BEATCALC:  Beat the Calculator!

___________________________________________
Back to Calculation Tips & Tricks
___________________________________________

From the BEATCALC mailing list:
a weekly service from B. Lee Clay, archived here by the Math Forum.
To subscribe to the BEATCALC mailing list, write to BEATCALC@aol.com.


 Squaring Numbers

 Multiplying Numbers

  1. same 1st digit
  2. same 1st digit, sum 10
  3. same 2nd digit
  4. 3 digits, middle 0
  5. 3 digits, middle 1
  6. 3 digits, middle 2
  7. 3 digits, middle 3
  8. 3 digits, middle 4
  9. 3 digits, middle 5
  10. difference of 1
  11. difference of 2
  12. difference of 3
  13. difference of 4
  14. difference of 6
  15. difference of 8
  16. difference of 10
  17. 2 digits by 1 1/25
  18. 2 digits by 1.1
  19. 2 digits by 1 1/9
  20. 2 digits by 1 1/8
  21. 2 digits by 1 1/7
  22. 2 digits by 1 1/6
  23. 2 digits by 1 1/5
  24. 2 digits by 1 2/9
  25. 2 digits by 1 1/4
  26. 2 digits by 1 2/7
  27. 2 digits by 1.3
  28. 2 digits by 1 1/3
  29. 2 digits by 1 3/8
  30. 2 digits by 1 2/5
  31. 2 digits by 1 3/7
  32. 2 digits by 1 1/2
  33. 2 digits by 1 4/7
  34. 2 digits by 1 3/5
  35. 2 digits by 1.6
  36. 2,3 digits by 1 2/3
  37. 2 digits by 1 5/7
  38. 2 digits by 1 3/4
  39. 2 digits by 1 4/5
  40. 2 digits by 1 5/6
  41. 2 digits by 1 6/7
  42. 2 digits by 1.9
  43. 2 digits by 2.1
  44. 2 digits by 2 1/9
  45. 2 digits by 2 1/7
  46. 2 digits by 2 1/5
  47. 2 digits by 2 2/9
  48. 2 digits by 2 1/4
  49. 2 digits by 2.3
  50. 2 digits by 2 1/3
  51. 2 digits by 2 3/8
  52. 2 digits by 2 2/5
  53. 2 digits by 2.4
  54. 2 digits by 2 4/9
  55. 2, 3 digits by 2 1/2
  56. 2 digits by 2 4/7
  57. 2 digits by 2.6
  58. 2 digits by 2 5/8
  59. 2 digits by 2 2/3
  60. 2 digits by 2.7
  61. 2 digits by 2 5/7
  62. 2 digits by 2 3/4
  63. 2 digits by 2 7/9
  64. 2 digits by 2 6/7
  65. 2 digits by 2.9
  66. 2 digits by 3.1
  67. 2 digits by 3 1/8
  68. 2 digits by 3 1/7
  69. 2 digits by 3 1/6
  70. 2 digits by 3.2
  71. 2 digits by 3 2/9
  72. 2 digits by 3 1/3
  73. 2 digits by 3.4
  74. 2 digits by 3 3/7
  75. 2 digits by 3 4/9
  76. 2 digits by 3 1/2
  77. 2 digits by 3.6
  78. 2 digits by 3 4/7
  79. 2 digits by 3 5/8
  80. 2 digits by 3 2/3
  81. 2 digits by 3.7
  82. 2 digits by 3 5/7
  83. 2 digits by 3 3/4
  84. 2 digits by 3 4/5
  85. 2 digits by 3 6/7
  86. 2 digits by 3 7/8
  87. 2 digits by 3.9
  88. 2 digits by 4.1
  89. 2 digits by 4 1/4
  90. 2 digits by 4 1/7
  91. 2 digits by 4 1/6
  92. 2 digits by 4 1/5
  93. 2 digits by 4 2/7
  94. 2 digits by 4.3
  95. 2 digits by 4.4
  96. 2 digits by 4 3/7
  97. 2 digits by 4 4/9
  98. 2 digits by 4 1/2
  99. 2 digits by 4 5/9
  100. 2 digits by 4.6
  101. 2 digits by 4.7
  102. 2 digits by 4 3/4
  103. 2 digits by 4 4/5
  104. 2 digits by 4 5/6
  105. 2 digits by 4 7/8
  106. 2 digits by 5.1
  107. 2 digits by 5 1/8
  108. 2 digits by 5 1/6
  109. 2 digits by 5.2
  110. 2 digits by 5 1/4
  111. 2 digits by 5.3
  112. 2 digits by 5 4/9
  113. 2 digits by 5 1/2
  114. 2 digits by 5 5/9
  115. 2 digits by 5.6
  116. 2 digits by 5.7
  117. 2 digits by 5 4/7
  118. 2 digits by 5 5/7
  119. 2 digits by 5 4/5
  120. 2 digits by 5 6/7
  121. 2 digits by 5.9
  122. 2 digits by 6.1
  123. 2 digits by 6 1/8
  124. 2 digits by 6 1/5
  125. 2 digits by 6 1/4
  126. 2 digits by 6.3
  127. 2 digits by 6 1/3
  128. 2 digits by 6 3/8
  129. 2 digits by 6.4
  130. 2 digits by 6 4/9
