1 00:00:01,340 --> 00:00:05,432 We're now going to have a look at adding and subtracting 2 00:00:05,432 --> 00:00:12,140 fractions. Let's start with 1/5 + 3 00:00:12,140 --> 00:00:16,094 2/5. Here I 4 00:00:16,094 --> 00:00:20,718 have 1/5. And here 2/5. 5 00:00:22,190 --> 00:00:23,960 If we add them together. 6 00:00:24,840 --> 00:00:28,728 We have 3/5. 7 00:00:29,320 --> 00:00:35,116 So what I've done is added the numerators of the two fractions. 8 00:00:35,116 --> 00:00:38,497 So 1 + 2 gives me 3/5. 9 00:00:39,110 --> 00:00:43,548 Let's have a look at another example. 10 00:00:44,770 --> 00:00:50,850 Let's say we have 1/8 another one 8th. 11 00:00:52,070 --> 00:00:59,860 And. 5/8 So in the same way. 12 00:01:00,570 --> 00:01:02,358 I have 1/8. 13 00:01:03,020 --> 00:01:04,885 Another rates, so that's 2 14 00:01:04,885 --> 00:01:10,047 eighths. And then 5 eights to add on. So that gives me 15 00:01:10,047 --> 00:01:11,515 a total of 7/8. 16 00:01:12,960 --> 00:01:19,548 If we're adding like fractions, so the fractions are all of the 17 00:01:19,548 --> 00:01:25,587 same size. Here we had eighths, so all the denominators were 18 00:01:25,587 --> 00:01:29,098 eight. We can just add the numerators. 19 00:01:30,180 --> 00:01:34,330 Here the denominators were fifths. They were the same size, 20 00:01:34,330 --> 00:01:36,820 so we could add the numerators. 21 00:01:38,590 --> 00:01:40,630 Subtraction is very similar. 22 00:01:41,350 --> 00:01:43,918 Let's have 5/8. 23 00:01:44,900 --> 00:01:49,317 And this time will take away 3/8. 24 00:01:51,140 --> 00:01:55,256 The denominators are the same, so we have the same type of 25 00:01:55,256 --> 00:02:01,721 fraction. So we can just do five takeaway. Three gives us 2 26 00:02:01,721 --> 00:02:06,994 eighths. And if we put that into its lowest form. 27 00:02:07,000 --> 00:02:08,308 That's one quarter. 28 00:02:09,760 --> 00:02:16,228 Let's have a look at another addition one now, this time 29 00:02:16,228 --> 00:02:19,168 let's have 3/5 + 4/5. 30 00:02:19,740 --> 00:02:26,988 And when we add them three at 4 gives us 7 fifths. 31 00:02:27,870 --> 00:02:31,866 So we've added two proper fractions and they've added 32 00:02:31,866 --> 00:02:35,862 together to give an improper fraction of fraction that's 33 00:02:35,862 --> 00:02:42,078 larger than one. And if we write it as a mixed fraction, 5 goes 34 00:02:42,078 --> 00:02:47,406 into Seven, once with two left over. So that's exactly the same 35 00:02:47,406 --> 00:02:49,182 as one and 2/5. 36 00:02:50,430 --> 00:02:56,183 OK, let's look now at what happens when we have fractions 37 00:02:56,183 --> 00:02:58,798 where the denominators are not 38 00:02:58,798 --> 00:03:06,470 the same. Let's say we have 1/2 39 00:03:06,470 --> 00:03:10,368 + 1/4. So let's have 40 00:03:10,368 --> 00:03:13,728 a look. We have 1/2. 41 00:03:14,420 --> 00:03:15,590 Plus 1/4. 42 00:03:17,030 --> 00:03:18,630 We can add them together. 43 00:03:19,140 --> 00:03:25,120 But what do we end up with? How can we describe the fraction 44 00:03:25,120 --> 00:03:26,500 that we have? 45 00:03:27,230 --> 00:03:29,720 Well, we know that 1/2. 46 00:03:30,380 --> 00:03:31,559 Is the same. 47 00:03:32,120 --> 00:03:35,618 That's two quarters. 48 00:03:36,420 --> 00:03:42,180 So if we change our half, we find an equivalent fraction of 49 00:03:42,180 --> 00:03:47,940 two quarters and then add our quarter. We are now in the 50 00:03:47,940 --> 00:03:51,300 situation where the denominators are the same. 51 00:03:51,800 --> 00:03:57,762 So we can simply add the numerators so we get 3/4. 