0:00:02.240,0:00:06.227 This tutorial is about the basic[br]concepts of fractions. 0:00:06.760,0:00:11.200 What they are, what they look[br]like, and why we have them. 0:00:12.340,0:00:17.048 A function is a way of writing[br]part of a whole. 0:00:17.770,0:00:22.814 And it's formed when we divide a[br]whole into an equal number of 0:00:22.814,0:00:27.370 pieces. Now let's have a look.[br]I've got a representation here. 0:00:28.120,0:00:29.080 Of a whole. 0:00:30.200,0:00:36.752 And let's say we want to divide[br]it into 4 equal pieces. 0:00:38.520,0:00:44.760 So there we've[br]taken 1 hole 0:00:44.760,0:00:51.000 and divided it[br]into 4 equal 0:00:51.000,0:00:57.240 pieces. So each[br]piece represents 1/4. 0:00:58.510,0:00:59.810 Wow. 0:01:00.870,0:01:04.180 I've now taken 1/4 away. 0:01:05.800,0:01:09.436 Now I've removed 0:01:09.436,0:01:15.060 two quarters. If[br]I take a third. 0:01:15.990,0:01:22.986 That's 3/4.[br]And if I take the false so I've 0:01:22.986,0:01:24.821 now got all four pieces. 0:01:25.440,0:01:30.401 I've taken all of them for[br]quarters, which is exactly the 0:01:30.401,0:01:32.656 same as taking the whole. 0:01:33.240,0:01:38.080 Let's just return for a moment[br]to the two quarters. 0:01:38.600,0:01:42.840 Now[br]two 0:01:42.840,0:01:46.494 quarters. Is exactly 0:01:46.494,0:01:52.695 the same. As if I'd started[br]with my whole and actually 0:01:52.695,0:01:54.210 divided it into. 0:01:55.010,0:01:57.610 2 pieces of equal size. 0:01:58.450,0:02:00.202 And you can see that that's 0:02:00.202,0:02:06.040 exactly the same. As two[br]quarters so I can write two 0:02:06.040,0:02:10.480 quarters. As one[br]half. 0:02:12.270,0:02:15.998 Let's have a look at[br]another illustration now. 0:02:17.190,0:02:19.395 Here I have a bar of chocolate. 0:02:20.740,0:02:22.369 It's been divided. 0:02:22.930,0:02:29.144 Into six pieces of equal size.[br]So we've taken a whole bar and 0:02:29.144,0:02:31.534 divide it into six pieces. 0:02:32.270,0:02:36.540 So each piece is[br]16. 0:02:38.330,0:02:42.506 Now, let's say I'm going to[br]share my bar of chocolate with 0:02:42.506,0:02:43.550 the camera man. 0:02:44.650,0:02:50.770 So I want to divide the bar[br]of chocolate into two pieces. 0:02:51.370,0:02:53.170 So if I do that. 0:02:55.160,0:02:59.060 Where each going to have one 0:02:59.060,0:03:05.940 236. So 1/2 is[br]exactly the same as 36. 0:03:06.810,0:03:11.139 But there's not just one[br]cameraman. We've got two 0:03:11.139,0:03:16.430 cameramen, so I need to share[br]it. Actually, between three of 0:03:16.430,0:03:23.475 us. So now if I put my bar back[br]together and I need to share it 0:03:23.475,0:03:27.060 between 3:00. Where[br]each going to get. 0:03:28.430,0:03:30.810 Two pieces. 0:03:32.550,0:03:38.110 So 1/3 is exactly the[br]same as 26. 0:03:38.910,0:03:45.540 But Let's say I[br]want to eat all my chocolate bar 0:03:45.540,0:03:51.169 myself, so I'm going to have all[br]six pieces, so they're all mine. 0:03:51.700,0:03:55.693 Not going to share them, so I[br]take all six pieces. 0:03:56.310,0:03:58.596 And I've taken away the whole 0:03:58.596,0:03:58.977 bar. 0:03:59.540,0:04:06.470 So.[br]Fractions we can look at. 0:04:07.010,0:04:08.348 In two ways. 0:04:09.320,0:04:13.200 We can look at it as the number 0:04:13.200,0:04:15.850 of pieces. That we've used. 0:04:17.130,0:04:23.610 Divided by the[br]number of pieces. 0:04:24.280,0:04:27.260 That make a whole. 0:04:27.260,0:04:32.950 Oh 0:04:33.990,0:04:36.888 As the whole. 