1 00:00:00,000 --> 00:00:00,660 2 00:00:00,660 --> 00:00:04,549 Multiply 1 and 3/4 times 7 and 1/5. 3 00:00:04,549 --> 00:00:08,759 Simplify your answer and write it as a mixed fraction. 4 00:00:08,759 --> 00:00:12,080 So the first thing we want to do is rewrite each of these 5 00:00:12,080 --> 00:00:14,990 mixed numbers as improper fractions. 6 00:00:14,990 --> 00:00:17,789 It's very difficult, or at least it's not easy for me, to 7 00:00:17,789 --> 00:00:19,679 directly multiply mixed numbers. 8 00:00:19,679 --> 00:00:22,559 One can do it, but it's much easier if you just make them 9 00:00:22,559 --> 00:00:24,179 improper fractions. 10 00:00:24,179 --> 00:00:25,620 So let's convert each of them. 11 00:00:25,620 --> 00:00:32,380 So 1 and 3/4 is equal to-- it's still going to be over 4, 12 00:00:32,380 --> 00:00:34,810 so you're still going to have the same denominator, but your 13 00:00:34,810 --> 00:00:37,710 numerator as an improper fraction is going to be 4 14 00:00:37,710 --> 00:00:39,615 times 1 plus 3. 15 00:00:39,615 --> 00:00:43,390 16 00:00:43,390 --> 00:00:48,750 And the reason why this makes sense is 1 is 4/4, or 1 is 4 17 00:00:48,750 --> 00:00:50,789 times 1 fourths, right? 18 00:00:50,789 --> 00:00:53,479 1 is the same thing as 4/4, and then you have three more 19 00:00:53,479 --> 00:00:56,669 fourths, so 4/4 plus 3/4 will give you 7/4. 20 00:00:56,670 --> 00:00:59,760 21 00:00:59,759 --> 00:01:02,670 So that's the same thing as 1 and 3/4. 22 00:01:02,670 --> 00:01:04,319 Now, let's do 7 and 1/5. 23 00:01:04,319 --> 00:01:09,590 24 00:01:09,590 --> 00:01:12,579 Same exact process. 25 00:01:12,579 --> 00:01:14,859 We're going to still be talking in terms of fifths. 26 00:01:14,859 --> 00:01:16,709 That's going to be the denominator. 27 00:01:16,709 --> 00:01:19,599 You take 5 times 7, because think about it. 28 00:01:19,599 --> 00:01:22,959 7 is the same thing as 35/5. 29 00:01:22,959 --> 00:01:29,149 So you take 5 times 7 plus this numerator right here. 30 00:01:29,150 --> 00:01:32,670 So 7 is 35/5, then you have one more fifth, so you're 31 00:01:32,670 --> 00:01:38,870 going to have 35 plus 1, which is equal to 36/5. 32 00:01:38,870 --> 00:01:42,320 So this product is the exact same thing as taking the 33 00:01:42,319 --> 00:01:51,349 product of 7/4 times 36/5. 34 00:01:51,349 --> 00:01:53,219 And we could multiply it out right now. 35 00:01:53,219 --> 00:01:57,099 Take the 7 times 36 as our new numerator, 4 times 5 as our 36 00:01:57,099 --> 00:01:59,780 new denominator, but that'll give us large numbers. 37 00:01:59,780 --> 00:02:02,370 I can't multiply 7 and 36 in my head, or I 38 00:02:02,370 --> 00:02:03,890 can't do it too easily. 39 00:02:03,890 --> 00:02:06,590 So let's see if we can simplify this first. 40 00:02:06,590 --> 00:02:09,319 Both our numerator and our denominator have numbers that 41 00:02:09,319 --> 00:02:12,219 are divisible by 4, so let's divide both the numerator and 42 00:02:12,219 --> 00:02:13,740 the denominator by 4. 43 00:02:13,740 --> 00:02:20,100 So in the numerator, we can divide the 36 by 4 and get 9. 44 00:02:20,099 --> 00:02:22,359 If you divide something in the numerator by 4, you need to 45 00:02:22,360 --> 00:02:25,020 divide something in the denominator by 4, and the 4 is 46 00:02:25,020 --> 00:02:28,890 the obvious guy, so 4 divided by 4 is 1. 47 00:02:28,889 --> 00:02:33,699 So now this becomes 7 times 9, and what's the 7 times 9? 48 00:02:33,699 --> 00:02:39,899 It's 63, over 1 times 5. 49 00:02:39,900 --> 00:02:42,920 So now we have our answer as an improper fraction, but they 50 00:02:42,919 --> 00:02:46,019 want it as a mixed number or as a mixed fraction. 51 00:02:46,020 --> 00:02:48,120 So what are 63/5? 52 00:02:48,120 --> 00:02:53,120 So to figure that out-- let me pick a nice color here-- we 53 00:02:53,120 --> 00:02:57,259 take 5 into 63. 54 00:02:57,259 --> 00:02:59,419 5 goes into 6 one time. 55 00:02:59,419 --> 00:03:01,319 1 times 5 is 5. 56 00:03:01,319 --> 00:03:02,259 You subtract. 57 00:03:02,259 --> 00:03:06,259 6 minus 5 is 1. 58 00:03:06,259 --> 00:03:08,329 Bring down the 3. 59 00:03:08,330 --> 00:03:11,219 5 goes into 13 two times. 60 00:03:11,219 --> 00:03:14,159 And you could have immediately said 5 goes into 63 twelve 61 00:03:14,159 --> 00:03:17,479 times, but this way, at least to me, it's a 62 00:03:17,479 --> 00:03:18,959 little bit more obvious. 63 00:03:18,960 --> 00:03:27,305 And then 2 times 5 is 12, and then we have sorry! 64 00:03:27,305 --> 00:03:32,390 2 times 5 is 10. 65 00:03:32,389 --> 00:03:33,659 That tells you not to switch gears in the 66 00:03:33,659 --> 00:03:34,560 middle of a math problem. 67 00:03:34,560 --> 00:03:37,599 2 times 5 is 10, and then you subtract, and you have a 68 00:03:37,599 --> 00:03:39,164 remainder of 3. 69 00:03:39,164 --> 00:03:42,039 70 00:03:42,039 --> 00:03:51,069 So 63/5 is the same thing as 12 wholes and 3 left over, or 71 00:03:51,069 --> 00:03:55,799 3/5 left over. 72 00:03:55,800 --> 00:03:58,460 And if you wanted to go back from this to that, just think: 73 00:03:58,460 --> 00:04:03,030 12 is the same thing as 60 fifths, or 60/5. 74 00:04:03,030 --> 00:04:07,949 60/5 plus 3/5 is 63/5, so these two things 75 00:04:07,949 --> 00:04:09,719 are the same thing. 76 00:04:09,719 --> 00:04:10,810 These two things are equivalent. 77 00:04:10,810 --> 00:04:12,979 This is as an improper fraction. 78 00:04:12,979 --> 00:04:16,389 This is as a mixed number or a mixed fraction. 79 00:04:16,389 --> 00:04:21,129 But this is our answer right there: 12 and 3/5.