1 00:00:02,240 --> 00:00:06,227 This tutorial is about the basic concepts of fractions. 2 00:00:06,760 --> 00:00:11,200 What they are, what they look like, and why we have them. 3 00:00:12,340 --> 00:00:17,048 A function is a way of writing part of a whole. 4 00:00:17,770 --> 00:00:22,814 And it's formed when we divide a whole into an equal number of 5 00:00:22,814 --> 00:00:27,370 pieces. Now let's have a look. I've got a representation here. 6 00:00:28,120 --> 00:00:29,080 Of a whole. 7 00:00:30,200 --> 00:00:36,752 And let's say we want to divide it into 4 equal pieces. 8 00:00:38,520 --> 00:00:44,760 So there we've taken 1 hole 9 00:00:44,760 --> 00:00:51,000 and divided it into 4 equal 10 00:00:51,000 --> 00:00:57,240 pieces. So each piece represents 1/4. 11 00:00:58,510 --> 00:00:59,810 Wow. 12 00:01:00,870 --> 00:01:04,180 I've now taken 1/4 away. 13 00:01:05,800 --> 00:01:09,436 Now I've removed 14 00:01:09,436 --> 00:01:15,060 two quarters. If I take a third. 15 00:01:15,990 --> 00:01:22,986 That's 3/4. And if I take the false so I've 16 00:01:22,986 --> 00:01:24,821 now got all four pieces. 17 00:01:25,440 --> 00:01:30,401 I've taken all of them for quarters, which is exactly the 18 00:01:30,401 --> 00:01:32,656 same as taking the whole. 19 00:01:33,240 --> 00:01:38,080 Let's just return for a moment to the two quarters. 20 00:01:38,600 --> 00:01:42,840 Now two 21 00:01:42,840 --> 00:01:46,494 quarters. Is exactly 22 00:01:46,494 --> 00:01:52,695 the same. As if I'd started with my whole and actually 23 00:01:52,695 --> 00:01:54,210 divided it into. 24 00:01:55,010 --> 00:01:57,610 2 pieces of equal size. 25 00:01:58,450 --> 00:02:00,202 And you can see that that's 26 00:02:00,202 --> 00:02:06,040 exactly the same. As two quarters so I can write two 27 00:02:06,040 --> 00:02:10,480 quarters. As one half. 28 00:02:12,270 --> 00:02:15,998 Let's have a look at another illustration now. 29 00:02:17,190 --> 00:02:19,395 Here I have a bar of chocolate. 30 00:02:20,740 --> 00:02:22,369 It's been divided. 31 00:02:22,930 --> 00:02:29,144 Into six pieces of equal size. So we've taken a whole bar and 32 00:02:29,144 --> 00:02:31,534 divide it into six pieces. 33 00:02:32,270 --> 00:02:36,540 So each piece is 16. 34 00:02:38,330 --> 00:02:42,506 Now, let's say I'm going to share my bar of chocolate with 35 00:02:42,506 --> 00:02:43,550 the camera man. 36 00:02:44,650 --> 00:02:50,770 So I want to divide the bar of chocolate into two pieces. 37 00:02:51,370 --> 00:02:53,170 So if I do that. 38 00:02:55,160 --> 00:02:59,060 Where each going to have one 39 00:02:59,060 --> 00:03:05,940 236. So 1/2 is exactly the same as 36. 40 00:03:06,810 --> 00:03:11,139 But there's not just one cameraman. We've got two 41 00:03:11,139 --> 00:03:16,430 cameramen, so I need to share it. Actually, between three of 42 00:03:16,430 --> 00:03:23,475 us. So now if I put my bar back together and I need to share it 43 00:03:23,475 --> 00:03:27,060 between 3:00. Where each going to get. 44 00:03:28,430 --> 00:03:30,810 Two pieces. 45 00:03:32,550 --> 00:03:38,110 So 1/3 is exactly the same as 26. 46 00:03:38,910 --> 00:03:45,540 But Let's say I want to eat all my chocolate bar 47 00:03:45,540 --> 00:03:51,169 myself, so I'm going to have all six pieces, so they're all mine. 48 00:03:51,700 --> 00:03:55,693 Not going to share them, so I take all six pieces. 