52 00:03:58,460 --> 00:04:05,084 Let's have a look 53 00:04:05,084 --> 00:04:08,396 at 3/4 54 00:04:08,396 --> 00:04:15,388 + 3/8. The denominators are not the same. 55 00:04:16,320 --> 00:04:19,356 So imagine now we have 3/4. 56 00:04:20,870 --> 00:04:23,070 And we have 3/8. 57 00:04:23,870 --> 00:04:25,580 What we need to do? 58 00:04:26,260 --> 00:04:28,048 Is to make these. 59 00:04:28,730 --> 00:04:34,110 Into eighths. Go back looking visually again. 60 00:04:37,120 --> 00:04:38,820 Those are three quarters. 61 00:04:40,100 --> 00:04:42,865 Nicer 62 00:04:42,865 --> 00:04:45,630 3/8. 63 00:04:46,170 --> 00:04:51,238 Well. In fact, visually we 64 00:04:51,238 --> 00:04:52,546 can see an answer. 65 00:04:53,660 --> 00:04:58,812 Straight away. We've got a whole one here and one 8th. 66 00:04:59,570 --> 00:05:01,270 But let's actually see. 67 00:05:02,380 --> 00:05:06,360 What is happening numerically here? We can't turn eighths into 68 00:05:06,360 --> 00:05:10,738 the quarters very easily if we've got two of them. Yes, 69 00:05:10,738 --> 00:05:14,718 that's a quarter. But we've got this one left over. 70 00:05:15,480 --> 00:05:18,608 But what we can do is turn our 71 00:05:18,608 --> 00:05:23,261 quarters. Into eighths because 2 eighths fit very 72 00:05:23,261 --> 00:05:25,393 nicely into a quarter. 73 00:05:26,780 --> 00:05:32,656 So what we have instead of 3/4 is 2 eighths there, 2 eighth 74 00:05:32,656 --> 00:05:34,916 there and two eighths there. 75 00:05:35,960 --> 00:05:38,970 So we have 6 eighths. 76 00:05:39,500 --> 00:05:42,420 Plus Are 77 00:05:42,420 --> 00:05:45,420 3/8. Now again. 78 00:05:45,970 --> 00:05:50,770 We have fractions with the same denominators, so we can just add 79 00:05:50,770 --> 00:05:55,570 the numerators, so we get 9 eighths which we saw at the 80 00:05:55,570 --> 00:05:57,570 beginning. Is a whole 1. 81 00:05:58,360 --> 00:06:00,248 With one 8th leftover. 82 00:06:01,220 --> 00:06:08,260 Now here we've used fractions where they're in the same sort 83 00:06:08,260 --> 00:06:13,380 of family because 8th fitted exactly into quarters. 84 00:06:14,100 --> 00:06:16,790 Quarters fit exactly into halfs. 85 00:06:17,410 --> 00:06:20,236 What happens when it's not quite 86 00:06:20,236 --> 00:06:22,650 so convenient? Well, let's have 87 00:06:22,650 --> 00:06:28,990 a look. At 1/2 + 1/3. 88 00:06:30,130 --> 00:06:32,080 So what we wanted to add 89 00:06:32,080 --> 00:06:34,969 together is 1/2. Plus the third. 90 00:06:36,600 --> 00:06:41,424 Now if we tried to turn the half into thirds, we'd have 91 00:06:41,424 --> 00:06:45,444 difficulty 'cause it doesn't fit a whole number of times. 92 00:06:46,220 --> 00:06:48,308 So what we need to find? 93 00:06:48,920 --> 00:06:51,185 Is a fraction of the 94 00:06:51,185 --> 00:06:53,801 denominator. That fits into 95 00:06:53,801 --> 00:06:56,540 thirds. As well as into half. 96 00:06:58,220 --> 00:06:59,800 And in this case. 97 00:07:00,480 --> 00:07:05,040 That fraction is 6. 98 00:07:07,000 --> 00:07:12,050 We can fit 26 into our third and a half. 99 00:07:12,840 --> 00:07:16,130 Is 36. 100 00:07:17,230 --> 00:07:24,326 So we're finding an equivalent fraction for half 101 00:07:24,326 --> 00:07:31,080 is 36. And a third is 26. 