  131. 2 digits by 6 1/2
  132. 2 digits by 6 5/9
  133. 2 digits by 6.6
  134. 2 digits by 6 2/3
  135. 2 digits by 6 7/9
  136. 2 digits by 6 5/6
  137. 2 digits by 6 6/7
  138. 2 digits by 6 8/9
  139. 2 digits by 7.1
  140. 2 digits by 7 1/7
  141. 2 digits by 7.2
  142. 2 digits by 7 1/4
  143. 2 digits by 7.3
  144. 2 digits by 7 2/7
  145. 2 digits by 7.4
  146. 2 digits by 7 1/2
  147. 2 digits by 7 3/5
  148. 2 digits by 7.6
  149. 2 digits by 7.7
  150. 2 digits by 7 3/4
  151. 2 digits by 7 4/5
  152. 2 digits by 8.1
  153. 2 digits by 8 1/6
  154. 2 digits by 8.2
  155. 2 digits by 8 2/7
  156. 2 digits by 8.3
  157. 2 digits by 8 1/3
  158. 2 digits by 8 3/7
  159. 2 digits by 8 4/7
  160. 2 digits by 8 1/2
  161. 2 digits by 8.6
  162. 2 digits by 8 5/8
  163. 2 digits by 8 2/3
  164. 2 digits by 8 5/7
  165. 2 digits by 8 7/9
  166. 2 digits by 8 7/8
  167. 2 digits by 8 8/9
  168. 2 digits by 9.1
  169. 2 digits by 9.2
  170. 2 digits by 9.3
  171. 2 digits by 9 1/3
  172. 2 digits by 9.4
  173. 2 digits by 9 1/2 (four steps)
  174. 2 digits by 9 1/2 (two steps)
  175. 2 digits by 9.6
  176. 2 digits by 9 2/3
  177. 2 digits by 9 5/7
  178. 2 digits by 9.7
  179. 2 digits by 9 3/4
  180. 2 digits by 9 7/9
  181. 2 digits by 9 4/5
  182. 2 digits by 9 5/6
  183. 2 digits by 9 6/7
  184. 2 digits by 9 7/8
  185. 2 digits by 9 8/9
  186. 2 digits by 10.1
  187. 2 digits by 10.4
  188. 2 digits by 10.7
  189. 2 digits by 10 1/2
  190. 2 digits by 11 1/2
  191. 2 digits by 12 1/2
  192. 2 digits by 15
  193. 2,3 digits by 16 2/3
  194. 2 digits by 18
  195. 2 digits by 19 1/2
  196. 2 digits by 20 1/2
  197. 2 digits by 21
  198. 2 digits by 22
  199. 2 digits by 23
  200. 2 digits by 24
  201. 2,3 digits by 25
  202. 2 digits by 26
  203. 2 digits by 27
  204. 2 digits by 28
  205. 2 digits by 29
  206. 2 digits by 29 1/2
  207. 2 digits by 30 1/2
  208. 2 digits by 31
  209. 2 digits by 32
  210. 2 digits by 33
  211. 2 digits by 33 1/3
  212. 2 digits by 34
  213. 2 digits by 35
  214. 2 digits by 36
  215. 2 digits by 37
  216. 2 digits by 37 1/2
  217. 2 digits by 38
  218. 2 digits by 39
  219. 2 digits by 39 1/2
  220. 2 digits by 40 1/2
  221. 2 digits by 42
  222. 2 digits by 43
  223. 2 digits by 44
  224. 2 digits by 45
  225. 2 digits by 46
  226. 2 digits by 47
  227. 2 digits by 48
  228. 2 digits by 49 (a)
  229. 2 digits by 49 (b)
  230. 2 digits by 49 1/2
  231. 2 digits by 50 1/2
  232. 2 digits by 51
  233. 2 digits by 52
  234. 2 digits by 53
  235. 2 digits by 54
  236. 2 digits by 55 (a)
  237. 2 digits by 55 (b)
  238. 2 digits by 56
  239. 2 digits by 57
  240. 2 digits by 58
  241. 2 digits by 59
  242. 2 digits by 59 1/2
  243. 2 digits by 60 1/2
  244. 2 digits by 61
  245. 2 digits by 62
  246. 2 digits by 63
  247. 2 digits by 64
  248. 2 digits by 65
  249. 2 digits by 66
  250. 2 digits by 67
  251. 2 digits by 68
  252. 2 digits by 69
  253. 2 digits by 69 1/2
  254. 2 digits by 70 1/2
  255. 2 digits by 71
  256. 2 digits by 72
  257. 2 digits by 73
  258. 2 digits by 74
  259. 2,3 digits by 75
  260. 2 digits by 76
  261. 2 digits by 77
  262. 2 digits by 78
  263. 2 digits by 79
  264. 2 digits by 79 1/2
  265. 2 digits by 80 1/2
  266. 2 digits by 81
  267. 2 digits by 82
  268. 2 digits by 83
  269. 2 digits by 84
  270. 2 digits by 85
  271. 2 digits by 86
  272. 2 digits by 87
  273. 2 digits by 88
  274. 2 digits by 89
  275. 2 digits by 89 1/2