49 00:03:56,310 --> 00:03:58,596 And I've taken away the whole 50 00:03:58,596 --> 00:03:58,977 bar. 51 00:03:59,540 --> 00:04:06,470 So. Fractions we can look at. 52 00:04:07,010 --> 00:04:08,348 In two ways. 53 00:04:09,320 --> 00:04:13,200 We can look at it as the number 54 00:04:13,200 --> 00:04:15,850 of pieces. That we've used. 55 00:04:17,130 --> 00:04:23,610 Divided by the number of pieces. 56 00:04:24,280 --> 00:04:27,260 That make a whole. 57 00:04:27,260 --> 00:04:32,950 Oh 58 00:04:33,990 --> 00:04:36,888 As the whole. 59 00:04:37,710 --> 00:04:44,173 Divided by. Number of pieces or number of people that we've 60 00:04:44,173 --> 00:04:45,484 divided it into. 61 00:04:46,290 --> 00:04:52,494 So here we have a whole bar divided into 6 pieces. 62 00:04:53,880 --> 00:04:57,510 Here we have the number of pieces that we've taken divided 63 00:04:57,510 --> 00:05:01,470 note 5 the number of pieces that make up the whole bar. 64 00:05:03,540 --> 00:05:10,828 Let's have a look at some other fractions. 65 00:05:10,830 --> 00:05:16,926 Let's say we have 66 00:05:16,926 --> 00:05:18,450 3/8. 67 00:05:20,000 --> 00:05:25,352 So we've divided a whole up into 8 pieces of equal size. 68 00:05:25,890 --> 00:05:27,636 And we've taken three of them. 69 00:05:28,270 --> 00:05:29,590 3/8 70 00:05:31,150 --> 00:05:34,960 We could have 11 twelfths. 71 00:05:35,800 --> 00:05:41,767 So we've divided a whole up into 12 pieces and taking eleven of 72 00:05:41,767 --> 00:05:46,060 them. We could have 7/10. 73 00:05:47,160 --> 00:05:52,424 Here we will have divided a hole into 10 pieces of equal size and 74 00:05:52,424 --> 00:05:53,928 taken Seven of them. 75 00:05:54,710 --> 00:05:56,238 And we can have. 76 00:05:56,800 --> 00:06:04,696 Any numbers in our fraction so we could have 105 hundreds or 77 00:06:04,696 --> 00:06:07,986 three 167th and so on. 78 00:06:08,900 --> 00:06:12,165 Now we've looked at representing 79 00:06:12,165 --> 00:06:16,897 fractions. Using piece of Cod circular representation are 80 00:06:16,897 --> 00:06:19,452 rectangle with our bar of 81 00:06:19,452 --> 00:06:24,008 chocolate. Let's have a look at one more before we move on and 82 00:06:24,008 --> 00:06:25,478 let's let's see it on. 83 00:06:26,110 --> 00:06:28,000 A section of number line. 84 00:06:29,560 --> 00:06:31,877 So let's say we have zero here. 85 00:06:32,540 --> 00:06:34,439 And one here. 86 00:06:34,950 --> 00:06:37,302 So let's look at what 3/8 might 87 00:06:37,302 --> 00:06:44,150 look like. While I need to divide my section into 8 pieces 88 00:06:44,150 --> 00:06:45,818 of equal size. 89 00:06:46,690 --> 00:06:49,993 Now obviously this is an illustration, so I'm not 90 00:06:49,993 --> 00:06:53,663 actually getting my router out to make sure I've got 91 00:06:53,663 --> 00:06:54,764 equal size pieces. 92 00:06:55,830 --> 00:07:01,894 But hopefully. That's about right. So we've got 12345678 93 00:07:01,894 --> 00:07:09,238 pieces of equal size and I'm going to take three of them. 94 00:07:09,238 --> 00:07:12,910 So if I take 1, two 95 00:07:12,910 --> 00:07:17,600 3/8. That's where my 3 eights will be. 96 00:07:20,630 --> 00:07:22,639 Let's have a look at another one. 97 00:07:24,590 --> 00:07:28,340 This time will look at 98 00:07:28,340 --> 00:07:33,206 11 twelfths. So we need to divide our line up into. 99 00:07:34,300 --> 00:07:40,033 Pieces so we have 12 pieces of equal size. 100 00:07:48,390 --> 00:07:55,350 OK, so we wanted eleven of them, so 101 00:07:55,350 --> 00:08:02,310 we need to count 11 one 23456789 ten 102 00:08:02,310 --> 00:08:05,790 11. So at 11 103 00:08:05,790 --> 00:08:08,800 twelfths. Is represented there. 