102 00:07:31,080 --> 00:07:34,464 So again, with the denominators now the same. 103 00:07:35,080 --> 00:07:41,604 We can just add the numerators and we see we've got a total of 104 00:07:41,604 --> 00:07:45,332 5, six, 3 + 2 giving us 5. 105 00:07:46,460 --> 00:07:48,780 Let's try another one now. 106 00:07:51,610 --> 00:07:57,502 Let's look at 1/4 107 00:07:57,502 --> 00:08:00,448 + 2/5. 108 00:08:01,490 --> 00:08:07,864 Now. We need to find a number 109 00:08:07,864 --> 00:08:09,406 for our denominator. 110 00:08:10,490 --> 00:08:14,210 That for is going to fit into so it can be divided. 111 00:08:14,900 --> 00:08:18,450 Into quarters, and that five is going to fit into. 112 00:08:19,160 --> 00:08:22,930 Well, let's have a look at some numbers that four and five fit 113 00:08:22,930 --> 00:08:25,688 into. Let's start with full. 114 00:08:26,360 --> 00:08:29,600 Well, two Forza 8. 115 00:08:29,600 --> 00:08:36,368 Three Forza 12. So these are all numbers 116 00:08:36,368 --> 00:08:39,752 multiples of four sixteen 117 00:08:39,752 --> 00:08:42,408 2024. And so on. 118 00:08:43,790 --> 00:08:50,797 And let's have a look at numbers that 5 fit into was 510. 119 00:08:51,740 --> 00:08:53,320 15 120 00:08:54,210 --> 00:09:01,176 20 Ha, I can stop there because I've now 121 00:09:01,176 --> 00:09:06,279 found a common number of one that's in both. 122 00:09:06,480 --> 00:09:10,090 The force on the fives 123 00:09:10,090 --> 00:09:13,880 so 20. Is a 124 00:09:13,880 --> 00:09:19,756 common denominator. So we're going to change our quarters. 125 00:09:20,290 --> 00:09:21,720 Into Twentieths. 126 00:09:23,360 --> 00:09:25,739 Well, how many? 127 00:09:26,890 --> 00:09:34,594 Did we need 12345? So five 20th is the same as a 128 00:09:34,594 --> 00:09:37,820 quarter? And 2/5. 129 00:09:39,520 --> 00:09:42,108 Well, we need it. 130 00:09:42,110 --> 00:09:47,340 1234 131 00:09:48,860 --> 00:09:54,570 20th make one face, but we've got 2/5 so we've 132 00:09:54,570 --> 00:09:56,283 got eight twentieths. 133 00:09:57,560 --> 00:10:02,235 So in total now we've got the denominate are the same. 134 00:10:02,770 --> 00:10:07,649 Eight at 5 gives us 13 twentieths. 135 00:10:08,770 --> 00:10:15,216 Let's have a look at this now numerically. We've done it 136 00:10:15,216 --> 00:10:19,860 by. Thinking about it by perhaps visualizing it in our heads, 137 00:10:19,860 --> 00:10:22,992 let's have a look at numerically what's actually happening. 138 00:10:23,830 --> 00:10:26,780 There's 1/4 139 00:10:26,780 --> 00:10:33,834 + 2/5. How did we arrive 140 00:10:33,834 --> 00:10:36,297 at this 20? 141 00:10:37,700 --> 00:10:42,344 Well, we were looking for a number that both four and five 142 00:10:42,344 --> 00:10:44,279 fitted into a common number. 143 00:10:46,600 --> 00:10:51,352 So what you could say we did here is actually multiplied. The 144 00:10:51,352 --> 00:10:52,936 four and the five. 145 00:10:54,930 --> 00:11:01,673 4. Goes into 25 times. So what we did is 146 00:11:01,673 --> 00:11:03,901 multiplied 4 by 5. 147 00:11:05,090 --> 00:11:08,788 Now. With our fractions, whatever we've done to the 148 00:11:08,788 --> 00:11:11,542 denominator to find an equivalent fraction, we must do 149 00:11:11,542 --> 00:11:13,072 the same to the numerator. 150 00:11:13,630 --> 00:11:17,860 So we had to multiply this one by five also. 151 00:11:20,020 --> 00:11:22,000 Our 2/5. 152 00:11:23,150 --> 00:11:28,109 We multiplied the five by four to make 20. 