Mental Math Tricks - How to multiply in your head! — Transcript

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1. 0:01Good day, and welcome to the Take Math
2. 0:02Channel. What I'm going to be having a
3. 0:03look at in this video is a very special
4. 0:05video. We're going to be looking at how
5. 0:06to multiply mentally. How to multiply
6. 0:09big numbers mentally.
7. 0:11So, bear with us. You might look at
8. 0:13parts of it and say say, "Hey, I can do
9. 0:15this much faster with a pen and paper."
10. 0:16But, this isn't about trying to multiply
11. 0:18with a pen and paper. This is actually
12. 0:20trying to get you eventually multiplying
13. 0:23mentally, which is where the real uh
14. 0:25challenge lies a lot of the time.
15. 0:27Okay, so I'm going to start this off
16. 0:29with an example.
17. 0:30Let's uh get you doing this one. What is
18. 0:33uh a nice easy one to start off with?
19. 0:353,021,
20. 0:36and we're going to times it by three.
21. 0:38So, the answer that you should get for
22. 0:40this is 9,000
23. 0:44and 63. Did you get that answer?
24. 0:48You know what? I reckon you probably
25. 0:49did, and I'll show you how I reckon you
26. 0:51probably got that. How I think you
27. 0:52probably got that.
28. 0:54Okay, I would expect the way you'd done
29. 0:56that
30. 0:57is you would do this because you were
31. 0:59doing this a written method that you
32. 1:00would go 1 * 3 is 3, 2 * 3 is 6, 3 *
33. 1:04nothing is nothing, 3 * 3 is 9. Okay.
34. 1:09Now, look.
35. 1:10That's nice and easy if you're doing it
36. 1:13on paper, but it does become a little
37. 1:14bit harder all of a sudden when you're
38. 1:16not able to actually see the numbers.
39. 1:19Okay? And in a second, I'm going to
40. 1:21actually uh I'll give you one without
41. 1:22the numbers, then I'll actually write it
42. 1:24down, and we'll work through how your
43. 1:25mind might want to get reprogrammed
44. 1:27because I do this slightly differently.
45. 1:29Instead, what what we tend to do is we
46. 1:31tend to work out questions
47. 1:33this way.
48. 1:34From right to left. Whereas, what we
49. 1:37actually when we think of numbers, we
50. 1:38actually think about them this way.
51. 1:40Okay? We don't think about this number
52. 1:42being three and 60 and 9,000. We think
53. 1:45about this as 9,063.
54. 1:47And this is the challenge with
55. 1:48multiplying mentally is to turn the way
56. 1:51around that you currently
57. 1:53work your multiplication so you think
58. 1:55about them in the way that actually
59. 1:58think about them, okay? In that in that
60. 1:59particular way, rather than actually
61. 2:00working against the way your mind
62. 2:02naturally wants to work. Okay? So, the
63. 2:05way that I would do this is a little bit
64. 2:07different, and this is what I mean with
65. 2:09how we would have to change the way that
66. 2:11we are
67. 2:13work. We do this. We times this by
68. 2:15three. But instead, what we would do is
69. 2:18we would go 3 * 3 is 9
70. 2:210 3 * 2 is 6 3. Okay? And we're actually
71. 2:25working this in the way that we actually
72. 2:28you know you that you think the number.
73. 2:31Okay?
74. 2:33I'll give you another example. So, I'll
75. 2:34rub this out and then I'm going to ask
76. 2:36you
77. 2:38for example to work out what is uh
78. 2:4051,231
79. 2:43* 3?
80. 2:45Okay? So,
81. 2:47it's quite hard if you are if if you're
82. 2:49not used to doing it that direction.
83. 2:52So, the answer by the way is 153,693.
84. 2:58Okay? Let's
85. 3:00uh I'll write that down.
86. 3:01So, let's I'm going to write the
87. 3:02question down first. Um
88. 3:0551,231
89. 3:08it was * 3.
90. 3:11So,
91. 3:12the way we do it is this.
92. 3:143 * 5 is 15. We put that down. So, we're
93. 3:16going from left to right.
94. 3:195 * 3 is 15.
95. 3:203 * 1 is 3.
96. 3:242 * 3 is 6. 3 * 3 is 9.
97. 3:281 * 3 is 3.
98. 3:31You see? We're we're working this way,
99. 3:33and this is the trick
100. 3:35to mental calculations, mental
101. 3:37multiplication. So,
102. 3:38I know what's going to happen. I'm going
103. 3:39to start getting probably comments,
104. 3:40people saying this is harder, this is
105. 3:42not what I'm used to because it's not
106. 3:43what you're used to.