104 00:08:10,240 --> 00:08:16,786 Let's look more closely at our 105 00:08:16,786 --> 00:08:18,968 fraction half. 106 00:08:20,040 --> 00:08:26,088 Now we've already seen that half is exactly the same as two 107 00:08:26,088 --> 00:08:31,174 quarters. And it's exactly the same as 36. 108 00:08:32,100 --> 00:08:38,832 Well, it's also the same as 4 eighths 5/10. 109 00:08:40,640 --> 00:08:44,210 2040 deaths 110 00:08:45,600 --> 00:08:50,770 9900 and 98th and so on. We could go on. 111 00:08:51,500 --> 00:08:58,116 And what we have here is actually equivalent 112 00:08:58,116 --> 00:09:05,376 fractions. Each one of these fractions are equivalent at the 113 00:09:05,376 --> 00:09:08,152 same as each other. 114 00:09:10,460 --> 00:09:14,090 Now, this form of the fraction 115 00:09:14,090 --> 00:09:20,985 half. Is our fraction in its lowest form, and often we need 116 00:09:20,985 --> 00:09:23,610 to write fractions in their 117 00:09:23,610 --> 00:09:29,122 lowest form. It's much easier to visualize them actually in this 118 00:09:29,122 --> 00:09:32,118 lowest form than it is in any 119 00:09:32,118 --> 00:09:36,355 other form. So we often want to find the lowest form. 120 00:09:37,710 --> 00:09:43,683 Well, let's have a look 1st at finding some other equivalent 121 00:09:43,683 --> 00:09:46,941 fractions. So let's say I take 122 00:09:46,941 --> 00:09:52,485 3/4. How do I find an equivalent fraction? Well, what 123 00:09:52,485 --> 00:09:58,185 I can do is multiply the top number and the bottom number. 124 00:09:59,270 --> 00:10:00,878 By the same number. 125 00:10:01,380 --> 00:10:05,258 So let's say I multiply by two. 126 00:10:05,870 --> 00:10:10,719 If I multiply the top number by two, I must also multiply the 127 00:10:10,719 --> 00:10:14,822 bottom number by two so that I'm not changing the fraction. 128 00:10:15,750 --> 00:10:19,691 3 * 2 six 4 * 2 129 00:10:19,691 --> 00:10:26,454 is 8. So 6 eighths is a fraction equivalent to 3/4. 130 00:10:28,370 --> 00:10:29,578 Let's try another one. 131 00:10:30,350 --> 00:10:33,710 This time, let's take our 3/4. 132 00:10:34,440 --> 00:10:39,434 And multiply it by three. The top numbers multiplied by three, 133 00:10:39,434 --> 00:10:45,336 so most the bottom number B3 threes and 9 three force or 12, 134 00:10:45,336 --> 00:10:50,330 so nine twelfths is equivalent to 6 eighths, and they're both 135 00:10:50,330 --> 00:10:51,692 equivalent to 3/4. 136 00:10:53,070 --> 00:10:57,437 Let's do one more this time. Let's multiply both the top 137 00:10:57,437 --> 00:11:02,598 number on the bottom number by 10. So we have 3 * 10. 138 00:11:03,350 --> 00:11:04,718 Giving us 30. 139 00:11:05,230 --> 00:11:11,260 And 4 * 10 giving us 40. So another fraction 140 00:11:11,260 --> 00:11:14,878 equivalent to 3/4 is 3040 deaths. 141 00:11:16,090 --> 00:11:20,743 So it's very easy to find equivalent fractions as long as 142 00:11:20,743 --> 00:11:25,819 you multiply the top number on the bottom number by the same 143 00:11:25,819 --> 00:11:29,203 number. Now we have some mathematical language here. 144 00:11:29,203 --> 00:11:34,279 Instead of using the word top number and write it down top 145 00:11:34,279 --> 00:11:38,668 number. And bottom number. 