0:00:01.480,0:00:05.791 Now we're going to look at[br]multiplying and dividing 0:00:05.791,0:00:12.248 fractions. Let's start with[br]4 * 1/3. 0:00:13.010,0:00:17.000 That means for lots of 1/3. 0:00:17.830,0:00:24.444 So. There I[br]have for lots of 1/3. 0:00:25.460,0:00:32.492 So I've got 1/3 + 1/3[br]+ 1/3 plus another third and 0:00:32.492,0:00:36.008 I've got a total of 4 0:00:36.008,0:00:41.177 thirds. Or if I put them as[br]a mixed fraction. 0:00:42.060,0:00:45.188 That's one and 1/3. 0:00:45.870,0:00:49.836 And that's exactly the same as 0:00:49.836,0:00:53.800 that. Usual multiplication if we 0:00:53.800,0:00:58.380 have. 4 * 5 for[br]example. 0:00:59.670,0:01:06.660 That means I've got five at 5 at[br]five at 5, which gives me 20. 0:01:08.190,0:01:10.577 Fractions work in exactly[br]the same way. 0:01:11.770,0:01:17.720 So if I had[br]2 * 1/5. 0:01:17.720,0:01:20.928 I'd have 1/5 + 0:01:20.928,0:01:23.918 1/5. Giving me to 5th. 0:01:25.700,0:01:31.052 Now multiplication is[br]commutative. I just write that 0:01:31.052,0:01:33.059 word down commutative. 0:01:35.940,0:01:37.680 Now that means in now. 0:01:38.200,0:01:41.775 Normal multiplication that 4 * 0:01:41.775,0:01:47.384 5. Is exactly the same[br]as 5 * 4. 0:01:48.050,0:01:55.550 Are 4 * 5 was 5[br]+ 5 + 5 + 5. 0:01:56.130,0:02:03.890 And our 5 * 4 or 5 lots[br]of four is 4 + 4 + 4 0:02:03.890,0:02:10.680 + 4 + 4, so we have 4[br]five times and they are exactly 0:02:10.680,0:02:13.105 the same, giving us 20. 0:02:14.070,0:02:19.602 So it doesn't matter[br]whether I write 4 * 5 or 5 0:02:19.602,0:02:22.368 * 4 because multiplication[br]is commutative. 0:02:23.830,0:02:27.229 Well, let's see what that means[br]when we're looking at fractions. 0:02:27.980,0:02:31.800 Let's say I have six 0:02:31.800,0:02:35.770 times third. Multiplication is 0:02:35.770,0:02:42.460 commutative. So that says it[br]should be the same as 1/3 * 6. 0:02:43.260,0:02:50.460 Let's have a look[br]what that means. Six 0:02:50.460,0:02:54.060 times the third 123456. 0:02:54.780,0:03:02.556 So there's a third[br]plus 1/3 third, 3rd, 0:03:02.556,0:03:05.472 third, plus 1/3. 0:03:06.060,0:03:12.378 On this side, I've got[br]a third of six. 0:03:13.170,0:03:16.341 So let's take 0:03:16.341,0:03:17.398 612. 0:03:18.160,0:03:22.110 34 56 0:03:23.360,0:03:29.072 And I want a third of that six,[br]so it's like sharing it out 0:03:29.072,0:03:30.296 between three people. 0:03:31.320,0:03:33.725 There's one person's another and 0:03:33.725,0:03:37.290 another. I want 1/3 so I'll just 0:03:37.290,0:03:41.110 remove. The other 2/3. 0:03:41.110,0:03:43.230 So my third of six. 0:03:43.860,0:03:45.700 Is just like doing 6. 0:03:46.300,0:03:48.868 Divided by three. 0:03:49.380,0:03:51.004 And that gives us an answer of 0:03:51.004,0:03:58.298 2. Well, what's my 1/3[br]add 1 third at 1/3? 0:03:58.940,0:04:01.370 And, uh, the others together. 0:04:01.930,0:04:09.850 And there I have two, so[br]here 12345 I get 6 thirds 0:04:09.850,0:04:12.490 which gives Me 2. 0:04:13.020,0:04:15.545 So I've shown that with 0:04:15.545,0:04:19.438 fractions. It's exactly the[br]same, it's commutative. 0:04:20.010,0:04:24.282 And that's what it looks like.[br]But with fractions you can see 0:04:24.282,0:04:26.418 it in the two different ways. 0:04:26.960,0:04:29.399 Either a fraction. 