How to Add Fractions

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When adding fractions, it's important to make sure that the denominators are the same. Discover how to find the least common denominator when adding fractions with help from a math teacher in this free video on fractions in math.

Part of the Video Series: Fractions & Proportions
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So how does one add fractions? Hi, I'm Jimmy. I've been teaching college math for nine years and fractions are not our favorite in the world, but you know we must deal with them, and so hence the operations with fractions. Now, today we're going to talk about how to add fractions, and, whether it be addition or subtraction, you have to focus on the denominator, because in order for you to add fractions you have to be sure that the denominators are the same. And, if they are, great. But if they're not, then well, you have to make an adjustment before you can actually add the two fractions together. So here's a quick example for you. Suppose you want to find out what 5/6 plus 1/30 is going to be. Now, since the denominators are not the same, you cannot add the two and call it 6 over 36, that would just be completely wrong. However, because the denominators are not the same, you can at least try to find common ground between the two. And this is where something called the least common denominator becomes very important, because what you need to ask yourself is, 'What number will both six and thirty go into?' That's where the least common denominator comes in. We're talking about the smallest number that both of these numbers will divide into. Well, the least common denominator between six and thirty is actually thirty because six and thirty will both go into thirty. Now, after you've found the LCD, or least common denominator, you have to ask yourself, for example, with six, 'Six times what number is thirty?' Well, if you know your multiplication tables, you'll know that six times five gives you thirty. Now, in order for adding fractions, you have to multiply the bottom and the top by the same number that you just multiplied. So, six times five is thirty, five times five is twenty-five. Now let's talk about the second fraction. Thirty times what is thirty? Well, thirty times one obviously gives you thirty, so there's not much of a change there, because when you multiply the top by one, one times one is still one. And so what you're really adding here is twenty-five thirtieths plus one thirtieth, and you get twenty-six over thirty. You add to the numerators, but you always keep the denominator the same, and so you have twenty-six over thirty. After that, you may have to ask yourself 'Do I need to reduce?' After looking at these two numbers, you see that two will go into twenty-six and thirty, so dividing both sides by two, you will get thirteen over fifteen, and that is going to be your final answer. So, I'm Jimmy, and that gives you a glimpse as to how to add fractions.

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