146 00:11:40,730 --> 00:11:45,720 We have two words that we use. The top number 147 00:11:45,720 --> 00:11:47,716 is called the numerator. 148 00:11:49,350 --> 00:11:52,605 On the bottom number the 149 00:11:52,605 --> 00:11:58,523 denominator. Now let's have a look at seeing how we go the 150 00:11:58,523 --> 00:12:03,176 other way. When we have an equivalent fraction, how do we 151 00:12:03,176 --> 00:12:05,714 find this fraction in its lowest 152 00:12:05,714 --> 00:12:08,300 form? Well, let's look at an 153 00:12:08,300 --> 00:12:13,419 example. Let's say we've got 8, one, hundreds. 154 00:12:14,890 --> 00:12:20,446 Now we need to find the number that the lowest form was 155 00:12:20,446 --> 00:12:24,815 multiplied by. And that we ended up with eight one hundredths. 156 00:12:25,610 --> 00:12:29,840 Well, the opposite of multiplying is dividing, so we 157 00:12:29,840 --> 00:12:34,540 need to divide both the numerator and the denominator by 158 00:12:34,540 --> 00:12:35,950 the same number. 159 00:12:36,460 --> 00:12:40,132 So that we get back to a fraction in its lowest form. 160 00:12:40,780 --> 00:12:46,282 Well, if we look at the numbers we have here 8 and 100, the 161 00:12:46,282 --> 00:12:50,605 first thing you should notice is actually the both even numbers. 162 00:12:51,130 --> 00:12:54,710 And if they're both even numbers, then obviously we can 163 00:12:54,710 --> 00:12:56,500 divide them both by two. 164 00:12:57,380 --> 00:13:03,188 So let's start by dividing the numerator by two and the 165 00:13:03,188 --> 00:13:04,772 denominator by two. 166 00:13:05,510 --> 00:13:11,850 8 / 2 is four 100 / 2 is 50. 167 00:13:12,970 --> 00:13:17,002 Now we need to look at our fraction. Again. We found an 168 00:13:17,002 --> 00:13:20,026 equivalent fraction, but is it in its lowest form? 169 00:13:20,830 --> 00:13:25,241 Well again, we can see that they're both even numbers, both 170 00:13:25,241 --> 00:13:30,053 4 and 50 even, and so we can divide by two again. 171 00:13:30,560 --> 00:13:38,100 4 / 4 gives us 2 and 50 / 2. 172 00:13:38,750 --> 00:13:44,100 Gives us 25, so another equivalent fraction, but is it 173 00:13:44,100 --> 00:13:46,240 in its lowest form? 174 00:13:46,960 --> 00:13:53,330 Well, we need to see if there is any number that goes both into 175 00:13:53,330 --> 00:13:56,970 the numerator and the denominator. Well, the only 176 00:13:56,970 --> 00:14:02,430 numbers that go into 2A one which goes into all numbers, so 177 00:14:02,430 --> 00:14:09,255 that's not going to help us. And two now 2 doesn't go into 25. So 178 00:14:09,255 --> 00:14:14,715 therefore we found the fraction in its lowest form, so 8 one 179 00:14:14,715 --> 00:14:17,445 hundreds. The lowest form is 220 180 00:14:17,445 --> 00:14:23,476 fifths. So when a fraction is in its lowest form, the only number 181 00:14:23,476 --> 00:14:27,744 that will go into both the numerator and the denominator is 182 00:14:27,744 --> 00:14:31,360 one. Those numbers have no other 183 00:14:31,360 --> 00:14:37,375 common factor. Now if we look here, we can see that in fact. 184 00:14:37,950 --> 00:14:41,910 We could have divided by 4. 185 00:14:41,910 --> 00:14:45,474 Straight away, instead of dividing by two twice, well, 186 00:14:45,474 --> 00:14:49,434 that's fine. If you've notice tthat for was a factor. 