0:04:29.920,0:04:31.288 Of a whole number. 0:04:31.800,0:04:33.200 Like we had here. 0:04:34.610,0:04:39.410 Or a fraction taking a[br]whole number of times like 0:04:39.410,0:04:40.850 we had here. 0:04:42.730,0:04:45.190 You guys out of the way. 0:04:46.700,0:04:53.966 Let's look at[br]another example, 5 0:04:53.966,0:04:57.350 lots. Of 2/3. 0:04:58.390,0:05:05.830 So we've got[br]2/3 five times. 0:05:12.820,0:05:20.338 So what we have here is 2[br]+ 2 + 2 + 2 + 0:05:20.338,0:05:23.560 2 or actually 5 * 2. 0:05:24.170,0:05:28.688 Thirds so we've[br]got 10 thirds. 0:05:29.740,0:05:32.084 And 10 thirds if we write it as 0:05:32.084,0:05:37.240 a mixed fraction. Is 3 whole[br]ones is 3 threes and nine and 0:05:37.240,0:05:38.712 one third left over. 0:05:41.960,0:05:44.732 Now any number can be[br]written as a fraction. 0:05:46.420,0:05:49.780 For example, the number 0:05:49.780,0:05:54.995 2. Can be written as[br]two over 1. 0:05:55.500,0:05:58.269 For over 2. 0:05:58.880,0:06:00.938 6 over 3. 0:06:01.520,0:06:05.405 And so on. So we can write a 0:06:05.405,0:06:10.110 whole number. With a[br]denominator, so it's a numerator 0:06:10.110,0:06:14.610 and denominator, and these are[br]all equivalent fractions to that 0:06:14.610,0:06:15.960 two over 1. 0:06:17.030,0:06:20.414 So another example, 2 0:06:20.414,0:06:27.620 * 3/4. We can write[br]as two over one, so we've made 0:06:27.620,0:06:29.048 our whole number. 0:06:29.600,0:06:31.208 Into a fraction. 0:06:32.110,0:06:35.220 Times 3/4. 0:06:37.960,0:06:41.544 So what we have here is 2 * 0:06:41.544,0:06:45.356 3. And 1 * 0:06:45.356,0:06:53.057 4. So 2 threes giving A6[br]and once for four. And if we put 0:06:53.057,0:06:59.284 this as a fraction in its lowest[br]form, then we divide both the 0:06:59.284,0:07:05.032 numerator and the denominator by[br]two. So we get three over 2. 0:07:05.710,0:07:10.435 Or as a mixed[br]fraction 1 1/2. 0:07:12.240,0:07:19.359 Let's look at another[br]example. This time 7 * 0:07:19.359,0:07:20.941 5 ninths. 0:07:22.160,0:07:28.606 So let's turn our Seven into[br]an equivalent fraction with. One 0:07:28.606,0:07:30.364 is the denominator. 0:07:31.030,0:07:34.290 Multiplied by five nights. 0:07:35.630,0:07:38.330 So we've got 7 * 5. 0:07:38.890,0:07:42.150 Over 1 * 9. 0:07:42.690,0:07:48.780 So we have[br]35 over 9. 0:07:48.870,0:07:50.750 Or as a mixed number. 0:07:52.660,0:07:57.968 That's three. And[br]eight ninths. 0:07:59.880,0:08:05.916 Now let's have a look at an[br]example where we're finding a 0:08:05.916,0:08:07.928 fraction multiplied by another 0:08:07.928,0:08:14.706 fraction. So let's take[br]1/3 * 1/2. 0:08:16.430,0:08:20.500 And this means we want to take[br]1/3 of 1/2. 0:08:22.060,0:08:23.368 So there's a half. 0:08:24.170,0:08:31.046 And we want to split it[br]up into 3 equal pieces. Let's 0:08:31.046,0:08:36.203 look numerically what we were[br]doing before multiplying the 0:08:36.203,0:08:38.495 numerators and multiplying the 0:08:38.495,0:08:46.014 denominators. So 1 * 1 is one[br]and 3 * 2 is 6, so we 0:08:46.014,0:08:48.269 get an answer of 1/6. 0:08:49.080,0:08:52.460 Well, let's have a look. If we[br]put some 6. 