153 00:11:29,190 --> 00:11:33,663 Whatever we multiply the denominator by, we must multiply 154 00:11:33,663 --> 00:11:37,639 the numerator by and our numerator was too. 155 00:11:38,450 --> 00:11:40,650 So we have to do 2 * 4. 156 00:11:41,780 --> 00:11:46,169 And this is how we arrived at our five 20th 155. 157 00:11:46,790 --> 00:11:48,338 4 fives are 20. 158 00:11:49,230 --> 00:11:51,420 2408 159 00:11:53,140 --> 00:11:59,860 So that's a plus, and five fours or 20, giving us a 160 00:11:59,860 --> 00:12:02,100 total of 13 twentieths. 161 00:12:03,610 --> 00:12:10,696 Let's have a look at Subtraction. 162 00:12:11,710 --> 00:12:17,938 This time, let's have 3/4 takeaway. 163 00:12:18,110 --> 00:12:25,054 16 So again, we're looking for numbers that both 164 00:12:25,054 --> 00:12:28,219 four and six fit into. 165 00:12:28,760 --> 00:12:35,808 Let's have a look at our force 48. 166 00:12:36,470 --> 00:12:42,981 1216 2024 and so 167 00:12:42,981 --> 00:12:49,860 on. And our sixes multiples 168 00:12:49,860 --> 00:12:53,640 of six 612-1824. 169 00:12:54,440 --> 00:12:56,360 And so on. 170 00:12:57,180 --> 00:13:03,046 The reason I've written so many is that I want to point out to 171 00:13:03,046 --> 00:13:04,303 you that there. 172 00:13:04,310 --> 00:13:06,902 Might be more than one common 173 00:13:06,902 --> 00:13:12,913 pair. 12 is a common denominator, both four and six 174 00:13:12,913 --> 00:13:14,554 fit into 12. 175 00:13:15,210 --> 00:13:17,000 But also there's another one 176 00:13:17,000 --> 00:13:20,820 here 24. And those four and six. 177 00:13:21,380 --> 00:13:27,050 Fit into 24 and in fact if we multiply 4 and six together we 178 00:13:27,050 --> 00:13:32,720 get 24. But as you can see in this case that's not the lowest 179 00:13:32,720 --> 00:13:37,175 common denominator. It's not the lowest number that is common to 180 00:13:37,175 --> 00:13:38,795 both of these denominators. 181 00:13:40,650 --> 00:13:45,130 We want to use the lowest one 'cause if we don't we then need 182 00:13:45,130 --> 00:13:48,650 the end of the calculation to actually reduce the fraction to 183 00:13:48,650 --> 00:13:52,170 its lowest form, and it's much easier to deal with smaller 184 00:13:52,170 --> 00:13:54,410 numbers. So we try and find the 185 00:13:54,410 --> 00:14:01,674 lowest one. So we want to write for. We want to turn it into an 186 00:14:01,674 --> 00:14:04,422 equivalent fraction with 12 as a 187 00:14:04,422 --> 00:14:09,488 denominator. So what have we done to fall to make it 12? 188 00:14:09,488 --> 00:14:14,086 We've multiplied by three, so we must multiply the numerator by 189 00:14:14,086 --> 00:14:19,515 three. What have we done to our six to make it 12? 190 00:14:20,610 --> 00:14:22,418 We've multiplied by two. 191 00:14:23,240 --> 00:14:28,088 So we must multiply our numerator by two. 192 00:14:28,090 --> 00:14:35,031 33943 twelve takeaway. Once too is 26 twos at 12, now 193 00:14:35,031 --> 00:14:41,972 are denominators are the same, so we can simply subtract the 194 00:14:41,972 --> 00:14:47,020 numerators, giving us a result of Seven twelfths. 195 00:14:49,230 --> 00:14:54,100 So what we're doing when we add and subtract fractions? 