0:04:37.710,0:04:44.173 Divided by. Number of pieces[br]or number of people that we've 0:04:44.173,0:04:45.484 divided it into. 0:04:46.290,0:04:52.494 So here we have a whole bar[br]divided into 6 pieces. 0:04:53.880,0:04:57.510 Here we have the number of[br]pieces that we've taken divided 0:04:57.510,0:05:01.470 note 5 the number of pieces that[br]make up the whole bar. 0:05:03.540,0:05:10.828 Let's have a look[br]at some other fractions. 0:05:10.830,0:05:16.926 Let's say[br]we have 0:05:16.926,0:05:18.450 3/8. 0:05:20.000,0:05:25.352 So we've divided a whole up into[br]8 pieces of equal size. 0:05:25.890,0:05:27.636 And we've taken three of them. 0:05:28.270,0:05:29.590 3/8 0:05:31.150,0:05:34.960 We could have 11 twelfths. 0:05:35.800,0:05:41.767 So we've divided a whole up into[br]12 pieces and taking eleven of 0:05:41.767,0:05:46.060 them. We could have[br]7/10. 0:05:47.160,0:05:52.424 Here we will have divided a hole[br]into 10 pieces of equal size and 0:05:52.424,0:05:53.928 taken Seven of them. 0:05:54.710,0:05:56.238 And we can have. 0:05:56.800,0:06:04.696 Any numbers in our fraction so[br]we could have 105 hundreds or 0:06:04.696,0:06:07.986 three 167th and so on. 0:06:08.900,0:06:12.165 Now we've looked at representing 0:06:12.165,0:06:16.897 fractions. Using piece of Cod[br]circular representation are 0:06:16.897,0:06:19.452 rectangle with our bar of 0:06:19.452,0:06:24.008 chocolate. Let's have a look at[br]one more before we move on and 0:06:24.008,0:06:25.478 let's let's see it on. 0:06:26.110,0:06:28.000 A section of number line. 0:06:29.560,0:06:31.877 So let's say we have zero here. 0:06:32.540,0:06:34.439 And one here. 0:06:34.950,0:06:37.302 So let's look at what 3/8 might 0:06:37.302,0:06:44.150 look like. While I need to[br]divide my section into 8 pieces 0:06:44.150,0:06:45.818 of equal size. 0:06:46.690,0:06:49.993 Now obviously this is an[br]illustration, so I'm not 0:06:49.993,0:06:53.663 actually getting my router[br]out to make sure I've got 0:06:53.663,0:06:54.764 equal size pieces. 0:06:55.830,0:07:01.894 But hopefully. That's about[br]right. So we've got 12345678 0:07:01.894,0:07:09.238 pieces of equal size and I'm[br]going to take three of them. 0:07:09.238,0:07:12.910 So if I take 1, two 0:07:12.910,0:07:17.600 3/8. That's where my 3[br]eights will be. 0:07:20.630,0:07:22.639 Let's have a look at[br]another one. 0:07:24.590,0:07:28.340 This time will look at 0:07:28.340,0:07:33.206 11 twelfths. So we need to[br]divide our line up into. 0:07:34.300,0:07:40.033 Pieces so we have 12 pieces[br]of equal size. 0:07:48.390,0:07:55.350 OK, so we wanted[br]eleven of them, so 0:07:55.350,0:08:02.310 we need to count[br]11 one 23456789 ten 0:08:02.310,0:08:05.790 11. So at 11 0:08:05.790,0:08:08.800 twelfths. Is represented there. 0:08:10.240,0:08:16.786 Let's look more[br]closely at our 0:08:16.786,0:08:18.968 fraction half. 0:08:20.040,0:08:26.088 Now we've already seen that half[br]is exactly the same as two 0:08:26.088,0:08:31.174 quarters. And it's exactly the[br]same as 36. 0:08:32.100,0:08:38.832 Well, it's also the same[br]as 4 eighths 5/10. 0:08:40.640,0:08:44.210 2040 deaths 0:08:45.600,0:08:50.770 9900 and 98th and so on. We[br]could go on. 0:08:51.500,0:08:58.116 And what we have[br]here is actually equivalent 0:08:58.116,0:09:05.376 fractions. Each one of these[br]fractions are equivalent at the 0:09:05.376,0:09:08.152 same as each other. 