0:08:53.420,0:08:55.170 On here we can see. 0:08:55.680,0:08:59.285 36 is the same as a half. 0:09:00.300,0:09:03.780 So if we split 1/2 into 3 equal 0:09:03.780,0:09:09.190 sized pieces. And we want 1/3.[br]We want one of those pieces. 0:09:09.190,0:09:11.045 Then we get one 6th. 0:09:12.710,0:09:15.812 Let's look at 0:09:15.812,0:09:22.116 another example.[br]Let's do 1/3 0:09:22.116,0:09:24.360 * 2/5. 0:09:26.180,0:09:32.102 So this time we want a[br]third of 2/5. 0:09:32.980,0:09:34.708 So there's 2/5. 0:09:36.110,0:09:38.084 And we want to split it into. 0:09:38.900,0:09:41.688 Three equally sized pieces. 0:09:43.500,0:09:47.300 Let's have a look again[br]numerically and then look to 0:09:47.300,0:09:49.500 see. What we get visually. 0:09:50.430,0:09:53.790 So 1 * 2 we multiply the 0:09:53.790,0:10:01.280 numerators. 3 * 5 multiplied[br]the denominators once too is 2, 0:10:01.280,0:10:08.375 three 5:15. So the answer is[br]2. Fifteenths. Well, how does 0:10:08.375,0:10:10.310 that come about? 0:10:11.750,0:10:18.390 Well. Instead of trying to[br]split those 2/5 into 3 pieces, 0:10:18.390,0:10:23.956 is actually much easier to[br]imagine it as splitting 1/5 into 0:10:23.956,0:10:30.171 3 pieces. The other fifth into[br]three pieces, and then taking 0:10:30.171,0:10:32.047 one section from each. 0:10:33.800,0:10:34.928 If we split. 0:10:35.580,0:10:40.896 5th into three pieces instead of[br]five pieces, making it a whole 0:10:40.896,0:10:45.562 1. Well, actually have 15[br]pieces making our whole one 0:10:45.562,0:10:49.442 'cause they'll be 3 pieces[br]from each of the fifths. 0:10:50.580,0:10:55.364 So that's where our 15th comes[br]from, and then we take one of 0:10:55.364,0:10:59.412 the three pieces from this[br]fifth and one of the three 0:10:59.412,0:11:03.092 pieces from this 5th, which[br]gets us are two fifteenths. 0:11:04.340,0:11:08.480 Let's do a few more[br]examples. 0:11:09.920,0:11:13.442 Let's say we have 2/5 * 0:11:13.442,0:11:19.562 4 ninths. So what we're doing[br]each time it was when 0:11:19.562,0:11:22.838 multiplying the numerators[br]together, and we're multiplying 0:11:22.838,0:11:24.242 their denominators together. 0:11:25.010,0:11:32.160 240859.[br]A 45 so we have 0:11:32.160,0:11:33.640 840 fifths. 0:11:34.760,0:11:40.478 And another one 2/3[br]* 4/5. 0:11:43.110,0:11:46.080 So we've got 2 * 4. 0:11:46.660,0:11:49.410 Divided by 3 * 5. 0:11:50.160,0:11:56.970 2 falls right three 5:15[br]so we have eight fifteenths. 0:11:58.830,0:12:04.077 Now, if we just think about[br]what we've been doing here, 0:12:04.077,0:12:07.893 we've been taking a fraction[br]of another fraction. 0:12:09.100,0:12:13.030 And because the fractions we've[br]been dealing with our proper 0:12:13.030,0:12:17.746 fractions there less than one,[br]so 2/3 is less than one. We're 0:12:17.746,0:12:22.462 taking 2/3 of four fifths. Then[br]we expect an answer that smaller 0:12:22.462,0:12:26.785 because we're taking a fraction[br]of the four fifths, or a 0:12:26.785,0:12:31.894 fraction of the four nights. So[br]in all these cases, we have an 0:12:31.894,0:12:35.824 answer which is actually smaller[br]than the fraction we started 0:12:35.824,0:12:40.147 with, which is what we expect is[br]we're taking a fraction. 0:12:40.210,0:12:42.190 Smaller fraction of it. 0:12:43.100,0:12:45.640 Let's do another example. 