# en/0Q3fwpNahN56.xml.gz
# xho/0Q3fwpNahN56.xml.gz
(src)="1"> Welcome to the presentation on multiplying and dividing negative numbers .
(trg)="2"> Wamkelekile kumboniso wophinda- phindo kunye nokwahlula amanani athabathayo .
(src)="2"> Let 's get started .
(trg)="3"> Masiqaliseni .
(src)="3"> I think you 're going to find that multiplying and dividing negative numbers are a lot easier than it might
(trg)="4"> Ndiyacinga uzakufumana uphinda- phindo nokwahlula amanani athabathayo iyinto elula kunonuba
(src)="6"> And I am going to teach probably in the future like I 'm actually going to give you more intuition on why there rules work .
(trg)="5"> ikufundisa kwixesha elizayo , ndizakunika .
(src)="7"> So the basic rules are when you multiply two negative numbers , so let 's say I had negative 2 times negative 2 .
(trg)="6"> Ngoko ke imithetho yokuqala xa uphinda- phinda mamnani amabini athabathayo , ngoko ke masithi ndino - 2 umphinda- phinde ngo 2 .
(src)="8"> First you just look at each of the numbers as if there was no negative sign .
(trg)="7"> Kuqala ujonga kwinani ngalinye ngathi bekungekho sichazi esithabathayo .
(src)="9"> Well you say well , 2 times 2 that equals 4 .
(trg)="8"> Kulungile utsho , 2 umphinda- phinde ngo 2 ufumana u4 .
(src)="10"> And it turns out that if you have a negative times a negative , that that equals a positive .
(src)="11"> So let 's write that first rule down .
(trg)="9"> Kwaye iyafumaneka ukuba xa unesichazi esithabathayo usiphinda- phinde ngesichazi esithabathayo , ufumana isichazi isidibanisayo . ngoko ke masibhale lomthetho wokuqala phantsi .
(src)="12"> A negative times a negative equals a positive .
(trg)="10"> Isichazi esithabathayo usiphinda- phinde ngesinye ufumna isichazi esidibanisayo .
(src)="13"> What if it was negative 2 times positive 2 ?
(trg)="11"> Ukuba ibingu - 2 umphinda- phinde ngo 2 ?
(src)="14"> Well in this case , let 's first of all look at the two numbers without signs .
(trg)="12"> Kulungile kwelicandelo , makhe siqale sijonge amanani amabini angenazichazi .
(src)="15"> We know that 2 times 2 is 4 .
(trg)="13"> Siyayazi ukuba 2 umphinda- phinde ngo 2 ngu 4 .
(src)="16"> But here we have a negative times a positive 2 , and it turns out that when you multiply a negative times a positive you get a negative .
(src)="17"> So that 's another rule .
(trg)="14"> Kodwa apha sinesichazi esithabathayo usiphinda- phinde ngo2k , kwaye icace phandle , xa uphinda- phinda isichazi esithabathayo nge sichazi esidibaniosayo ufumana esithabathayo . ngoko ke ngomnye umthetho .
(src)="18"> Negative times positive is equal to negative .
(trg)="15"> Thabatha umphinda- phinde ngo dibanisa ufumana uthabatha .
(src)="19"> What happens if you have a positive 2 times a negative 2 ?
(trg)="16"> Kwenzeka ntoni xa unodibanisa 2 phinda- phinda thabatha 2 ?
(src)="20"> I think you 'll probably guess this one right , as you can tell that these two are pretty much the same thing by , I believe it 's the transitive property -- no , no I think it 's the communicative property .
(trg)="17"> Ndiyacinga ukuba lena uzakuyifumana kakuhle , nje ngokuba ungatsho ukuba ezi zimbini ziyafana kakhulu , ndiyakholelwa yinjongo yendawo -- haiy , hayi ndiyacinga yi kunxulumana kwendawo .
(src)="21"> I have to remember that .
(trg)="18"> Kufuneka ndiyikhumbule lonto .
(src)="22"> But 2 times negative 2 , this also equals negative 4 .
(src)="23"> So we have the final rule that a positive times a negative also equals the negative .