0:09:10.460,0:09:14.090 Now, this form of the fraction 0:09:14.090,0:09:20.985 half. Is our fraction in its[br]lowest form, and often we need 0:09:20.985,0:09:23.610 to write fractions in their 0:09:23.610,0:09:29.122 lowest form. It's much easier to[br]visualize them actually in this 0:09:29.122,0:09:32.118 lowest form than it is in any 0:09:32.118,0:09:36.355 other form. So we often want to[br]find the lowest form. 0:09:37.710,0:09:43.683 Well, let's have a look 1st at[br]finding some other equivalent 0:09:43.683,0:09:46.941 fractions. So let's say I take 0:09:46.941,0:09:52.485 3/4. How do I find an[br]equivalent fraction? Well, what 0:09:52.485,0:09:58.185 I can do is multiply the top[br]number and the bottom number. 0:09:59.270,0:10:00.878 By the same number. 0:10:01.380,0:10:05.258 So let's say I multiply by two. 0:10:05.870,0:10:10.719 If I multiply the top number by[br]two, I must also multiply the 0:10:10.719,0:10:14.822 bottom number by two so that I'm[br]not changing the fraction. 0:10:15.750,0:10:19.691 3 * 2 six 4 * 2 0:10:19.691,0:10:26.454 is 8. So 6 eighths[br]is a fraction equivalent to 3/4. 0:10:28.370,0:10:29.578 Let's try another one. 0:10:30.350,0:10:33.710 This time, let's take our 3/4. 0:10:34.440,0:10:39.434 And multiply it by three. The[br]top numbers multiplied by three, 0:10:39.434,0:10:45.336 so most the bottom number B3[br]threes and 9 three force or 12, 0:10:45.336,0:10:50.330 so nine twelfths is equivalent[br]to 6 eighths, and they're both 0:10:50.330,0:10:51.692 equivalent to 3/4. 0:10:53.070,0:10:57.437 Let's do one more this time.[br]Let's multiply both the top 0:10:57.437,0:11:02.598 number on the bottom number by[br]10. So we have 3 * 10. 0:11:03.350,0:11:04.718 Giving us 30. 0:11:05.230,0:11:11.260 And 4 * 10 giving us[br]40. So another fraction 0:11:11.260,0:11:14.878 equivalent to 3/4 is 3040[br]deaths. 0:11:16.090,0:11:20.743 So it's very easy to find[br]equivalent fractions as long as 0:11:20.743,0:11:25.819 you multiply the top number on[br]the bottom number by the same 0:11:25.819,0:11:29.203 number. Now we have some[br]mathematical language here. 0:11:29.203,0:11:34.279 Instead of using the word top[br]number and write it down top 0:11:34.279,0:11:38.668 number. And bottom[br]number. 0:11:40.730,0:11:45.720 We have two words that[br]we use. The top number 0:11:45.720,0:11:47.716 is called the numerator. 0:11:49.350,0:11:52.605 On the bottom number the 0:11:52.605,0:11:58.523 denominator. Now let's have a[br]look at seeing how we go the 0:11:58.523,0:12:03.176 other way. When we have an[br]equivalent fraction, how do we 0:12:03.176,0:12:05.714 find this fraction in its lowest 0:12:05.714,0:12:08.300 form? Well, let's look at an 0:12:08.300,0:12:13.419 example. Let's say we've[br]got 8, one, hundreds. 0:12:14.890,0:12:20.446 Now we need to find the number[br]that the lowest form was 0:12:20.446,0:12:24.815 multiplied by. And that we ended[br]up with eight one hundredths. 0:12:25.610,0:12:29.840 Well, the opposite of[br]multiplying is dividing, so we 0:12:29.840,0:12:34.540 need to divide both the[br]numerator and the denominator by 0:12:34.540,0:12:35.950 the same number. 0:12:36.460,0:12:40.132 So that we get back to a[br]fraction in its lowest form. 0:12:40.780,0:12:46.282 Well, if we look at the numbers[br]we have here 8 and 100, the 0:12:46.282,0:12:50.605 first thing you should notice is[br]actually the both even numbers. 0:12:51.130,0:12:54.710 And if they're both even[br]numbers, then obviously we can 0:12:54.710,0:12:56.500 divide them both by two. 0:12:57.380,0:13:03.188 So let's start by dividing the[br]numerator by two and the 0:13:03.188,0:13:04.772 denominator by two. 0:13:05.510,0:13:11.850 8 / 2 is four 100[br]/ 2 is 50. 