0:12:46.570,0:12:52.499 This time let's have[br]2/3 * 9/10. 0:12:54.040,0:13:00.110 So we have 2 * 9[br]/ 3 * 10. 0:13:01.470,0:13:05.930 290 eighteen[br]three tens 30. 0:13:06.950,0:13:12.900 Now we need to realize that this[br]is not a fraction in its lowest 0:13:12.900,0:13:18.425 form, so we would need to find[br]the lowest form the both even 0:13:18.425,0:13:23.100 numbers. So we can divide both[br]numerator and denominator by two 0:13:23.100,0:13:24.800 and get 9 fifteenths. 0:13:25.740,0:13:31.746 But let's just look back at this[br]stage. If I write it out again. 0:13:31.750,0:13:34.798 And we could have avoided that. 0:13:35.320,0:13:40.180 Because what we can do is some[br]counseling before we actually do 0:13:40.180,0:13:45.367 the calculation. We can see[br]we've got a 9 here and the three 0:13:45.367,0:13:49.411 here so we can divide both the[br]numerator and the denominator by 0:13:49.411,0:13:54.370 three. When we divide the[br]numerator by three 3, three to 0:13:54.370,0:13:58.627 nine goes three times. When we[br]divide the denominator by three, 0:13:58.627,0:13:59.788 it goes once. 0:14:00.420,0:14:04.424 And if we look further, we can[br]see that we can also divide by 0:14:04.424,0:14:11.048 two. Two goes into two once and[br]two goes into 10 five times. 0:14:11.810,0:14:19.118 So this is actually 1 * 3 / 1[br]* 5 and we get 3/5 and in fact 0:14:19.118,0:14:23.178 you can see here that I didn't[br]look closely enough. 0:14:23.810,0:14:28.990 And divide in fact by three.[br]It's easy to miss. So if you can 0:14:28.990,0:14:33.060 make it easier for yourself and[br]do some counseling, then you 0:14:33.060,0:14:36.020 should do so. So we end up with 0:14:36.020,0:14:43.131 3/5. Let's look at[br]one more, this time 0:14:43.131,0:14:48.369 involving three[br]fractions. So let's have 0:14:48.369,0:14:50.988 1/2 * 3/4. 0:14:52.060,0:14:54.658 Multiplied by 2/3. 0:14:55.360,0:14:59.152 Exactly the same process as[br]before when multiplying 0:14:59.152,0:15:03.418 fractions, so we multiply the[br]numerators doesn't matter how 0:15:03.418,0:15:07.210 many there are, so it's 1 * 3 0:15:07.210,0:15:14.586 * 2. And we multiply the[br]denominators so it's 2 * 4 * 3. 0:15:15.110,0:15:18.830 Now before we go any further,[br]let's have a look if there's 0:15:18.830,0:15:20.070 anything we can cancel. 0:15:20.660,0:15:25.249 Well, yes, we've got two goes[br]into two. Once two goes into two 0:15:25.249,0:15:28.670 once. We can divide by 0:15:28.670,0:15:36.130 three. So we end up with 1[br]* 1 * 1. The top that's one and 0:15:36.130,0:15:41.098 1 * 4 * 1. Just giving us an[br]answer of 1/4. 0:15:42.860,0:15:48.138 OK, So what happens when we have[br]mixed fractions and we want to 0:15:48.138,0:15:52.854 multiply them? Well, let's have[br]a look at some examples. 0:15:53.830,0:15:59.366 We've got two and assert[br]multiplied by 3/4. 0:16:00.420,0:16:05.659 Well, what we need to do is to[br]turn this mixed fraction into 0:16:05.659,0:16:09.689 an improper fraction, because[br]when we've done that, we can 0:16:09.689,0:16:13.719 simply do as well do what[br]we've already been doing, 0:16:13.719,0:16:16.137 multiply the numerators[br]multiplied the denominators. 