196 00:14:55,580 --> 00:15:01,436 Is we need to make sure that the denominators are the same 197 00:15:01,436 --> 00:15:06,316 before we do the addition of the subtraction. If they're 198 00:15:06,316 --> 00:15:11,684 not the same, then we need to find the lowest common 199 00:15:11,684 --> 00:15:15,100 denominator between the fractions and then find 200 00:15:15,100 --> 00:15:19,492 equivalent fractions, and then we can do the additional 201 00:15:19,492 --> 00:15:19,980 subtraction. 202 00:15:21,950 --> 00:15:27,709 What we need to look at now is when we have mixed fractions. 203 00:15:28,350 --> 00:15:33,634 Let's say we've got 204 00:15:33,634 --> 00:15:37,597 5 and 3/4. 205 00:15:38,960 --> 00:15:45,694 And we're going to take away one and four fifths. How do we deal 206 00:15:45,694 --> 00:15:48,100 with that? Well. 207 00:15:48,600 --> 00:15:53,122 The first thing that we need to do is to turn them into improper 208 00:15:53,122 --> 00:15:58,063 fractions. We need to make them so that they're all over, in 209 00:15:58,063 --> 00:16:00,887 this case quarters, and with this one, fifths. 210 00:16:01,490 --> 00:16:05,798 Then we can do the process that we've just done finding common 211 00:16:05,798 --> 00:16:07,234 denominators and actually doing 212 00:16:07,234 --> 00:16:12,280 the Subtraction. So first of all, we need to find out how 213 00:16:12,280 --> 00:16:16,416 many quarters we have here. Well, we've got five whole ones 214 00:16:16,416 --> 00:16:20,928 we want to make them into quarters. So we multiplied by 4. 215 00:16:22,040 --> 00:16:25,563 And then we're going to add the sorry that we've got there. So 216 00:16:25,563 --> 00:16:26,918 that's how many quarters we 217 00:16:26,918 --> 00:16:30,190 have. I'm going to take away. 218 00:16:31,440 --> 00:16:33,288 One and four fifths. 219 00:16:33,980 --> 00:16:40,754 So. 1 * 5 that's how many fifths are in a whole one 220 00:16:40,754 --> 00:16:42,125 plus the four. 221 00:16:42,880 --> 00:16:44,932 And that's how many fifths we 222 00:16:44,932 --> 00:16:51,860 have. 4 fives are 20 + 3 is 20 three quarters. 223 00:16:52,480 --> 00:16:58,600 Take away once five is 5 plus, the four is 9 fifths. 224 00:16:59,470 --> 00:17:01,840 Now we need to find. 225 00:17:02,390 --> 00:17:04,875 The common denominator of four 226 00:17:04,875 --> 00:17:10,474 and five. Well, as we found before, that's 20. 227 00:17:10,980 --> 00:17:18,134 What have we multiplied 4 by to make 20 that's five, so we have 228 00:17:18,134 --> 00:17:20,689 to have 23 * 5. 229 00:17:21,460 --> 00:17:28,181 Take away 20th. What do we multiply 5 by to get 20? Well 230 00:17:28,181 --> 00:17:31,800 that was four so 9 * 4. 231 00:17:32,520 --> 00:17:35,340 So 23 * 5. 232 00:17:36,060 --> 00:17:42,812 Five 20s or 100 three 5:15 so it's 233 00:17:42,812 --> 00:17:48,720 115 twentieths takeaway for 9:30 six 20th. 234 00:17:49,500 --> 00:17:52,149 Now I denominators. 235 00:17:52,650 --> 00:17:57,780 Are the same. We can simply subtract the numerators. 236 00:17:58,480 --> 00:18:05,662 115 takeaway 36 is 79 so we have 70 nine 20th and usually if 237 00:18:05,662 --> 00:18:11,818 our question is given in terms of a mixed fraction then we 238 00:18:11,818 --> 00:18:15,409 ought to give our answer in the 239 00:18:15,409 --> 00:18:22,930 same form. So 20s into 79 or twenty 20th make one 240 00:18:22,930 --> 00:18:28,910 whole 1. And we've got three whole ones there. Three 20s are 241 00:18:28,910 --> 00:18:35,962 60. And then we've got 19 twentieths leftover. So the 242 00:18:35,962 --> 00:18:39,850 answer is 3 and 19 twentieths. 243 00:18:40,670 --> 00:18:44,774 Let's have a look at one more example. 