0:13:12.970,0:13:17.002 Now we need to look at our[br]fraction. Again. We found an 0:13:17.002,0:13:20.026 equivalent fraction, but is it[br]in its lowest form? 0:13:20.830,0:13:25.241 Well again, we can see that[br]they're both even numbers, both 0:13:25.241,0:13:30.053 4 and 50 even, and so we can[br]divide by two again. 0:13:30.560,0:13:38.100 4 / 4 gives us[br]2 and 50 / 2. 0:13:38.750,0:13:44.100 Gives us 25, so another[br]equivalent fraction, but is it 0:13:44.100,0:13:46.240 in its lowest form? 0:13:46.960,0:13:53.330 Well, we need to see if there is[br]any number that goes both into 0:13:53.330,0:13:56.970 the numerator and the[br]denominator. Well, the only 0:13:56.970,0:14:02.430 numbers that go into 2A one[br]which goes into all numbers, so 0:14:02.430,0:14:09.255 that's not going to help us. And[br]two now 2 doesn't go into 25. So 0:14:09.255,0:14:14.715 therefore we found the fraction[br]in its lowest form, so 8 one 0:14:14.715,0:14:17.445 hundreds. The lowest form is 220 0:14:17.445,0:14:23.476 fifths. So when a fraction is in[br]its lowest form, the only number 0:14:23.476,0:14:27.744 that will go into both the[br]numerator and the denominator is 0:14:27.744,0:14:31.360 one. Those numbers have no other 0:14:31.360,0:14:37.375 common factor. Now if we look[br]here, we can see that in fact. 0:14:37.950,0:14:41.910 We could have divided by 4. 0:14:41.910,0:14:45.474 Straight away, instead of[br]dividing by two twice, well, 0:14:45.474,0:14:49.434 that's fine. If you've notice[br]tthat for was a factor. 0:14:49.990,0:14:54.577 Of both the numerator and the[br]denominator, you could have gone 0:14:54.577,0:15:01.249 straight there doing 8 / 4 was[br]two and 100 / 4 was 25 and then 0:15:01.249,0:15:06.670 check to see if you were in the[br]lowest form. That's fine, but 0:15:06.670,0:15:11.052 often. With numbers, larger[br]numbers is not always easy to 0:15:11.052,0:15:15.100 see what the highest common[br]factor is of these two numbers, 0:15:15.100,0:15:18.044 the numerator and the[br]denominator. So often it's 0:15:18.044,0:15:22.092 easier to work down to some[br]smaller numbers, and then you 0:15:22.092,0:15:25.772 can be certain that there are no[br]other common factors. 0:15:28.020,0:15:28.540 Now. 0:15:29.880,0:15:33.516 If we take all the[br]pieces of a fraction 0:15:33.516,0:15:37.152 like I did with my[br]chocolate, I took all 0:15:37.152,0:15:38.364 six of them. 0:15:39.760,0:15:43.596 That's the same as 6 / 6. 0:15:44.110,0:15:45.590 And that was our whole. 0:15:47.430,0:15:53.406 And any whole number can be[br]written this way, so we could 0:15:53.406,0:15:59.561 have. 3 thirds if we take all[br]the pieces, we've got one. 0:15:59.870,0:16:05.865 8 eighths, if we take all the[br]pieces, we've got one. 0:16:05.870,0:16:09.340 Now I'm going to rewrite. 0:16:09.900,0:16:13.239 Mathematical words numerator. 0:16:13.790,0:16:17.438 Divided fight denominator. 0:16:18.530,0:16:22.270 Because we're now going to 0:16:22.270,0:16:28.190 look. Add fractions[br]where the numerator. 0:16:30.490,0:16:33.938 Smaller than the denominator. 0:16:36.590,0:16:41.378 And we have a name for these[br]type of fractions and they 0:16:41.378,0:16:42.575 called proper fractions. 0:16:47.530,0:16:50.860 And examples. 0:16:50.860,0:16:52.330 Half. 0:16:53.320,0:16:58.140 3/4[br]16 0:16:59.380,0:17:06.660 7/8 5/10 and[br]seeing all these cases, the 0:17:06.660,0:17:10.060 numerator is smaller number than 0:17:10.060,0:17:16.410 the denominator. And as long as[br]that is the case, then we have a 0:17:16.410,0:17:20.730 proper fraction so we can have[br]any numbers 100 hundred and 50th 0:17:20.730,0:17:24.554 for example. Now if 0:17:24.554,0:17:30.700 the numerator.