0:16:17.370,0:16:22.844 So here we need to turn our two[br]whole ones into thirds, so it 0:16:22.844,0:16:27.536 needs to go over three, so two[br]whole ones times by three. 0:16:28.200,0:16:31.872 Then at this one here, and[br]that's how many thirds we have. 0:16:32.970,0:16:35.529 Multiplied by 3/4. 0:16:37.020,0:16:43.257 236 plus one so that[br]7 thirds times 3/4. 0:16:44.290,0:16:50.637 Three goes into three, once in[br]2, three once, so having 0:16:50.637,0:16:56.984 cancelled, we end up with Seven[br]quarters or one and 3/4. 0:16:57.830,0:17:03.242 One[br]more 0:17:03.242,0:17:08.610 example.[br]One and 2/5. 0:17:09.410,0:17:13.550 Multiplied by[br]two and five 6. 0:17:15.710,0:17:19.490 Again, mixed fractions need to[br]be turned into improper 0:17:19.490,0:17:22.230 fractions. So here we have. 0:17:22.910,0:17:26.834 1 * 5 'cause that[br]tells us how many. 0:17:28.110,0:17:33.479 5th we have with our whole 1[br]five of them, plus the two 0:17:33.479,0:17:37.609 that's our total number of[br]fifths multiplied by. We need 0:17:37.609,0:17:43.391 the two whole ones in terms of[br]Sixths, so that's two lots of 6. 0:17:44.110,0:17:45.898 Plus the five. 0:17:46.550,0:17:49.268 And that's a number of 6th. 0:17:50.510,0:17:57.422 Once five is 5 + 2[br]is 7 Seven fifths multiplied by 0:17:57.422,0:18:04.334 two, 6 is a 12 plus[br]the five is 17 / 6. 0:18:05.510,0:18:11.555 Quick check now. There's nothing[br]we can cancel their so 7 * 17. 0:18:12.090,0:18:18.399 Seven 10s of $0.77 of[br]49. So it's 119. 0:18:18.560,0:18:22.204 Six 5:30 so it's 0:18:22.204,0:18:27.837 119th 30th. And we[br]had mixed fractions to start 0:18:27.837,0:18:31.446 with, so let's turn this back[br]into mixed fractions. 0:18:32.030,0:18:36.750 Well, three 30s are 90, so[br]that's three whole ones. 0:18:37.330,0:18:41.840 And 20 nine 30th[br]leftover. 0:18:43.080,0:18:47.336 So to multiply fractions,[br]you multiply the numerators 0:18:47.336,0:18:51.060 together, and you multiply[br]the denominators together. 0:18:52.140,0:18:55.847 If you start with a mixed[br]fraction, you need to turn 0:18:55.847,0:18:59.217 it to an improper fraction[br]first before you do the 0:18:59.217,0:18:59.554 multiplication. 0:19:00.720,0:19:04.576 Let's go on to 0:19:04.576,0:19:05.540 division. 0:19:06.100,0:19:14.489 1/4[br]Divided by two. 0:19:15.460,0:19:17.970 So we'll look at 1/4. 0:19:19.300,0:19:21.940 We want to split it up into two 0:19:21.940,0:19:25.208 pieces. So 2 equal pieces. 0:19:26.530,0:19:29.038 Well, 2 equal pieces. 0:19:29.840,0:19:33.368 That's two equal pieces[br]fitting on top. 0:19:36.350,0:19:42.530 Each one is 1/8, so we split it[br]in half and we've got eights. If 0:19:42.530,0:19:45.002 you can imagine our whole 1. 0:19:46.150,0:19:48.280 And we had four quarters. 0:19:50.050,0:19:55.570 If we have eighths, we have[br]eight pieces, each one is an 0:19:55.570,0:19:59.710 eighth, so 2 eighths fit into[br]1/4, so 1/4. 0:20:00.230,0:20:03.954 Divided into 2 bits[br]gives us 1/8. 0:20:07.700,0:20:10.680 Now dividing by two. 0:20:11.490,0:20:14.310 Is the same. 0:20:14.370,0:20:17.100 Is multiplying. 