187 00:14:49,990 --> 00:14:54,577 Of both the numerator and the denominator, you could have gone 188 00:14:54,577 --> 00:15:01,249 straight there doing 8 / 4 was two and 100 / 4 was 25 and then 189 00:15:01,249 --> 00:15:06,670 check to see if you were in the lowest form. That's fine, but 190 00:15:06,670 --> 00:15:11,052 often. With numbers, larger numbers is not always easy to 191 00:15:11,052 --> 00:15:15,100 see what the highest common factor is of these two numbers, 192 00:15:15,100 --> 00:15:18,044 the numerator and the denominator. So often it's 193 00:15:18,044 --> 00:15:22,092 easier to work down to some smaller numbers, and then you 194 00:15:22,092 --> 00:15:25,772 can be certain that there are no other common factors. 195 00:15:28,020 --> 00:15:28,540 Now. 196 00:15:29,880 --> 00:15:33,516 If we take all the pieces of a fraction 197 00:15:33,516 --> 00:15:37,152 like I did with my chocolate, I took all 198 00:15:37,152 --> 00:15:38,364 six of them. 199 00:15:39,760 --> 00:15:43,596 That's the same as 6 / 6. 200 00:15:44,110 --> 00:15:45,590 And that was our whole. 201 00:15:47,430 --> 00:15:53,406 And any whole number can be written this way, so we could 202 00:15:53,406 --> 00:15:59,561 have. 3 thirds if we take all the pieces, we've got one. 203 00:15:59,870 --> 00:16:05,865 8 eighths, if we take all the pieces, we've got one. 204 00:16:05,870 --> 00:16:09,340 Now I'm going to rewrite. 205 00:16:09,900 --> 00:16:13,239 Mathematical words numerator. 206 00:16:13,790 --> 00:16:17,438 Divided fight denominator. 207 00:16:18,530 --> 00:16:22,270 Because we're now going to 208 00:16:22,270 --> 00:16:28,190 look. Add fractions where the numerator. 209 00:16:30,490 --> 00:16:33,938 Smaller than the denominator. 210 00:16:36,590 --> 00:16:41,378 And we have a name for these type of fractions and they 211 00:16:41,378 --> 00:16:42,575 called proper fractions. 212 00:16:47,530 --> 00:16:50,860 And examples. 213 00:16:50,860 --> 00:16:52,330 Half. 214 00:16:53,320 --> 00:16:58,140 3/4 16 215 00:16:59,380 --> 00:17:06,660 7/8 5/10 and seeing all these cases, the 216 00:17:06,660 --> 00:17:10,060 numerator is smaller number than 217 00:17:10,060 --> 00:17:16,410 the denominator. And as long as that is the case, then we have a 218 00:17:16,410 --> 00:17:20,730 proper fraction so we can have any numbers 100 hundred and 50th 219 00:17:20,730 --> 00:17:24,554 for example. Now if 220 00:17:24,554 --> 00:17:30,700 the numerator. Is greater than 221 00:17:30,700 --> 00:17:32,820 the denominator? 222 00:17:36,980 --> 00:17:41,556 Then the fraction is called an improper fraction. 223 00:17:47,160 --> 00:17:50,289 And some examples. 224 00:17:50,350 --> 00:17:53,098 Three over two or three halfs. 225 00:17:53,930 --> 00:17:59,490 7 fifths. Eight quarters 226 00:18:00,960 --> 00:18:03,650 We could have 12 bytes. 227 00:18:05,120 --> 00:18:08,708 Or we could have 201 hundredths. 228 00:18:09,780 --> 00:18:14,873 And in all these cases, the numerator is larger than the 229 00:18:14,873 --> 00:18:19,590 denominator. And it shows that what we've got is actually more 230 00:18:19,590 --> 00:18:20,619 than whole 1. 231 00:18:21,540 --> 00:18:26,090 All these fractions, the proper ones are smaller than a 232 00:18:26,090 --> 00:18:31,095 whole one. We haven't taken all of the pieces 3/4. We've 233 00:18:31,095 --> 00:18:37,465 only taken 3 out of the four 161 out of the six, so that 234 00:18:37,465 --> 00:18:41,560 all smaller than a whole one with improper fractions. 