107. 3:45But then again, you also might realize
108. 3:47that the method you're used to is no
109. 3:49good for mental multiplication. So, this
110. 3:50is It does take a bit of practice, but
111. 3:53this is the way to do it mentally. This
112. 3:55is well, one of the ways to do it
113. 3:57mentally.
114. 3:58So,
115. 4:00I'm going to give you a
116. 4:02another one now. What about we deal with
117. 4:05uh hopefully you do pretty good with
118. 4:06this. Um
119. 4:07What about we do a different one here?
120. 4:09What about we do something say like uh
121. 4:1161,413?
122. 4:14I'll write that number down.
123. 4:1661,413
124. 4:20and we'll times that number by four.
125. 4:23Now, from now on, rather than saying
126. 4:24them, I'm going to actually you know So,
127. 4:27without actually writing it down, you
128. 4:28might go 4 * 6 is 24, 1 * 4 is 4 and
129. 4:31then the 16. Wait a sec. How you going
130. 4:33to deal with this carry here? What? You
131. 4:36say I don't even know what just went on.
132. 4:38I'll explain to you slowly what the
133. 4:39problem will be here.
134. 4:41Okay. So, when we're doing this, we have
135. 4:43a bit of a problem because what we do is
136. 4:44we go 6 * 4 is 24.
137. 4:471 * 4
138. 4:49is 4.
139. 4:504 * 4 is 16. Wait a second, that means
140. 4:53we're going to have to carry something.
141. 4:54So, we're going to put the six there
142. 4:56and we're going to carry the one. So,
143. 4:57this is going to become a five.
144. 5:001 * 4 is 4 and then 3 * 4 is 12. So, the
145. 5:04two's going to go there and the one's
146. 5:06going to get carried across and that
147. 5:07will also
148. 5:09become a five.
149. 5:11Now,
150. 5:12the carrying all of a sudden can become
151. 5:14a bit of a problem when we talk about
152. 5:16mental calculation because carrying
153. 5:18numbers in your head tends to throw
154. 5:19things a little bit.
155. 5:21What we tend to have to do is we have to
156. 5:22carry as we go, but we also have to
157. 5:24start doing this little thing which I
158. 5:26call pre-carrying, okay? It just
159. 5:28involves glancing at the next part of
160. 5:30your answer to to work out what
161. 5:32what your your current answer will be.
162. 5:34I'll show you what I mean by this, okay?
163. 5:36And we'll go through a couple of
164. 5:38examples with this. So, say for example,
165. 5:41I do
166. 5:42uh
167. 5:43this one here.
168. 5:4531,616.
169. 5:47If I times this number by four.
170. 5:51Okay.
171. 5:52I'll work through how this concept of
172. 5:55pre-carrying works. So, first off, we do
173. 5:58this 3 * 4 and we get the answer of 12,
174. 6:01but before I write down 12, I look at
175. 6:03the next part of the answer and I go 1 *
176. 6:054, the answer's below 10, I'm not going
177. 6:07to have to carry anything.
178. 6:09So, I can put down my 12. If I did have
179. 6:11to carry something, I'd carry it across
180. 6:13and put that as part of my answer and
181. 6:15you'll see how I would have done this
182. 6:16one right now. 1 * 4 is 4.
183. 6:19So, I quickly look at the next part and
184. 6:216 * 4 is 24.
185. 6:2324, I'm going to have to carry this two.
186. 6:26Okay, so this is what I'm going to
187. 6:28pre-carry. I'm going to pre-carry it
188. 6:29across. So, 1 * 4 is 4 plus that two
189. 6:32from the next part is going to be six.
190. 6:35Okay?
191. 6:37All right, we'll see how we go with
192. 6:38that.
193. 6:39Um, so the next one was 6 * 4 is 24.
194. 6:42We've already written down that two
195. 6:43there, we pre-carried that. The number
196. 6:45afterwards is 1 * 4. We're not going to
197. 6:47have to carry anything across, so I can
198. 6:48just put down that four.
199. 6:51Okay? For our 1 * 4,
200. 6:55I look at the next part.
201. 6:57Okay? And that's 6 * 4 is 24, I'm going
202. 7:00to have to pre-carry two across. Okay?
203. 7:02So, 1 * 4 is 4
204. 7:04plus two
205. 7:06is six.