0:20:18.590,0:20:19.660 By half 0:20:22.730,0:20:27.160 So quarter Divided by[br]two. 0:20:28.340,0:20:31.958 Is equal to the same as 0:20:31.958,0:20:37.010 a quarter? Multiplied[br]by half. 0:20:38.490,0:20:40.365 I went back to multiplying 0:20:40.365,0:20:46.210 fractions. What's 1 *[br]1 at the top and 4 * 0:20:46.210,0:20:48.625 2 giving us our 8th? 0:20:49.840,0:20:54.823 So this statement here is[br]exactly the same as this one 0:20:54.823,0:20:57.088 here, because dividing by two. 0:20:57.700,0:21:00.150 Is the same as[br]multiplying by half. 0:21:02.180,0:21:07.207 Let's have a look at another[br]example, a third this time. 0:21:07.900,0:21:10.648 Divided by 4. 0:21:12.450,0:21:15.138 So we want to split our third. 0:21:15.950,0:21:17.660 Into four pieces. 0:21:20.100,0:21:22.520 Well, dividing by 4. 0:21:23.550,0:21:26.628 This is the same as multiplying 0:21:26.628,0:21:33.690 by quarter. So what we have[br]is 1 * 1 for 0:21:33.690,0:21:40.509 the numerator. And 3 *[br]4 which is 12 for the 0:21:40.509,0:21:44.677 denominator. So we're third[br]split into four pieces. 0:21:45.300,0:21:46.740 Gives us a 12th. 0:21:47.780,0:21:49.440 Again, if you sync. 0:21:50.670,0:21:54.430 Of each of these thirds being[br]split into four pieces. 0:21:55.080,0:21:59.373 We've got for their for[br]their, for their, so 0:21:59.373,0:22:01.758 our whole is 12 pieces. 0:22:04.220,0:22:06.470 And we've taken one of them[br]because we wanted. 0:22:07.990,0:22:13.870 1/3 / 1/4 divided into 4 bits.[br]So we take one of them, so we've 0:22:13.870,0:22:15.046 got a 12th. 0:22:20.420,0:22:28.020 Let's do 1/2 / 2[br]back to an easier one 0:22:28.020,0:22:34.436 to see. There's a half split it[br]into and we all know what we 0:22:34.436,0:22:37.660 get. Well, let's do it. 0:22:38.400,0:22:42.998 Are divided by two is the same[br]as multiplying by 1/2? 0:22:43.670,0:22:49.410 1/2 * 1/2 one times one is 122[br]to four 1/4, which exactly what 0:22:49.410,0:22:53.920 we expected. Cut 1/2 in two and[br]you get a quarter. 0:22:54.850,0:22:59.803 Now as we can write any whole[br]number as a fraction, I could 0:22:59.803,0:23:01.708 write this as a half. 0:23:02.210,0:23:05.350 Divided by two over 1. 0:23:06.250,0:23:11.164 And then what's happening[br]here is what I'm doing 0:23:11.164,0:23:16.078 when I multiply is. I'm[br]turning this upside down. 0:23:17.340,0:23:24.594 So to divide fractions, what you[br]do is you take the divisor, the 0:23:24.594,0:23:27.384 one that's doing the Dividing. 0:23:28.090,0:23:30.148 And you turn it upside down. 0:23:30.740,0:23:31.850 And you multiply. 0:23:32.480,0:23:36.170 Let's do some 0:23:36.170,0:23:42.830 more examples. Let's[br]do 1/2 divided 0:23:42.830,0:23:44.930 by quarter. 0:23:48.520,0:23:49.888 So we have 1/2. 0:23:50.500,0:23:52.688 We take the divisor. 0:23:53.290,0:23:57.690 We turn it upside down and[br]instead of dividing, we 0:23:57.690,0:24:04.255 multiply. So what we have here[br]is 1 * 4 over 2 * 1, which is 0:24:04.255,0:24:06.810 2. So we end up with two. 0:24:07.630,0:24:12.050 So 1/2 /, 1/4? Well, let's just[br]look at that. 0:24:12.580,0:24:18.924 That's a half, and that's saying[br]how many times does 1/4 fit into 0:24:18.924,0:24:25.720 a half? Well, we know that[br]I've quarter fits into our half 0:24:25.720,0:24:28.974 two times. And that's the answer 0:24:28.974,0:24:36.300 we had. 3rd divided[br]by a fifth 0:24:36.300,0:24:42.881 this time. So we've[br]got a third and we take the 0:24:42.881,0:24:46.562 divisor. We turn it upside down[br]and we multiply. 