[br]Is greater than 0:17:30.700,0:17:32.820 the denominator? 0:17:36.980,0:17:41.556 Then the fraction is called[br]an improper fraction. 0:17:47.160,0:17:50.289 And some examples. 0:17:50.350,0:17:53.098 Three over two or three halfs. 0:17:53.930,0:17:59.490 7 fifths.[br]Eight quarters 0:18:00.960,0:18:03.650 We could have 12 bytes. 0:18:05.120,0:18:08.708 Or we could have 201 hundredths. 0:18:09.780,0:18:14.873 And in all these cases, the[br]numerator is larger than the 0:18:14.873,0:18:19.590 denominator. And it shows that[br]what we've got is actually more 0:18:19.590,0:18:20.619 than whole 1. 0:18:21.540,0:18:26.090 All these fractions, the[br]proper ones are smaller than a 0:18:26.090,0:18:31.095 whole one. We haven't taken[br]all of the pieces 3/4. We've 0:18:31.095,0:18:37.465 only taken 3 out of the four[br]161 out of the six, so that 0:18:37.465,0:18:41.560 all smaller than a whole one[br]with improper fractions. 0:18:42.790,0:18:45.052 They are all larger than one 0:18:45.052,0:18:50.866 whole 1. So if we take three[br]over 2 for example, what we've 0:18:50.866,0:18:52.896 actually got is 3 halfs. 0:18:54.790,0:18:58.993 Oh, improper fractions can be[br]written in this form. 0:18:59.730,0:19:05.466 All they can be written[br]as mixed fractions. 0:19:08.280,0:19:12.753 So let's have a look[br]at our three halfs. 0:19:14.450,0:19:19.078 And what we can do is put two[br]hearts together to make the 0:19:19.078,0:19:25.392 whole 1. And we've got 1/2 left[br]over, so that can be written as 0:19:25.392,0:19:26.976 one and a half. 0:19:28.040,0:19:32.324 So there are exactly the same,[br]but written in a different form 0:19:32.324,0:19:34.109 1 as a mixed fraction. 0:19:34.620,0:19:39.714 And one other top heavy[br]fraction, an improper fraction 0:19:39.714,0:19:44.242 where the numerator is larger[br]than the denominator. 0:19:46.390,0:19:48.202 Let's have a look at another 0:19:48.202,0:19:53.906 example. Let's say we[br]had 8 thirds. 0:19:53.910,0:19:55.238 This out the way. 0:19:56.780,0:20:00.320 Let's count 0:20:00.320,0:20:05.790 out 1234567.[br]8 thirds 0:20:06.900,0:20:11.047 How else can we write that?[br]How do we write that as a 0:20:11.047,0:20:11.685 mixed fraction? 0:20:13.110,0:20:16.140 Well, what we're looking[br]for is how many whole ones 0:20:16.140,0:20:17.049 we've got there. 0:20:18.310,0:20:22.398 Well, if something's been[br]divided into 3 pieces. 0:20:23.420,0:20:26.150 It takes 3 pieces to make the 0:20:26.150,0:20:28.760 whole 1. So that's one whole 1. 0:20:30.510,0:20:34.026 There we have another whole 12. 0:20:34.890,0:20:42.114 And we've got 2/3 left over,[br]so 8 thirds is exactly the 0:20:42.114,0:20:45.124 same as two and 2/3. 0:20:48.770,0:20:50.710 Let's look at one more. 0:20:51.710,0:20:55.485 Let's say we had Seven 0:20:55.485,0:21:00.999 quarters. Now we know that there[br]are four quarters in each hole, 0:21:00.999,0:21:06.446 one. So we see how many fours go[br]into Seven. Well, that's one. 0:21:06.960,0:21:13.080 And we've got 3 left over, so[br]we've got one and 3/4. 0:21:14.180,0:21:16.784 Let's have a look at one more. 0:21:18.090,0:21:21.300 37 tenths 0:21:22.920,0:21:27.892 Now we've split something up[br]into 10 pieces of equal size. 0:21:28.930,0:21:34.030 So we need 10 of those to make a[br]whole one, so we need to see how 0:21:34.030,0:21:37.030 many 10s, how many whole ones[br]there are in 37. 0:21:38.130,0:21:43.267 Well, three 10s makes 30, so[br]that's three whole ones, and 0:21:43.267,0:21:47.937 we've got 7 leftover, so we've[br]got 3 and 7/10. 