As we're learning how to solve different types of math problems, sometimes it's easier to work with decimals instead of fractions. So in this lesson we're going to learn some strategies for converting fractions into decimals. Here's our first example. Write three fifths as a decimal. So our fraction is three over five and we want to convert it into a decimal. If you remember, fractions represent division. So we can treat any fraction as a division problem, which is really just the numerator divided by the denominator. So we can treat this as three divided by five. Or as long division, we would set it up like this. Once we solve this long division problem, the answer that we get as our quotient will be written as a decimal. So let's go ahead and solve this long division problem. Well, five goes into 3 zero times, five times zero is zero, subtract that and we have a remainder of three. Well, that doesn't help us much. We really don't want a remainder with these types of problems. We want our answer to be set up as a decimal, which means we have no remainder. So we're going to add a decimal point followed by a zero at the end of our number, after the three. Now we can bring that down and continue this division problem. So five goes into 3.0, o if it's more helpful, you can think of it as 5 goes into 30, 6 times. But we'll just place a decimal point before it there to make sure that we have our decimal point lined up in our answer. And then five times 0.6 gives us 3.0. Or you can think of it as five times six gives you 30. Just put the decimal point in between. We subtract and we have no remainder, so we know that we're done and our decimal is 0.6. For this example, we'll write four and a half as a decimal. So this time we have a mixed fraction that has the whole number part, the four, and the fraction part, the one half. When we're converting mixed fractions to decimals, there's different strategies that we can use. I'm going to show you two different ways. The first method involves converting the mixed fraction to an improper fraction first. So four and one over two as an improper fraction becomes nine halves, nine over two. And if you need a refresher on how to convert to improper fractions, you can go back and review that lesson. And now we can use long division to convert nine halves to a decimal. So it'll become nine divided by two and we'll set it up as long division. Two goes into nine four times. Multiply those, we get eight with a remainder of one and we don't want a remainder, so we have to keep going. We'll add zero after the nine, bring it down. Two goes into 1.0 five times. Or you can think of it as two goes into ten, five times. Just place the decimal point. Multiply the two times the 0.5, get 1.0, subtract. And now we have no remainder. And that's what we want, to have zero as our remainder. And we know that we're done at that point. So our solution is 4.5. Now we'll look at the same mixed fraction, but using a second strategy. So our second method involves treating the mixed number as an addition problem. So four and one half can be thought of as four plus one half. So now we can focus just on the one half and convert that part to the decimal. And then we'll join it back with the whole number with the four at the end. So let's focus on the one over two, which we can treat as one divided by two and set it up for long division. Two goes into 1 zero times, multiply, subtract. We have a remainder of one. We don't want a remainder. So add zero after the one, bring it down and we can continue. Two goes into 1.0 five times, multiply, subtract. Now we have no remainder. So one half as a decimal is 0.5. Now we're going to add that to our whole number of four. So four plus the 0.5 equals 4.5. And that's the same answer that we got with our first method when we converted four and a half to an improper fraction. So either way, you should always end up with the same decimal as your answer.