0:24:47.490,0:24:54.540 So we end up with[br]five thirds, or one and 0:24:54.540,0:24:58.752 2/3. So what we're saying is,[br]we've got a third. 0:25:00.350,0:25:01.910 How many fifths? 0:25:02.610,0:25:04.478 Fit into a third. 0:25:07.200,0:25:10.548 Well, those are 5th. 0:25:11.230,0:25:15.780 Well, we can see that it goes[br]one whole one and part leftover. 0:25:15.780,0:25:19.280 It doesn't go as much as twice.[br]It's part leftover. 0:25:19.910,0:25:24.240 So there's our answer[br]one and 2/3, so it goes 0:25:24.240,0:25:26.405 the whole time and 2/3. 0:25:27.760,0:25:35.260 Let's look at a whole number[br]now divided by a fraction. So 0:25:35.260,0:25:39.010 let's look at 2 / 1/8. 0:25:39.770,0:25:41.750 So we're saying we've got two 0:25:41.750,0:25:46.731 whole ones. And we want to know[br]how many eighths fit into the 0:25:46.731,0:25:50.823 two whole ones. Well, if we[br]think about it, we know that 0:25:50.823,0:25:53.551 there are 8 eights in a whole 1. 0:25:54.470,0:26:00.224 So if we've got two whole ones,[br]there must be 16 eighths, so we 0:26:00.224,0:26:02.279 know our answer is 16. 0:26:03.600,0:26:07.740 Well, let's see what that looks[br]like if we use our rule. 0:26:09.030,0:26:11.250 So we take out two. 0:26:12.880,0:26:17.148 The divisor is our 8th,[br]so we turn it upside down 0:26:17.148,0:26:21.416 and we multiply. And yet[br]we've got 2, eight, 416 / 0:26:21.416,0:26:23.744 1 and we get our 16. 0:26:25.330,0:26:28.360 Let's do 4. 0:26:29.140,0:26:31.000 Divided by 1/3. 0:26:35.070,0:26:40.389 So how many thirds fit into[br]four whole ones? 0:26:41.460,0:26:45.588 We know that there are three[br]thirds in each hole. One, and 0:26:45.588,0:26:47.308 we've got four of them. 0:26:48.230,0:26:50.582 So we're going to end up with an 0:26:50.582,0:26:56.430 answer of 12. But again, let's[br]look at that using our method. 0:26:56.430,0:26:59.130 Here we multiply an we turn. 0:26:59.740,0:27:03.907 The divisor upside down. So yes,[br]we get 12. 0:27:04.730,0:27:09.149 Now so far without division,[br]we've only looked at. 0:27:10.210,0:27:12.450 Fractions with[br]numerators of one. 0:27:14.040,0:27:16.398 Let's now look at some others. 0:27:17.280,0:27:21.200 Let's say we've got 0:27:21.200,0:27:24.088 3/4. Divided by two. 0:27:25.250,0:27:29.288 Same message[br]3/4. 0:27:30.950,0:27:38.165 We can write the whole 1 as a[br]fraction so it's two over one to 0:27:38.165,0:27:42.975 divide which in the divisor[br]upside down and we multiply. 0:27:42.980,0:27:49.892 So we have 3 * 1 three over 2[br]floors are eight, so we have an 0:27:49.892,0:27:55.508 answer of 3/8 and if we think[br]about it, if you visualize 3/4 0:27:55.508,0:27:57.668 and splitting it in half. 0:27:58.230,0:28:00.680 Quarter, split in half eighths. 0:28:01.470,0:28:05.488 3/4 split in half will[br]be 3/8. 0:28:06.930,0:28:10.158 3/5 this time. 0:28:11.910,0:28:15.120 Divided by 4. 0:28:16.080,0:28:22.920 So we're taking 3/5 splitting[br]up into four pieces. What 0:28:22.920,0:28:26.340 do we end up with? 0:28:26.640,0:28:33.860 3/5 We going to[br]divide by. Let's put it as a 0:28:33.860,0:28:35.852 fraction 4 over 1. 