 Video: Add and Subtract Unlike Fractions Using LCM | Nagwa Video: Add and Subtract Unlike Fractions Using LCM | Nagwa

# Video: Add and Subtract Unlike Fractions Using LCM

When adding or subtracting fractions with different denominators, find their least common multiple and create equivalent fractions with common denominators in order to complete the calculation.

11:45

### Video Transcript

Today we’re gonna take a look at how to add and subtract unlike fractions using the least common multiple. Before we jump in to adding and subtracting unlike fractions, let’s quickly do a vocabulary review. There are three things that I wanna review with you; the first one is the least common multiple. The least common multiple sometimes called the LCM of two numbers is the smallest multiple that both of the numbers have in common. Let me show you an example. Here are the multiples of three and the multiples of seven. The ones boxed in red are common multiples of three and seven. But the least common multiple is twenty-one because it’s the smallest of the common multiples. Keep this in mind as it’s an important tool in adding unlike fractions.

Next step, order of operations. Order of operations is the order in which we solve problems. We start with parentheses. Then move to anything with exponents. Next comes multiplication and division, but remember we do this from left to right, so multiplication and division from left to right. And finally, we have addition and subtraction also as we’re moving from left to right. And last but not least, let’s talk quickly about simplifying fractions. When I say simplify fractions, I mean reduce them to their lowest terms. We simplify fractions when there’s a larger number on the top and a smaller number on the bottom, so when the numerator is larger than the denominator. Here’s an example of when we have a numerator that’s bigger than our denominator. And in this video, any time we have an improper fraction, a fraction that has a numerator that’s larger than the denominator, we’re gonna simplify it and turn it into a mixed number. So here to simplify this fraction seven-fifths, I turned it into the mixed number one and two-fifths.

Okay! Enough review. Let’s start adding and subtracting unlike fractions. I’m sure you’ve seen something like this before where you add four-tenths and five-tenths for a final answer of nine-tenths, but today we wanna add something like this: one-fourth plus one-third. To do that, I’m gonna start by finding the least common multiple of four and three. The least common multiple for four and three is twelve. We’re going to use the least common multiple to create a common denominator for one-fourth and one-third; the common denominator is their least common multiple of twelve. So what we’re gonna do is ask the question how many twelfths is one-fourth. and how many twelfths is one-third. We answer this question by thinking what can I multiply four by that equals twelve and then again what can I multiply three by that equals twelve. four times three is twelve, and then three times four equals twelve. But in order to keep the fractions equal, if we multiply the bottom by three or by four, we have to multiply the top by that same value. We would need to multiply the top of the one-fourth fraction by three and the numerator of the one-third fraction by four, so one times three is three and one times four is four. We’ve now found equivalent fractions that have a common denominator and can be added easily three-twelfths plus four-twelfths equals seven-twelfths. I wanna stop quickly and show you why we can multiply that those fractions by three and by four and come out with equivalent fractions. On the other screen, we multiplied one-fourth; we multiplied the numerator by three and the denominator by three. We also multiplied one-third by four over four; we multiplied the numerator by four and the denominator by four. If you look at these fractions in red, three over three is the same thing as multiplying something by one; four over four is the same as multiplying something by one. Here we can see that we’re not actually changing the value of these fractions. When you multiply something by one, you get itself. So we’re making it look a little different, but the value is actually the same. These are equivalent fractions: three-twelfths is equivalent to one-fourth, and four-twelfths is equivalent to one-third.

The next example is a subtraction problem, but we’re gonna follow this same process. Start by searching for the least common multiple. Here we see that six and fifteen have a least common multiple of thirty. So I know that I need a new denominator for both of these pieces of thirty. To change the denominator of six to thirty, I need to multiply by five; and to change the denominator of fifteen to thirty, I need to multiply by two. But remember that we need to do that for the numerator and the denominator. five times five is twenty-five; eleven times two? twenty-two; twenty-five minus twenty-two is three, so we get three over thirty. But three over thirty is not in its most simple form, so we also wanna simplify this fraction. Both the numerator and denominator here are divisible by three, so the most simple form of this fraction is one over ten, one tenth as our final answer.