0:21:49.020,0:21:52.426 Just move 0:21:52.426,0:21:59.202 those. Now let's have[br]a look at doing the reverse 0:21:59.202,0:22:05.676 process. So if we start with a[br]mixed fraction, how do we turn 0:22:05.676,0:22:08.166 it into an improper fraction? 0:22:08.740,0:22:11.902 Let's look at three and a 0:22:11.902,0:22:16.498 quarter. And if we look at this[br]visually, we've got. 0:22:17.170,0:22:18.658 3 hole once. 0:22:20.540,0:22:23.870 And one quarter. 0:22:27.500,0:22:29.432 And what we want to turn it 0:22:29.432,0:22:33.599 into. Is all[br]quarters. 0:22:34.640,0:22:36.470 So we have a whole 1. 0:22:37.360,0:22:43.769 And if we split it into[br]quarters, we know that a whole 1 0:22:43.769,0:22:45.248 needs four quarters. 0:22:45.770,0:22:47.280 So we have four there. 0:22:47.810,0:22:49.118 Another for their. 0:22:49.680,0:22:52.680 Another folder plus this one. 0:22:53.310,0:22:56.124 So we've got three force or 12. 0:22:56.640,0:23:04.032 Plus the one gives us 13[br]quarters, so 3 1/4 is exactly 0:23:04.032,0:23:07.112 the same as 13 quarters. 0:23:07.660,0:23:12.423 Well, let's have a look at how[br]you might do this. 0:23:14.000,0:23:15.500 If you haven't got the visual 0:23:15.500,0:23:21.500 aid. Well, what we've actually[br]got here is our whole number. 0:23:22.550,0:23:23.639 And the fraction. 0:23:24.240,0:23:25.940 We wanted in quarters. 0:23:27.070,0:23:30.686 So what we're doing[br]is right it again. 0:23:31.920,0:23:36.550 We're actually saying We want[br]four quarters for every hole 0:23:36.550,0:23:39.791 one, so we've got three lots of 0:23:39.791,0:23:44.910 four. And then what were[br]ranting on is our one, and 0:23:44.910,0:23:46.378 these are all quarters. 0:23:47.600,0:23:51.425 So it's the whole number[br]multiplied by the denominator. 0:23:52.460,0:23:56.930 We've added the extra that[br]we have here. Whatever this 0:23:56.930,0:24:01.400 number is, and those are the[br]number of quarters we've 0:24:01.400,0:24:07.211 got. So we've got our 3/4 of[br]12 + 1/4, so 13 quarters. 0:24:08.940,0:24:10.956 Let's have a look at one more 0:24:10.956,0:24:16.478 example. Let's say we've got[br]five and two ninths. 0:24:18.310,0:24:21.086 We want to turn it[br]into this format. 0:24:22.360,0:24:28.632 Ninths well, if we want to take[br]a whole one, we wouldn't need 9 0:24:28.632,0:24:34.904 ninths and we've got five whole[br]ones, so we're going to have 5 * 0:24:34.904,0:24:37.592 9 lots of 9th this time. 0:24:38.250,0:24:42.660 And then we need to add on the[br]two nights that we have here. 0:24:42.670,0:24:50.530 So 5 nines of 45 plus[br]the two and that all 9th. 0:24:50.530,0:24:53.805 So we have 47 ninths. 0:24:57.170,0:25:00.734 Any whole number can be written[br]as a fraction. 0:25:01.270,0:25:04.078 So for example, if we take[br]the number 2. 0:25:05.930,0:25:10.097 If we write it with the[br]denominator of one. 0:25:11.580,0:25:13.860 We've written it as a fraction. 0:25:15.050,0:25:20.143 And any equivalent form, so we[br]could have 4 over 2. 0:25:20.770,0:25:24.370 30 over 0:25:24.370,0:25:31.193 15. And so on.[br]So any whole number can be 0:25:31.193,0:25:35.963 written as a fraction with a[br]numerator and a denominator. 0:25:37.560,0:25:45.186 So fractions.[br]They can appear in a number 0:25:45.186,0:25:50.460 of different forms. You might[br]see proper fractions, improper 0:25:50.460,0:25:52.218 fractions, mixed fractions. 0:25:53.060,0:25:57.272 And you can see lots of[br]different equivalent fractions. 0:25:57.870,0:26:00.255 So that all different[br]ways that we see them.