the calculation and think all what I have to do is to add the top numbers and add the bottom numbers or try to deal with the numbers as they’re written. But in this particular calculation, the only way we can add them together is to convert both fractions. And so the trick is understanding what I need to do is my need to convert both fractions so they have a common denominator.
With this particular problem, we multiplied five by four to find a common denominator of 20. And we knew that we could convert fifths and quarters into twentieths. One-fifth was the same as four twentieths. And three-quarters was the same as fifteen twentieths.
And so one-fifth plus three-quarters equals nineteen twentieths.