206. 7:07Okay, did you get that? And then the
207. 7:09last part, well, that's just going to be
208. 7:11whatever that units part was going to
209. 7:12be. You know, 6 * 4 is 24, so that's how
210. 7:15we got that four goes down. But, this is
211. 7:16the concept of pre-carrying, okay?
212. 7:19And it's a it's a the biggest part of
213. 7:21this trick is to be able to get the
214. 7:22pre-carry right, okay? If you can get
215. 7:24the pre-carry right, you're really on
216. 7:26the way to getting these mentally uh
217. 7:28correct. So, what about I give you
218. 7:31another example?
219. 7:33Okay.
220. 7:35Uh,
221. 7:36we'll write this one down.
222. 7:38Um, what about, for instance,
223. 7:4121,000
224. 7:43613
225. 7:46and we times that by five. Okay, just
226. 7:48going to make sure we're going to get
227. 7:49some numbers where we are going to have
228. 7:50to carry and pre-carry things across.
229. 7:53Okay, so first off, what we do going
230. 7:55from left to right,
231. 7:572 * 5 is 10. Now, we look at 1 * 5,
232. 8:01no pre-carry. So, I can put down my 10.
233. 8:04Okay. I'll
234. 8:05put a little tick there to show that's
235. 8:06what I've done.
236. 8:07Okay, 1 * 5, okay, that's going to be
237. 8:10five and I'm going to have to pre-carry.
238. 8:136 * 5 30, I'm going to have to pre-carry
239. 8:15three. Okay, cuz 6 * 5 is 30, I'm going
240. 8:17to pre-carry three. So, 1 * 5 is 5 + 3,
241. 8:22okay,
242. 8:24is going to be
243. 8:25eight.
244. 8:28All right, I'll tick that one off. 6 * 5
245. 8:30is 30. I've already pre-carried the
246. 8:33three, so I've got that zero and then 1
247. 8:35* 5, I'm not going to have to pre-carry
248. 8:37anything. So,
249. 8:38with that, I can put down the zero
250. 8:41from the 30. Okay, I've already
251. 8:43pre-carried the three.
252. 8:44Now, that one done.
253. 8:461 * 5 is 5 and then I'll look at the
254. 8:48next one, 3 * 5 is 15, I'm going to have
255. 8:50to pre-carry you guessed it, one. Okay?
256. 8:53Because 3 * 5 is 15, I'm going to
257. 8:55pre-carry the one off the 15. So, 5 + 1
258. 9:00is six.
259. 9:02Okay, and then what I do is I put down
260. 9:05that last bit, which was that five.
261. 9:09How did you go with that? Did you get
262. 9:10that answer? Did you get 108,065?
263. 9:15Hopefully, you'll be able to actually uh
264. 9:18start seeing how to do this. It's all a
265. 9:20matter of working out the pre-carry.
266. 9:23Okay?
267. 9:24Is it easy?
268. 9:25At the start, no. This does require
269. 9:27practice. And what I'd recommend is you
270. 9:29would start with smaller numbers to at
271. 9:31the start off with, okay? You would
272. 9:32start with say something
273. 9:34I I you know, something like uh
274. 9:37possibly, you know,
275. 9:39what about 423?
276. 9:43And we're going to times that by four.
277. 9:46Okay?
278. 9:48So,
279. 9:49that's a good one because it's a nice
280. 9:50three-digit. It's not too huge. 4 * 4 is
281. 9:5316. 2 * 4 is 8. So, it's less than 10,
282. 9:56so I can put down the 16. I can think
283. 9:5716. I can keep that in my head. 2 * 4 is
284. 10:008. 3 * 4 is 12. I'm going to pre-carry
285. 10:03that one, so it's going to be a nine and
286. 10:05a two.
287. 10:08How did you go with that?
288. 10:09Hopefully pretty good. Anyway, see how
289. 10:11you go with that. Before you start
290. 10:13getting upset and saying you despise
291. 10:15this method or whatever like that, give
292. 10:16it a fair go because this is trying to
293. 10:19reprogram your mind and so you are you
294. 10:22will actually be able to do this
295. 10:23mentally, okay? But don't expect it's
296. 10:25going to come to you in 3 seconds flat,
297. 10:28okay?
298. 10:28This does take a little bit of practice.
299. 10:30Sometimes this does take a little bit of
300. 10:32practice, these sorts of things. Anyway,
301. 10:34with a bit of practice, your mental math
302. 10:36will get faster. Good luck on that.
303. 10:38Anyway, thanks. See you.