  276. 2 digits by 90 1/2
  277. 2 digits by 91
  278. 2 digits by 92
  279. 2 digits by 93
  280. 2 digits by 94
  281. 2 digits by 97
  282. 2 digits by 99
  283. 3 digits by 99
  284. 2,3 digits by 101
  285. 2 digits by 102 + 11
  286. 2 digits by 103 + 12
  287. 2 digits by 125
  288. 3 digits by 143
  289. 2 digits by 166 2/3
  290. 2 digits by 198
  291. 2 digits by 201 + 11
  292. 2 digits by 202 + 11
  293. 2 digits by 250
  294. 2 digits by 297
  295. 2 digits by 375
  296. 2 digits by 396
  297. 2 digits by 495
  298. 2 digits by 594
  299. 2 digits by 625
  300. 2 digits by 693
  301. 2 digits by 792
  302. 2 digits by 875
  303. 2 digits by 891
  304. 2 digits by 999
  305. 2,3 digits by 1001 + 21,201
  306. 2-4 digits by 1000, + 21, 201, 2001
  307. 2-5 digits by 100001
  308. 1 rep. by 9 rep.
  309. 1 rep. by 12 rep.
  310. 1 rep. by 14 rep.
  311. 1 rep. by 15 rep.
  312. 1 rep. by 16 rep.
  313. 1 rep. by 17 rep.
  314. 1 rep. by 18 rep.
  315. 1 rep. by 19 rep.
  316. 1 rep. by 21
  317. 1 rep. by 22
  318. 1 rep. by 24
  319. 1 rep. by 25
  320. 1 rep. by 26
  321. 1 rep. by 27
  322. 1 rep. by 29
  323. 1 rep. by 33
  324. 1 rep. by 41
  325. 1 rep. by 44
  326. 1 rep. by 45
  327. 1 rep. by 55
  328. 1 rep. by 66
  329. 1 rep. by 77
  330. 1 rep. by 88
  331. 1 rep. by 99
  332. 1 rep. by 222
  333. 1 rep. by 333
  334. 2 rep. by 5 rep.
  335. 2 rep. by 9 rep.
  336. 2 rep. by 12
  337. 2 rep. by 16
  338. 2 rep. by 17
  339. 2 rep. by 22
  340. 2 rep. by 28
  341. 2 rep. by 33
  342. 2 rep. by 44
  343. 2 rep. by 55
  344. 2 rep. by 66
  345. 2 rep. by 77
  346. 2 rep. by 88
  347. 2 rep. by 99
  348. 3 rep. by 6 rep.
  349. 3 rep. by 9 rep.
  350. 3 rep. by 13
  351. 3 rep. by 15
  352. 3 rep. by 23
  353. 3 rep. by 35
  354. 3 rep. by 55
  355. 3 rep. by 66
  356. 3 rep. by 77
  357. 3 rep. by 88
  358. 3 rep. by 99
  359. 4 rep. by 15
  360. 4 rep. by 17
  361. 4 rep. by 22
  362. 4 rep. by 24
  363. 4 rep. by 28
  364. 4 rep. by 31
  365. 4 rep. by 36
  366. 4 rep. by 42
  367. 4 rep. by 44
  368. 4 rep. by 55
  369. 4 rep. by 88
  370. 4 rep. by 3 rep.
  371. 4 rep. by 5 rep.
  372. 4 rep. by 9 rep.
  373. 5 rep. by 25
  374. 5 rep. by 28
  375. 5 rep. by 33
  376. 5 rep. by 66
  377. 5 rep. by 88
  378. 5 rep. by 9 rep.
  379. 6 rep. by 9 rep.
  380. 6 rep. by 12
  381. 6 rep. by 16
  382. 6 rep. by 22
  383. 6 rep. by 31
  384. 6 rep. by 32
  385. 6 rep. by 33
  386. 6 rep. by 43
  387. 6 rep. by 66
  388. 6 rep. by 77
  389. 6 rep. by 88
  390. 6 rep. by 444
  391. 6 rep. by 888
  392. 7 rep. by 9 rep.
  393. 7 rep. by 17
  394. 7 rep. by 32
  395. 7 rep. by 33
  396. 7 rep. by 42
  397. 7 rep. by 44
  398. 7 rep. by 55
  399. 7 rep. by 88
  400. 8 rep. by 9 rep.
  401. 8 rep. by 22
  402. 8 rep. by 23
  403. 8 rep. by 29
  404. 8 rep. by 36
  405. 8 rep. by 44
  406. 8 rep. by 55
  407. 8 rep. by 66
  408. 8 rep. by 88
  409. 9 rep. by 14
  410. 9 rep. by 22
  411. 9 rep. by 25
  412. 9 rep. by 27
  413. 9 rep. by 33
  414. 9 rep. by 44
  415. 9 rep. by 55
  416. 9 rep. by 77
  417. 9 rep. by 99
  418. 3 repeating by 2, /37
  419. 3 repeating by 5, /37
  420. 9 rep. by 3, /12345679
  421. multi-digits by 8 + last digit
  422. by 8, add number, - 20
  423. integer + 1/2 times, + 1
  424. sum,difference of 2,1 digits
  425. two mixed numbers
  426. two mixed numbers,fractions
  427. 4 digits by 99
  428. 4 digits by 137, then 73; -1200
  429. 5 digits by 9091, then 11; -1200

