In this lesson we're going to learn how to add and subtract fractions that have unlike denominators. So here we have two fifths minus one fourth. Notice that the denominators are different, so we can't just subtract the numerators like we did before when we have the same denominator. So we have to have a different strategy here. The first method that we're going to use involves changing the fractions to equivalent ones that have like denominators. So the goal is to try to get both of these fractions to have the same denominator. And to do this we're going to use the least common multiple of the denominators. So the least common multiple of five and four is 20. So we want to change both of these fractions so that they have a denominator of 20. Now remember, with fractions, as long as we multiply the numerator and denominator of the fraction by the same number, we're not changing the value. So we're just going to come up with an equivalent fraction that has a denominator of 20. So our first fraction here is two fifths. We want the denominator to be 20. So what can we do to that five in the denominator so that it becomes a 20? We can multiply it by four. Of course, whatever we do to one part of the fraction, we have to do the same thing to the other part of the fraction. So we also have to multiply the numerator by four. So now this fraction becomes eight over 20. Now we go to the second fraction, the one fourth. We also want it to have a denominator of 20. So we can multiply by five, do the same thing for the numerator, and now the fraction becomes 5/20. So now these two new fractions are equivalent to the ones that we started with. So we haven't changed the problem really, but now we just made sure that they have the same denominator. Of course this is subtraction. So we bring down our subtraction sign and now since they have the same denominator, we can subtract the numerators. Eight minus five will give us three and then we keep the denominator the same. So our final answer is 3/20. Now we're going to look at another method for solving the same problem. With this method we're first going to add, or in this case subtract since it's a subtraction problem, the cross products to get the numerator of our answer. And then we're going to multiply the denominators of these fractions to get the denominator of the answer. So let's do the first step. First step tells us what the numerator of our answer is. So the cross products, remember, we look at the two numbers that are on a diagonal from each other and multiply them together. So the five times one gives us five. Now multiply the other way, two times four gives us eight. So those are our cross products, eight and five. And since we have a subtraction problem. We're going to subtract these cross products. Eight minus five gives us three as the numerator of our answer. Now, to find the denominator of our answer, we multiply the two denominators of the fractions in our problem. So five times four gives us 20. So now we can see our answer is the same as we got the first way, we still end up with three twentieths. So we're adding and subtracting fractions that have unlike denominators. First method is to change the fractions to equivalent ones that do have like denominators. And then the second method was to add or subtract the cross products to get the numerator and then multiply the denominators to get the denominator of the answer. And just a couple of reminders if you start off with mixed fractions, they need to be converted to improper fractions first to keep the problem simple for you. And then if the answer needs to be simplified, you always want to simplify your answer.