244 00:18:45,850 --> 00:18:52,222 This time using three fractions, so one and 3/4. 245 00:18:53,050 --> 00:18:56,590 Plus 6 and 2/5. 246 00:18:58,320 --> 00:19:02,310 +5 halfs so we've got a mixture 247 00:19:02,310 --> 00:19:06,280 here. Of mixed fractions and an 248 00:19:06,280 --> 00:19:10,924 improper fraction. Well, as before, the first thing we need 249 00:19:10,924 --> 00:19:14,642 to do is to turn these mixed fractions into improper ones. 250 00:19:15,380 --> 00:19:19,238 Here we have one whole 1. 251 00:19:20,310 --> 00:19:26,610 We need to turn it into quarters so we multiply by 4 and we add 252 00:19:26,610 --> 00:19:29,970 the three. That's how many quarters we have. 253 00:19:30,680 --> 00:19:36,400 And then we add six whole ones. We turn them into fifths, we 254 00:19:36,400 --> 00:19:37,720 multiply by 5. 255 00:19:38,380 --> 00:19:44,060 We add the two not so many fests we have 256 00:19:44,060 --> 00:19:46,332 plus our five halves. 257 00:19:47,530 --> 00:19:54,640 Once for is 4 + 3 is 7 quarters plus 258 00:19:54,640 --> 00:20:01,039 six 530 + 2. Thirty 2/5 + 5 halfs. 259 00:20:02,490 --> 00:20:07,722 Now this time we need to find common denominator of all three 260 00:20:07,722 --> 00:20:09,030 of these denominators. 261 00:20:09,890 --> 00:20:16,162 Now it's easier to think perhaps of the largest 1 first, so if I 262 00:20:16,162 --> 00:20:18,850 think and count up, perhaps in 263 00:20:18,850 --> 00:20:24,284 fives. 5 obviously is not common to these two 10. Well two goes 264 00:20:24,284 --> 00:20:26,366 into 10, but the four doesn't. 265 00:20:26,910 --> 00:20:31,167 So let's keep going 15. That's no good 20. 266 00:20:31,690 --> 00:20:36,548 Yep, five goes into 20. Two were going to 20 and so will fall. 267 00:20:37,100 --> 00:20:42,482 So 20 is going to be my common denominator. 268 00:20:42,590 --> 00:20:45,218 So it's just right. All the 269 00:20:45,218 --> 00:20:47,970 denominators in. So what did I 270 00:20:47,970 --> 00:20:54,239 do to fall? To get 20 I multiplied by 5. 271 00:20:55,110 --> 00:20:57,714 So 7 must be multiplied by 5. 272 00:20:58,890 --> 00:21:06,426 What did I do to five to get 20? I multiplied by 4, so I must 273 00:21:06,426 --> 00:21:12,078 do 32 * 4. The numerator and the denominator must be multiplied 274 00:21:12,078 --> 00:21:13,962 by the same number. 275 00:21:13,970 --> 00:21:19,724 And finally, what did I do to the two to get the 20? I 276 00:21:19,724 --> 00:21:24,245 multiplied by 10, so I must multiply the numerator by 10. 277 00:21:24,860 --> 00:21:28,276 7 fives gives us 278 00:21:28,276 --> 00:21:36,064 35. Plus 430 twos for 30s or 122, Forza 279 00:21:36,064 --> 00:21:42,448 8 says 120, eight, 20th plus 50 twentieths. 280 00:21:43,540 --> 00:21:45,580 And if we add these altogether. 281 00:21:46,470 --> 00:21:50,222 We get 100 and 282 00:21:50,222 --> 00:21:51,160 28178. 283 00:21:52,140 --> 00:21:57,380 213 20th. 284 00:21:59,090 --> 00:22:04,022 And again, let's turn that back to a mixed fraction. How many 285 00:22:04,022 --> 00:22:07,721 20s? How many whole ones are there in 213? 286 00:22:08,270 --> 00:22:15,602 Well, 20 * 10 gets us to 200, so that's ten whole 287 00:22:15,602 --> 00:22:18,657 ones and 13 twentieths leftover. 288 00:22:19,200 --> 00:22:24,764 So if we add one and three quarters 6 and 2/5 and five 289 00:22:24,764 --> 00:22:27,760 halfs, we get 10 and 13 twentieths.