0:00:00.000,0:00:00.730 0:00:00.730,0:00:02.910 Sarah has $48. 0:00:02.910,0:00:07.050 She wants to save 1/3 of[br]her money for a trip. 0:00:07.050,0:00:09.990 How many dollars should[br]she set aside? 0:00:09.990,0:00:13.530 So we essentially want to think[br]about what 1/3 of 48 is. 0:00:13.530,0:00:16.170 Use 48 as the denominator[br]and find an 0:00:16.170,0:00:19.480 equivalent fraction to 1/3. 0:00:19.480,0:00:22.070 So what they want us to do in[br]this problem is they want us 0:00:22.070,0:00:26.500 to say, OK, we want 1/3 of her[br]money, but we want to write 0:00:26.500,0:00:30.530 this as an equivalent fraction[br]where we have 48 in the 0:00:30.530,0:00:31.100 denominator. 0:00:31.100,0:00:36.590 So this is equal to something,[br]some blank up here. 0:00:36.590,0:00:39.425 This is equal to something[br]over 48. 0:00:39.425,0:00:44.120 So how can we get it to that[br]something over 48? 0:00:44.120,0:00:46.160 So let's think about what[br]this means for a second. 0:00:46.160,0:00:50.430 So 1/3, if we were to draw[br]1/3, it looks like this. 0:00:50.430,0:00:55.980 You could imagine a box[br]or a pie, I guess. 0:00:55.980,0:01:00.690 So let's say that this is my[br]pie, and I have it split into 0:01:00.690,0:01:01.840 three pieces. 0:01:01.840,0:01:04.860 So let me split it into[br]three even pieces. 0:01:04.860,0:01:09.020 And 1/3 is one of those[br]three pieces. 0:01:09.020,0:01:11.550 That is what 1/3 means. 0:01:11.550,0:01:15.140 Now, if we want express this as[br]a fraction over 48, how can 0:01:15.140,0:01:15.740 we do that? 0:01:15.740,0:01:17.220 Well, we're going to[br]have to split this 0:01:17.220,0:01:19.280 thing into 48 pieces. 0:01:19.280,0:01:22.350 How can we split something[br]into 48? 0:01:22.350,0:01:28.540 Well, 3 times 16 is 48, so if we[br]split each of these into 16 0:01:28.540,0:01:30.810 pieces-- and it's going[br]to be hard to draw 0:01:30.810,0:01:32.300 here, but you can imagine. 0:01:32.300,0:01:38.130 Let's see, you split it into[br]two, now we've split it into 0:01:38.130,0:01:42.620 four, now you split[br]it into eight. 0:01:42.620,0:01:44.280 You're just going to end up with[br]a bunch of lines here, 0:01:44.280,0:01:47.360 but you can imagine, you can[br]just split each of these. 0:01:47.360,0:01:51.120 If you split each of these into[br]enough, you would have 16 0:01:51.120,0:01:54.140 pieces, so those would[br]be 16 right there. 0:01:54.140,0:01:58.050 You would have 16 right there[br]and you have 16 right there. 0:01:58.050,0:01:59.740 And I can just keep doing it. 0:01:59.740,0:02:01.280 Let me do it in the[br]green over here. 0:02:01.280,0:02:05.780 So if we just kept splitting[br]it up, we would get 48, 0:02:05.780,0:02:09.050 because you have this first[br]third would be 16 pieces, the 0:02:09.050,0:02:11.700 second third would be 16,[br]and then this third 0:02:11.700,0:02:13.820 third would be 16 pieces. 0:02:13.820,0:02:16.470 Altogether, you would[br]have 48 pieces. 0:02:16.470,0:02:19.110 Now, that 1/3, what does[br]that represent? 0:02:19.110,0:02:23.230 Well, that represents[br]16 of the 48. 0:02:23.230,0:02:26.450 It represents these[br]16 right here. 0:02:26.450,0:02:31.370 It represents these 16 right[br]there, so 1 over 3 is the 0:02:31.370,0:02:33.090 exact same thing. 0:02:33.090,0:02:41.120 So 1 over 3 is the exact same[br]thing as 16 over 48. 0:02:41.120,0:02:43.420 Now, we did it just by thinking[br]about it kind of 0:02:43.420,0:02:48.890 intuitively what 1/3 of 48 is,[br]but one way to do it more-- I 0:02:48.890,0:02:53.600 guess a process for doing it--[br]we would say, well, look, to 0:02:53.600,0:02:58.840 get the denominator, the bottom[br]number, from 3 to 48, 0:02:58.840,0:03:02.020 we multiply by 16. 0:03:02.020,0:03:04.790 3 times 16 is 48. 0:03:04.790,0:03:07.760 And that's literally the process[br]of going from 3 pieces 0:03:07.760,0:03:08.960 to 48 pieces. 0:03:08.960,0:03:11.460 We have to multiply by 16. 0:03:11.460,0:03:14.500 We have to turn each of our[br]pieces into 16 pieces. 0:03:14.500,0:03:15.990 That's what we did. 0:03:15.990,0:03:20.030 Now, you can't just multiply[br]only the denominator by 16. 0:03:20.030,0:03:24.650 You have to multiply the[br]numerator by the same number. 0:03:24.650,0:03:29.750 And so if each of my pieces[br]now become 16 pieces, then 0:03:29.750,0:03:32.730 that one piece will[br]now become 16. 0:03:32.730,0:03:36.370 So one way to think about it,[br]you just say, well, 3 times 16 0:03:36.370,0:03:41.920 is 48, so 1 times 16 will be my[br]numerator, so it'll be 16. 0:03:41.920,0:03:45.180 So 1/3 is equal to 16/48. 0:03:45.180,0:03:47.040 And another way you could think[br]about it, which you'll 0:03:47.040,0:03:53.930 learn in more detail later on,[br]is we want 1/3 of 48, right? 0:03:53.930,0:04:00.060 That's how much she wants to[br]save. 1/3 of 48 is equal to 0:04:00.060,0:04:03.950 1/3 times 48. 0:04:03.950,0:04:08.130 And when you multiply-- let me[br]write it like this-- 1/3 times 0:04:08.130,0:04:13.370 48, and you could rewrite[br]48 as a fraction 48/1. 0:04:13.370,0:04:16.510 It literally represents[br]48 wholes. 0:04:16.510,0:04:18.380 And when you multiply fractions,[br]you can just 0:04:18.380,0:04:20.470 multiply the numerators. 0:04:20.470,0:04:25.370 So this is equal to 48 over--[br]and then you just multiply the 0:04:25.370,0:04:26.300 denominators. 0:04:26.300,0:04:29.970 48/3, 1 times 48 is 48. 0:04:29.970,0:04:31.560 We'll see this in more[br]detail in the future. 0:04:31.560,0:04:33.480 Don't worry about it[br]if it confuses you. 0:04:33.480,0:04:38.350 In the denominator, 3 times 1 is[br]3, and 48 divided by 3, or 0:04:38.350,0:04:41.320 48/3, is equal to 16. 0:04:41.320,0:04:47.960 So 1/3 of 48 is 16,[br]or 16/48 is 1/3. 0:04:47.960,0:04:50.310 Hopefully, that make[br]sense to you.