235 00:18:42,790 --> 00:18:45,052 They are all larger than one 236 00:18:45,052 --> 00:18:50,866 whole 1. So if we take three over 2 for example, what we've 237 00:18:50,866 --> 00:18:52,896 actually got is 3 halfs. 238 00:18:54,790 --> 00:18:58,993 Oh, improper fractions can be written in this form. 239 00:18:59,730 --> 00:19:05,466 All they can be written as mixed fractions. 240 00:19:08,280 --> 00:19:12,753 So let's have a look at our three halfs. 241 00:19:14,450 --> 00:19:19,078 And what we can do is put two hearts together to make the 242 00:19:19,078 --> 00:19:25,392 whole 1. And we've got 1/2 left over, so that can be written as 243 00:19:25,392 --> 00:19:26,976 one and a half. 244 00:19:28,040 --> 00:19:32,324 So there are exactly the same, but written in a different form 245 00:19:32,324 --> 00:19:34,109 1 as a mixed fraction. 246 00:19:34,620 --> 00:19:39,714 And one other top heavy fraction, an improper fraction 247 00:19:39,714 --> 00:19:44,242 where the numerator is larger than the denominator. 248 00:19:46,390 --> 00:19:48,202 Let's have a look at another 249 00:19:48,202 --> 00:19:53,906 example. Let's say we had 8 thirds. 250 00:19:53,910 --> 00:19:55,238 This out the way. 251 00:19:56,780 --> 00:20:00,320 Let's count 252 00:20:00,320 --> 00:20:05,790 out 1234567. 8 thirds 253 00:20:06,900 --> 00:20:11,047 How else can we write that? How do we write that as a 254 00:20:11,047 --> 00:20:11,685 mixed fraction? 255 00:20:13,110 --> 00:20:16,140 Well, what we're looking for is how many whole ones 256 00:20:16,140 --> 00:20:17,049 we've got there. 257 00:20:18,310 --> 00:20:22,398 Well, if something's been divided into 3 pieces. 258 00:20:23,420 --> 00:20:26,150 It takes 3 pieces to make the 259 00:20:26,150 --> 00:20:28,760 whole 1. So that's one whole 1. 260 00:20:30,510 --> 00:20:34,026 There we have another whole 12. 261 00:20:34,890 --> 00:20:42,114 And we've got 2/3 left over, so 8 thirds is exactly the 262 00:20:42,114 --> 00:20:45,124 same as two and 2/3. 263 00:20:48,770 --> 00:20:50,710 Let's look at one more. 264 00:20:51,710 --> 00:20:55,485 Let's say we had Seven 265 00:20:55,485 --> 00:21:00,999 quarters. Now we know that there are four quarters in each hole, 266 00:21:00,999 --> 00:21:06,446 one. So we see how many fours go into Seven. Well, that's one. 267 00:21:06,960 --> 00:21:13,080 And we've got 3 left over, so we've got one and 3/4. 268 00:21:14,180 --> 00:21:16,784 Let's have a look at one more. 269 00:21:18,090 --> 00:21:21,300 37 tenths 270 00:21:22,920 --> 00:21:27,892 Now we've split something up into 10 pieces of equal size. 271 00:21:28,930 --> 00:21:34,030 So we need 10 of those to make a whole one, so we need to see how 272 00:21:34,030 --> 00:21:37,030 many 10s, how many whole ones there are in 37. 273 00:21:38,130 --> 00:21:43,267 Well, three 10s makes 30, so that's three whole ones, and 274 00:21:43,267 --> 00:21:47,937 we've got 7 leftover, so we've got 3 and 7/10. 275 00:21:49,020 --> 00:21:52,426 Just move 276 00:21:52,426 --> 00:21:59,202 those. Now let's have a look at doing the reverse 277 00:21:59,202 --> 00:22:05,676 process. So if we start with a mixed fraction, how do we turn 278 00:22:05,676 --> 00:22:08,166 it into an improper fraction? 279 00:22:08,740 --> 00:22:11,902 Let's look at three and a 280 00:22:11,902 --> 00:22:16,498 quarter. And if we look at this visually, we've got. 281 00:22:17,170 --> 00:22:18,658 3 hole once. 282 00:22:20,540 --> 00:22:23,870 And one quarter. 