(trg)="19"> Kodwa 2 phinda- phinde ngo - 2 , lento ilingana no - 4 . ngoko ke sinemithetho epheleleyo ethi dibanisa umphinda- phinde ngo thabatha kwakhona ulingana no thabatha
(src)="24"> And actually these second two rules , they 're kind of the same thing .
(trg)="20"> Kwaye ngqo lemithetho yesibini , zibu fana .
(src)="25"> A negative times a positive is a negative , or a positive times a negative is negative .
(trg)="21"> Thabatha umphinda- phinde ngo dibanisa ngu thabatha , okanye dibanisa umphinda- phinde ngothabatha ngu thabatha .
(src)="26"> You could also say that as when the signs are different and you multiply the two numbers , you get a negative number .
(trg)="22"> Ungaphinda utsho ukuba xa izichazi zahlukile kwaye uphinda- phinde amanani amabini , ufumana inani elithabathayo .
(src)="27"> And of course , you already know what happens when you have a positive times a positive .
(trg)="23"> Kwaye ngokucacileyo , uyayazi into eyenzekayo xa udibanisa umphinda- phinde ngodibanisa .
(src)="28"> Well that 's just a positive .
(trg)="24"> Kulungile ngu dibanisa .
(src)="29"> So let 's review .
(trg)="25"> Ngoko ke masiphinde siqwalasele .
(src)="30"> Negative times a negative is a positive .
(trg)="26"> Uthabatha umphinda- phinde ngothabatha ufumana udibanisa .
(src)="31"> A negative times a positive is a negative .
(trg)="27"> Into ethabathayo uyiphinda- phinde ngodibanisa ufumana uthabatha .
(src)="32"> A positive times a negative is a negative .
(trg)="28"> Into edibanisayo uyiphinda- phinde ngothabatha ufumana uthabatha .
(src)="33"> And positive times each other equals positive .
(trg)="29"> Kwaye dibanisa umphinda- phinde kwangaye ilingana nodibanisa .
(src)="34"> I think that last little bit completely confused you .
(trg)="30"> Ndiyacinga aukuba lena yokugqibela ikubhidile mpela .
(src)="35"> Maybe I can simplify it for you .
(trg)="31"> Okanye ndingayicalucalula ukulungiselela wena .
(src)="36"> What if I just told you if when you 're multiplying and they 're the same signs that gets you a positive result .
(trg)="32"> Ungathini ukuba ndingathi xa uphinda- phinda kwaye izinto zakho zinezichazi ezifanayo ufumana iziphumo ezidibanisayo .
(src)="37"> And different signs gets you a negative result .
(trg)="33"> Kwaye izichazi ezahlukileyo zikunika iziphumo ezithabathayo .
(src)="38"> So that would be either , let 's say a 1 times 1 is equal to 1 , or if I said negative 1 times negative 1 is equal to positive 1 as well .
(src)="39"> Or if I said 1 times negative 1 is equal to negative 1 , or negative 1 times 1 is equal to negative 1 .
(trg)="34"> Ngoko ke maxa wambi , masithi 1 umphinda- phinde ngo 1 ilingana no1 . okanye ukuba ndithi - 1 umphinda- phinde ngo - 1 ufumana +1 kwakhona . oknaye ukubandithi 1 umphinda- phinde ngo - 1 ilingna no - 1 , okanye
(src)="40"> You see how on the bottom two problems I had two different signs , positive 1 and negative 1 ?
(trg)="36"> Uyabona kwezinxaki zimbini zingentla ndibe nezinto ezimbini ezahlukeneyo izichazi , enye edibanisa kunye nenye ethabathayo ?
(src)="41"> And the top two problems , this one right here both 1s are positive .
(trg)="37"> Kwaye kwezinxaki zimbini zinntla , lena ilapha zombini ziyadibanisa .
(src)="42"> And this one right here both 1s are negative .
(trg)="38"> Kwaye lena ilapha zombini ziyathabatha .
