WEBVTT Kind: captions Language: en 00:00:00.320 --> 00:00:03.600 Fractions represent pieces or part of something. 00:00:03.600 --> 00:00:08.660 In a picture, we can display this by taking a full shape like a circle and splitting it up into equal parts. 00:00:08.660 --> 00:00:13.360 You can choose how many parts you want to split it up into. In this case, we're looking at four. 00:00:13.360 --> 00:00:19.780 So, if we cut the circle into four equal pieces we'll have four out of four or still the whole one. 00:00:19.780 --> 00:00:24.880 In the orange diagram in the corner, you can see you can then start looking at taking pieces 00:00:24.880 --> 00:00:29.460 of the whole, for example, you can take one quarter away and leave three quarters. 00:00:29.460 --> 00:00:35.300 One over four you take away and then three over four you leave behind. 00:00:35.300 --> 00:00:40.360 When representing a fraction you always need two numbers, you need a top and a bottom. 00:00:40.360 --> 00:00:44.320 Technically, the top is called the numerator and the bottom is called the denominator, 00:00:44.320 --> 00:00:46.080 however, in most math classes 00:00:46.080 --> 00:00:49.840 if you just talk about the top and the bottom people won't usually correct you. 00:00:49.840 --> 00:00:54.820 So, here you can see an example of one over two. We've got a circle cut in half and then in 00:00:54.820 --> 00:01:01.040 purple, we have ten over fifteen so we have ten purple parts out of fifteen total pieces. 00:01:01.040 --> 00:01:04.160 A fraction also represents a division. 00:01:04.160 --> 00:01:07.680 The notation for a fraction also represents a division because a 00:01:07.680 --> 00:01:10.479 fraction and division actually works the same way. 00:01:10.479 --> 00:01:14.159 So, anytime you see one number over top the other you can actually replace it 00:01:14.160 --> 00:01:16.580 with any of the following kinds of notation. 00:01:16.580 --> 00:01:20.940 You could have three divided by five using the line with two dots in the top and bottom, 00:01:20.940 --> 00:01:25.600 you could have three divided by five using the long division notation, 00:01:25.600 --> 00:01:29.700 you could have three over five but written with just a slash, 00:01:29.700 --> 00:01:33.980 and you can have the notation we were using of three divided by five, three over five. 00:01:33.980 --> 00:01:39.759 These are all different notations for division and you should try to get comfortable with all of them. 00:01:39.759 --> 00:01:43.600 Now, whenever you have a fraction you must have equal parts. 00:01:43.600 --> 00:01:48.079 You cannot have someone's half being bigger than the other person's half. 00:01:48.079 --> 00:01:51.439 You also don't have to use circles as the only shape. You could use rectangles, 00:01:51.439 --> 00:01:55.119 you could use triangles, you could use a square, anything will 00:01:55.119 --> 00:01:58.240 work as long as you subdivide it into equal pieces. 00:01:58.240 --> 00:02:00.910 You can use fractions to represent parts of anything. 00:02:00.910 --> 00:02:05.840 What we'll see later is that fraction notation can also be used to describe a ratio. 00:02:05.840 --> 00:02:09.360 Let's take a look at this example. Let's say in total we have nine pets 00:02:09.360 --> 00:02:14.160 but those nine pets are made up of three dogs, four cats, and two pigs. 00:02:14.160 --> 00:02:18.160 You could then have these three fractions: three dogs out of nine pets, 00:02:18.160 --> 00:02:21.599 four over nine - four cats out of nine pets, 00:02:21.599 --> 00:02:26.400 or two pigs out of nine pets. You could also have a test example where you wrote 00:02:26.400 --> 00:02:29.440 a test and you answered sixteen of the twenty questions correctly 00:02:29.440 --> 00:02:33.599 so, your overall grade of the test is sixteen out of twenty or sixteen over twenty. 00:02:33.599 --> 00:02:37.920 Or, you could convert this to a percent which we'll see in a later unit. 00:02:37.920 --> 00:02:41.200 Now, there's a few different kinds of fractions. Even though these different 00:02:41.200 --> 00:02:44.020 definitions do exist, you don't have to let that scare you because 00:02:44.020 --> 00:02:49.480 once we start doing the math all of these different fractions will behave in the same way. 00:02:49.480 --> 00:02:56.060 So, we do have a zero fraction. A zero fraction is the first example and that's when the numerator or the top is zero. 00:02:56.060 --> 00:02:59.780 If the numerator is zero then the fraction always represents zero 00:02:59.780 --> 00:03:04.239 no matter what the denominator is unless you have zero as both the numerator and the 00:03:04.239 --> 00:03:06.720 denominator then that's technically undefined 00:03:06.720 --> 00:03:10.000 and something you would cover in a later math course. 00:03:10.000 --> 00:03:14.319 The next one is proper fractions. So, a fraction is supposed to represent part of a whole 00:03:14.320 --> 00:03:20.080 and that's why this is the proper fraction. When the numerator, the top, is smaller than the bottom, the denominator. 00:03:20.080 --> 00:03:25.880 Any fraction like that will always be a proper fraction and it's smaller than one. 00:03:25.880 --> 00:03:31.360 Next is a whole fraction. When the number in the top or the numerator is equal to the number in the bottom, 00:03:31.360 --> 00:03:33.840 or the denominator then that is a whole fraction 00:03:33.840 --> 00:03:38.240 because whenever you divide something by itself you get one and you have the whole part back. 00:03:38.240 --> 00:03:40.879 Lastly, we have an improper fraction. 00:03:40.879 --> 00:03:44.159 Sometimes the numerator or the top is bigger than the bottom and that fraction 00:03:44.159 --> 00:03:47.680 represents something bigger than one, so, if you have seven over five for 00:03:47.680 --> 00:03:50.400 example, you actually have one whole piece 00:03:50.400 --> 00:03:54.959 plus two pieces more in the next hole. With those definitions in mind 00:03:54.959 --> 00:03:58.159 we can place each of these kinds of fractions on the number line. 00:03:58.159 --> 00:04:01.680 Maybe this illustration will help make these definitions more clear. 00:04:01.680 --> 00:04:05.439 First, we have the zero fraction so, on the left of the number line without 00:04:05.439 --> 00:04:10.879 getting into the negatives we see the zero fraction right at zero. 00:04:10.879 --> 00:04:14.400 Next is a proper fraction. Any time you have a fraction that is 00:04:14.400 --> 00:04:17.919 part of the whole just like the original definition, that is where you have a 00:04:17.919 --> 00:04:21.440 proper fraction. Then, right at the one, you have the whole 00:04:21.440 --> 00:04:24.240 fraction. So, if the top is equal to the bottom 00:04:24.240 --> 00:04:29.440 then you have the whole piece. Lastly, improper fractions are anywhere 00:04:29.440 --> 00:04:33.360 greater than one. So, any time you have a larger numerator 00:04:33.360 --> 00:04:37.520 than denominator, you have an improper fraction. As you can see 00:04:37.520 --> 00:04:41.520 going from left to right, a zero fraction is less than a proper fraction which 00:04:41.520 --> 00:04:48.800 then is less than a whole fraction and those are all less than an improper fraction.