0:28:35.890,0:28:42.830 Turn the divisor upside down[br]and multiply so we have 0:28:42.830,0:28:49.770 3 * 1 is 3[br]over 4 fives a twentieths. 0:28:49.770,0:28:53.282 One more 0:28:53.282,0:28:56.810 example. 2/3 0:28:58.030,0:29:01.580 Divided by. 3/4 0:29:04.180,0:29:06.200 What we're looking at here? 0:29:07.430,0:29:09.029 Those are 2/3. 0:29:10.370,0:29:14.096 We want to know there's 3/4. 0:29:15.140,0:29:18.848 How many times 3/4? 0:29:19.540,0:29:21.439 Fits into 2/3. 0:29:22.020,0:29:25.400 Well, you can see it doesn't go[br]a whole 1. 0:29:26.050,0:29:30.307 So we can expect our answer to[br]be less than one. 0:29:30.960,0:29:36.922 Because 3/4 is actually bigger[br]than 2/3. Well, let's have a 0:29:36.922,0:29:43.436 look. 2/3 turn the[br]divisor upside down and 0:29:43.436,0:29:49.584 multiply. So we have two falls[br]at 8 and 3 threes and nine so we 0:29:49.584,0:29:54.218 get 8 ninths, 9 nights or whole[br]one. So it's just under a whole 0:29:54.218,0:29:58.852 one which is what we can see[br]when we look at it visually. How 0:29:58.852,0:30:00.838 many times this fits into this? 0:30:01.610,0:30:08.270 Finally, how do we deal[br]with mixed fractions? Well, 0:30:08.270,0:30:15.670 let's have a look at[br]an example. We've got one 0:30:15.670,0:30:19.370 and 2/3 /, 2 1/4. 0:30:19.460,0:30:25.674 And it's exactly the same as we[br]did before. We must turn mixed 0:30:25.674,0:30:29.498 fractions into improper[br]fractions before we do the 0:30:29.498,0:30:31.888 division. So one and 2/3. 0:30:32.470,0:30:39.197 Is one lot of[br]3 + 2/3. 0:30:39.200,0:30:44.696 Divided by two and a quarter[br]turn the two whole ones into 0:30:44.696,0:30:50.192 quarters. That's 2 * 4. Add the[br]1/4. That's how many quarters 0:30:50.192,0:30:57.566 we've got. Once three is[br]3 + 2, is 5 thirds 0:30:57.566,0:31:01.370 divided by 248 Plus One is 0:31:01.370,0:31:08.753 nine quarters. To divide, we[br]turn the divisor upside down and 0:31:08.753,0:31:14.036 we multiply so that becomes[br]multiplied by 4. Ninths. 0:31:14.820,0:31:17.277 Can we do any counseling now? We 0:31:17.277,0:31:20.200 can't. Four 520 0:31:20.700,0:31:26.244 Three 927 Seven answer of[br]2020 sevenths. 0:31:27.620,0:31:33.276 And another[br]example, 2 0:31:33.276,0:31:38.932 4/5 /[br]4 and 0:31:38.932,0:31:44.337 2/3. We need to[br]turn these into improper 0:31:44.337,0:31:49.869 fractions, so we've got two lots[br]of five. That's the whole ones 0:31:49.869,0:31:54.479 turned into fifths. Plus the[br]four. That's how many fifths 0:31:54.479,0:32:00.011 we've got divided by four whole[br]ones. We need them turned into 0:32:00.011,0:32:02.316 thirds. That's 4 * 3. 0:32:03.080,0:32:06.335 Plus the two, that's how[br]many thirds. 0:32:07.750,0:32:14.490 2 fives are 10 +[br]4 is 14 fifths divided 0:32:14.490,0:32:20.556 by 3/4 of 12 +[br]2 is 14 thirds. 0:32:21.100,0:32:27.196 To divide fractions, you[br]turn the divisor upside 0:32:27.196,0:32:30.244 down and you multiply. 0:32:31.280,0:32:35.965 Check for. Anything that's[br]common to both so we can divide 0:32:35.965,0:32:38.170 through here by 14. That saves a 0:32:38.170,0:32:43.046 lot of calculation. And we[br]end up with once three is 3 0:32:43.046,0:32:46.786 at the top five 15. So an[br]answer of 3/5.