(src)="43"> So let 's do a bunch of problems now , and hopefully it 'll hit the point home , and you also could try to do along the practice problems and also give the hints and give you what rules to you so that should help you as well
(trg)="39"> Ngoko ke masenze iqela lemizekelo ngoku , kwaye ngethemba izakunika umfanekiso wokwazi ubuyele ekhaya , kwaye kwakhona ungazama ukwenza kawakunye nenxaki zokuziqhelanisa kwaye kwakhona unike inltuva kunye nantoni
(src)="44"> So if I said negative 4 times positive 3 , well 4 times 3 is 12 , and we have a negative and a positive .
(src)="45"> So different signs mean negative .
(trg)="40"> Ngoko ke ukuba ndithi - 4 umphinda- phinde ngo +3 , kulungile 4 umphimda- phinde ngo 3 ngu 12 , kwaye sinothabatha kunye nodibanisa . ngoko ke izichazi ezahlukileyo zithetha nguthabatha .
(src)="46"> So negative 4 times 3 is a negative 12 .
(trg)="41"> Ngoko ke - 4 umhpinda- phinde ngo 3 ngu - 12 .
(src)="47"> That makes sense because we 're essentially saying what 's negative 4 times itself three times , so it 's like negative 4 plus negative 4 plus negative 4 , which is negative 12 .
(trg)="42"> Lonto enza ucacelwe ngoba kanye kanye sithi ngubani
(trg)="43"> - 4 uphinda- phinde kwangaye amatyeli amathathu , ngoko ke kufana nokuthi - 4 dibanisa - 4 dibanisa - 4 , ukutsho ngu - 12 .
(src)="48"> If you 've seen the video on adding and subtracting negative numbers , you probably should watch first .
(trg)="44"> Ukuba ubumbonile umboniso wodibaniso kunye nokuthabatha amanai athabatha kukhangeleka ukuba kufuneka uyibukele kuqala .
(src)="49"> Let 's do another one .
(trg)="45"> Masinze enye .
(src)="50"> What if I said minus 2 times minus 7 .
(trg)="46"> Ukuba ndingathi - 2 phinda- phinda - 7 .
(src)="51"> And you might want to pause the video at any time to see if you know how to do it and then restart it to see what the answer is .
(trg)="47"> Kwaye ungafuna ukumisa kancinci umboniso nangaliphi na ixesha ukubona ukuba uyayazi ukuba yenziwa njani kwaye kwangoko uqalele ukubona ukuba impendulo ithini .
(src)="52"> Well , 2 times 7 is 14 , and we have the same sign here , so it 's a positive 14 -- normally you wouldn 't have to write the positive but that makes it a little bit more explicit .
(src)="53"> And what if I had -- let me think -- 9 times negative 5 .
(trg)="48"> Kulungile , 2 phinda- phinda 7 ngu 14 , kwaye sinezichazi manani ezifananyo apha , ngoko ke ngu dibanisa 14 -- ngokwesiqhelo awunokuyibhala isichazi esidibanisayo kodwa lonto iyenza kancinci icace kakhulu . kwaye ukuba bendino -- mandithi
(src)="54"> Well , 9 times 5 is 45 .
(trg)="49"> Kulungile , 9 phinda- phinda 5 ngu 45 .
(src)="55"> And once again , the signs are different so it 's a negative .
(trg)="50"> Kwaye kwakhona , izichazi manani zahlukile lonto yenza uthabatha .
(src)="56"> And then finally what if it I had -- let me think of some good numbers -- minus 6 times minus 11 .
(trg)="51"> Kwaye kwangoko ekugqibeleni mandithi ndino -- mandicinge ngamanani amahle -- - 6 phinda- phinda - 11 .
(src)="57"> Well , 6 times 11 is 66 and then it 's a negative and negative , it 's a positive .
(trg)="52"> Kulungile , 6 phinda- phinda 11 ngu 66 kwaye kwangoko nguthabatha kwaye thabatha , ngu dibanisa .
(src)="58"> Let me give you a trick problem .
(trg)="53"> Mandikunike inxaki anobuqhinga .
(src)="59"> What is 0 times negative 12 ?
(src)="60"> Well , you might say that the signs are different , but 0 is actually neither positive nor negative .
(trg)="54"> Ngubani u0 phinda- phinda - 12 ? kulungile , ungathi izichazi manani azifani , kodwa 0 akanasichazi noba siyadibanisa okanye siyathabtha .
