WEBVTT 00:00:02.640 --> 00:00:04.640 Amelia is entering a baking contest. 00:00:04.640 --> 00:00:08.560 She wants to make a total of six pies so that she can choose the best one as her entry. 00:00:09.200 --> 00:00:16.840 If the recipe for one pie calls for two and a quarter cups of flour, and she has 14 cups in total, how many cups of flour will she have left? 00:00:18.680 --> 00:00:25.760 So if we take a look at this problem, we can see that there is a proportional relationship between the number of pies and the cups of flour needed. 00:00:26.240 --> 00:00:33.680 So if Amelia needs two and quarter cups of flour for one pie, then what calculation will we need to carry out to find out how to solve this problem? 00:00:35.360 --> 00:00:39.680 Well, what we want to do first of all is find out how many cups of flour are required for six pies. 00:00:40.000 --> 00:00:42.520 So we’re gonna do six multiplied by two and a quarter. 00:00:44.120 --> 00:00:47.400 What we’re gonna look at is take a look at a couple of ways we can carry out this calculation. 00:00:48.280 --> 00:00:56.320 So first of all, in the calculation on the left-hand side, what we’re going to do is convert two and a quarter into a top-heavy or improper fraction. 00:00:57.680 --> 00:01:01.840 So when we do that, we’re gonna get six multiplied by nine over four or nine-quarters. 00:01:03.160 --> 00:01:06.600 And we got that because there are eight-quarters in two whole ones. 00:01:07.040 --> 00:01:08.120 And then we’ve got one other quarter. 00:01:08.120 --> 00:01:09.720 So, that’s nine-quarters or nine over four. 00:01:10.440 --> 00:01:12.400 Also, we can think about it in the way that was shown in pink. 00:01:12.920 --> 00:01:19.240 And that is we multiply our integer value by the denominator, so here two multiplied by four. 00:01:19.680 --> 00:01:22.160 Then we add on what the numerator was, which in this case was one. 00:01:22.560 --> 00:01:24.240 And then we put it over the original denominator. 00:01:24.520 --> 00:01:26.680 Okay, so we’ve got six multiplied by nine over four. 00:01:28.360 --> 00:01:30.760 So what we can do first of all is cross cancel. 00:01:31.240 --> 00:01:36.200 So we can divide six and our four, because that’s on the denominator, by two. 00:01:36.400 --> 00:01:38.160 And when we do that, we get three and two. 00:01:38.160 --> 00:01:43.800 So we’ve got three multiplied by nine over two, which is gonna give us 27 over two. 00:01:44.400 --> 00:01:51.280 And that’s because what we do is we multiply the three by the nine because we can think of three as three over one. 00:01:51.520 --> 00:01:54.880 So if we multiply fractions, we multiply the numerators then multiply the denominators. 00:01:55.080 --> 00:01:59.960 So we’d have three multiplied by nine, as we said, which gives us our 27, and then one multiplied by two, which gives us two. 00:02:01.280 --> 00:02:05.120 So we’ve got 27 over two, which is an improper fraction. 00:02:05.720 --> 00:02:08.200 So, what are we gonna do now to turn us back into a mixed number? 00:02:10.080 --> 00:02:13.560 Well, two goes into 27 13 times with one left over. 00:02:13.800 --> 00:02:15.400 So we’re gonna get 13 and a half. 00:02:15.640 --> 00:02:16.200 Okay, great. 00:02:16.760 --> 00:02:18.160 So let’s have a quick look at the other method. 00:02:19.720 --> 00:02:21.640 Well, the other method is to split it into parts. 00:02:21.640 --> 00:02:25.440 So first of all, we have six multiplied by two, and then we add six multiplied by a quarter. 00:02:26.000 --> 00:02:27.680 Well, six multiplied by two is 12. 00:02:29.360 --> 00:02:33.120 And then if we cross cancel, we’ll get three multiplied by a half. 00:02:33.120 --> 00:02:35.120 And that’s because both six and four would divide by two. 00:02:36.000 --> 00:02:45.000 So we’ve got three multiplied by a half, which is three over two or three-halves, which we can also write as one and a half. 00:02:45.280 --> 00:02:50.600 So now, we’ve got 12 plus one and a half, which is 13 and a half, like we got in the first method. 00:02:50.880 --> 00:02:51.480 Okay, great. 00:02:51.960 --> 00:02:53.000 But have we solved the problem? 00:02:53.320 --> 00:02:58.440 Well, no, because what we want to know is, in total, how many cups of flour will be left over? 00:03:00.200 --> 00:03:08.720 Well, if we’ve got 14 cups of flour in total, then what we need to do is take 13 and a half away from 14, which is equal to a half. 00:03:09.360 --> 00:03:12.960 So therefore, Amelia will have half a cup of flour left over.