 Dividing Numbers

 Adding Numbers

 Subtracting Numbers

 Finding Percents

Calculation
Practice Exercises

Full List


   Multiplying two 2-digit numbers
                (same 1st digit)

  1. Select two 2-digit numbers with the same first digit.
  2. Multiply their second digits (keep the carry).   _ _ _ X
  3. Multiply the sum of the second digits by the first digit,
    add the carry (keep the carry).   _ _ X _
  4. Multiply the first digits (add the carry).   X X _ _

   Example:

  1. If the first number is 42, choose 45 as the second number (any 2-digit number with first digit 4).
  2. Multiply the last digits: 2 × 5 = 10 (keep carry)  
    _ _ _ 0
  3. Multiply the sum of the 2nd digits by the first:
    5 + 2 = 7; 7 × 4 = 28; 28 + 1 = 29 (keep carry)  
    _ _ 9 _
  4. Multiply the first digits (add the carry)
    4 × 4 = 16; 16 + 2 = 18                           
    1 8 _ _

  5. So 42 × 45 = 1890.

   See the pattern?

  1. If the first number is 62, choose 67 as the second number
    (any 2-digit number with first digit 6).
  2. Multiply the last digits: 2 × 7 = 14 (keep carry)  
    _ _ _ 4
  3. Multiply the sum of the 2nd digits by the first (add carry):
    2 + 7 = 9; 6 × 9 = 54; 54 + 1 = 55 (keep carry)  
    _ _ 5 _
  4. Multiply the first digits (add the carry)
    6 × 6 = 36; 36 + 5 = 41                           
    4 1 _ _

  5. So 62 × 67 = 4154.


[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994-2008 Drexel University. All rights reserved.
http://mathforum.org/
 The Math Forum is a research and educational enterprise of the Drexel School of Education.The Math Forum is a research and educational enterprise of the Drexel School of Education.

3 November 1997
Web page design by Sarah Seastone