(src)="61"> And 0 times anything is still 0 .
(trg)="55"> Kwaye 0 phinda- phinda nantoni na ihlala ingu 0 .
(src)="62"> It doesn 't matter if the thing you multiply it by is a negative number or a positive number .
(trg)="56"> Ayithethi into ophinda- phinda ngayo li nani e4lithabathayo okanye linani elidibanisayo .
(src)="63"> 0 times anything is still 0 .
(trg)="57"> 0 phinda- phinda nantoni na ngu 0 .
(src)="64"> So let 's see if we can apply these same rules to division .
(trg)="58"> Ngoko ke , masijonge ukuba singakwazi na ukusebenzisa lemithetho naxa sisahlula .
(src)="65"> It actually turns out that the same rules apply .
(trg)="59"> Icacili phandle ukuba lemithetho singayisebenzisa .
(src)="66"> If I have 9 divided by negative 3 .
(trg)="60"> Ukuba ndino 9 umahlule ngo - 3 .
(src)="67"> Well , first we say what 's 9 divided by 3 ?
(trg)="61"> Kulungile , kuqala sithi ngubani u 9 umahlule ngo 3 ?
(src)="68"> Well that 's 3 .
(trg)="62"> Kunjalo ngu 3 .
(src)="69"> And they have different signs , positive 9 , negative 3 .
(trg)="63"> Kwaye zinezichazi ezhlukileyo , +9 , - 3 .
(src)="70"> So different signs means a negative .
(trg)="64"> Ngoko ke izichazi manani ezingafaniyo zithetha uthabatha .
(src)="71"> 9 divided by negative 3 is equal to negative 3 .
(trg)="65"> Kwaye zinezichazi ezhlukileyo , +9 , - 3 .
(src)="72"> What is minus 16 divided by 8 ?
(trg)="66"> Ngunbani - 16 umahlule ngo 8 ?
(src)="73"> Well , once again , 16 divided by 8 is 2 , but the signs are different .
(trg)="67"> Kulungile , kwakhona 16 umahlule ngo 8 ngu 2 , kodwa izichazi manani zahlukile .
(src)="74"> Negative 16 divided by positive 8 , that equals negative 2 .
(trg)="68"> - 16 umahlule ngo +8 , ilingana no - 2 .
(src)="75"> Remember , different signs will get you a negative result .
(src)="76"> What is minus 54 divided by minus 6 ?
(trg)="69"> Khumbula , izichazi amanani ezahlukileyo zikunika iziphumo ezithabathayo . ngubani - 54 umahlule ngo +6 ?
(src)="77"> Well , 54 divided by 6 is 9 .
(trg)="70"> Kulungile , 54 umahlule ngo 6 ngu 9 .
(src)="78"> And since both terms , the divisor and the dividend , are both negative -- negative 54 and negative 6 -- it turns out that the answer is positive .
(trg)="71"> Kwaye kuba zombini , umahluli kunye nomahlulwa , be nezichazi manani ezithabathayo -- ngu - 54 kwaye - 6 -- icace phandle
(src)="80"> Let 's do one more .
(trg)="72"> Masenye enye yokugqibela .
(src)="81"> Obviously , 0 divided by anything is still 0 .
(trg)="73"> Icacile , 0 umahlule nanga ntoni na izakuhlala ingu 0 .
(src)="82"> That 's pretty straightforward .
(trg)="74"> Ngeyona ilula kakhulu .
(src)="83"> And of course , you can 't divide anything by 0
(trg)="75"> Kwaye ngokunjalo , awunokwazi ukwahlula ngo 0
(src)="84"> -- that 's undefined .
(trg)="76"> lonto ayichazeki .
(src)="85"> Let 's do one more .
(src)="86"> What is -- I 'm just going to think of random numbers -- 4 divided by negative 1 ?
(trg)="77"> Masenze enye . ngubani -- ndizakucinga ngamanani ahlukeneyo -- 4 umahlule ngo - 1 ?
(src)="87"> Well , 4 divided by 1 is 4 , but the signs are different .
(trg)="78"> Kulungile , 4 umahlule ngo 1 ngu 4 , kodwa izichazi manai zahlukile .