283 00:22:27,500 --> 00:22:29,432 And what we want to turn it 284 00:22:29,432 --> 00:22:33,599 into. Is all quarters. 285 00:22:34,640 --> 00:22:36,470 So we have a whole 1. 286 00:22:37,360 --> 00:22:43,769 And if we split it into quarters, we know that a whole 1 287 00:22:43,769 --> 00:22:45,248 needs four quarters. 288 00:22:45,770 --> 00:22:47,280 So we have four there. 289 00:22:47,810 --> 00:22:49,118 Another for their. 290 00:22:49,680 --> 00:22:52,680 Another folder plus this one. 291 00:22:53,310 --> 00:22:56,124 So we've got three force or 12. 292 00:22:56,640 --> 00:23:04,032 Plus the one gives us 13 quarters, so 3 1/4 is exactly 293 00:23:04,032 --> 00:23:07,112 the same as 13 quarters. 294 00:23:07,660 --> 00:23:12,423 Well, let's have a look at how you might do this. 295 00:23:14,000 --> 00:23:15,500 If you haven't got the visual 296 00:23:15,500 --> 00:23:21,500 aid. Well, what we've actually got here is our whole number. 297 00:23:22,550 --> 00:23:23,639 And the fraction. 298 00:23:24,240 --> 00:23:25,940 We wanted in quarters. 299 00:23:27,070 --> 00:23:30,686 So what we're doing is right it again. 300 00:23:31,920 --> 00:23:36,550 We're actually saying We want four quarters for every hole 301 00:23:36,550 --> 00:23:39,791 one, so we've got three lots of 302 00:23:39,791 --> 00:23:44,910 four. And then what were ranting on is our one, and 303 00:23:44,910 --> 00:23:46,378 these are all quarters. 304 00:23:47,600 --> 00:23:51,425 So it's the whole number multiplied by the denominator. 305 00:23:52,460 --> 00:23:56,930 We've added the extra that we have here. Whatever this 306 00:23:56,930 --> 00:24:01,400 number is, and those are the number of quarters we've 307 00:24:01,400 --> 00:24:07,211 got. So we've got our 3/4 of 12 + 1/4, so 13 quarters. 308 00:24:08,940 --> 00:24:10,956 Let's have a look at one more 309 00:24:10,956 --> 00:24:16,478 example. Let's say we've got five and two ninths. 310 00:24:18,310 --> 00:24:21,086 We want to turn it into this format. 311 00:24:22,360 --> 00:24:28,632 Ninths well, if we want to take a whole one, we wouldn't need 9 312 00:24:28,632 --> 00:24:34,904 ninths and we've got five whole ones, so we're going to have 5 * 313 00:24:34,904 --> 00:24:37,592 9 lots of 9th this time. 314 00:24:38,250 --> 00:24:42,660 And then we need to add on the two nights that we have here. 315 00:24:42,670 --> 00:24:50,530 So 5 nines of 45 plus the two and that all 9th. 316 00:24:50,530 --> 00:24:53,805 So we have 47 ninths. 317 00:24:57,170 --> 00:25:00,734 Any whole number can be written as a fraction. 318 00:25:01,270 --> 00:25:04,078 So for example, if we take the number 2. 319 00:25:05,930 --> 00:25:10,097 If we write it with the denominator of one. 320 00:25:11,580 --> 00:25:13,860 We've written it as a fraction. 321 00:25:15,050 --> 00:25:20,143 And any equivalent form, so we could have 4 over 2. 322 00:25:20,770 --> 00:25:24,370 30 over 323 00:25:24,370 --> 00:25:31,193 15. And so on. So any whole number can be 324 00:25:31,193 --> 00:25:35,963 written as a fraction with a numerator and a denominator. 325 00:25:37,560 --> 00:25:45,186 So fractions. They can appear in a number 326 00:25:45,186 --> 00:25:50,460 of different forms. You might see proper fractions, improper 327 00:25:50,460 --> 00:25:52,218 fractions, mixed fractions. 328 00:25:53,060 --> 00:25:57,272 And you can see lots of different equivalent fractions. 329 00:25:57,870 --> 00:26:00,255 So that all different ways that we see them.