(src)="88"> So it 's negative 4 .
(trg)="79"> Ngoko ke ngu - 4 .
(src)="89"> I hope that helps .
(trg)="80"> Ndiyathemba lonto iyanceda .
(src)="90"> Now what I want you to do is actually try as many of these multiplying and dividing negative numbers as you can .
(trg)="81"> Ngoku into endifuna uyenze kukuzama ezininzi eziphinda- phindayo kwaye nezahlulayo ezinamanani athabathayo kanga ngoko ndinako .
(src)="91"> And you click on hints and it 'll remind you of which rule to use .
(trg)="82"> Kwaye icofa kwintluva kwaye izakukhumbuza imithetho ozakuyisebenzisa .
(src)="92"> In your own time you might want to actually think about why these rules apply and what it means to multiply a negative number times a positive number .
(trg)="83"> Ngelakho ixesha ungafuna ukucinga ukuba kutheni
(src)="93"> And even more interesting , what it means to multiply a negative number times a negative number .
(src)="94"> But I think at this point , hopefully , you are ready to start doing some problems .
(trg)="84"> lemithetho isebenza kwaye ithetha ntoni ukuphinda- phinda inani elithabathayo uliphinda- phinde ngelidibanisayo . kwaye inikisa umdla kakhulu , ithetha ntoni ukuphinda- phinda inani elithabathayo uliphinda- phinde ngeliothabathayo . kodwa ndiyacinga kulendawongethemba ukulungele ukuqalisa ukwenza inxaki .
(src)="95"> Good luck .
(trg)="85"> Ndlela ntle .
# en/0ZbIvSy8uGqi.xml.gz
# xho/0ZbIvSy8uGqi.xml.gz
(src)="1"> In the last video we did a couple of lattice multiplication problems and we saw it was pretty straightforward .
(trg)="1"> Kumboniso udlulileyo silenzile iqelana lesakhelo lophindaphindo kwaye sibonile ukuba ibiyindlelalula .
(src)="2"> You got to do all your multiplication first and then do all of your addition .
(trg)="2"> Kufuneka ulenze lonke uphindaphindo kuqala kwaye ulenze lonke udibaniso .
(src)="3"> Well , let 's try to understand why exactly it worked .
(trg)="3"> Kanjalo , makhesizame ukuqonda kutheni kanye kanye isebenza .
(src)="4"> It almost seemed like magic .
(trg)="4"> Iphantse yabonakala njengomlingo .
(src)="5"> And to see why it worked I 'm going to redo this problem up here and then I 'll also try to explain what we did in the longer problems .
(trg)="5"> Ukuze siyibone ukuba kutheni isebenzile ndizakuyiphinda kwakhona apha kwaye ndizakuzama ukucacisa lento besiyenzile kwimisebenzi emide .
(src)="6"> So when we multiplied twenty- seven -- so you write your two and your seven just like that -- times forty- eight .
(trg)="6"> Ngoko ke xa siphindaphinda amashumi amabini anesixhenxe ngoko ke ubhala isibini sakho nesixhenxe , nje ngolohlobo -- uphindaphinde ngamashumi amane anesibhozo .
(src)="7"> I 'm just doing exactly what we did in the previous video .
(trg)="7"> Ndenza kanye lento besiyenzile kumboniso odlulileyo .
(src)="8"> We drew a lattice , gave the two a column and the seven a column .
(trg)="8"> Sizobile isakhelo , sannika imihlathi emibini kunye nemihlathi esixhenxe .
(src)="9"> Just like that .
(trg)="9"> Nje ngolohlobo .
(src)="10"> We gave the four a row and we gave the eight a row .
(trg)="10"> Sanika isine sokrozo kwaye sanika isibhozo ukrozo .
(src)="11"> And then we drew our diagonal .
(trg)="11"> Kwaye sasizoba isixwesi sethu .
(src)="12"> And the key here is the diagonals , as you can imagine , otherwise we wouldn 't be drawing them .
(trg)="12"> Kwaye undoqo apha zizixwesi , njengokuba ungabanombono okanye asinokuzizoba .
(src)="13"> So you have your diagonals .
(trg)="13"> Ngoko ke unazo izixwesi zakho .