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 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 2.8
  64. 2 digits by 2 7/9
  65. 2 digits by 2 6/7
  66. 2 digits by 2.9
  67. 2 digits by 3.1
  68. 2 digits by 3 1/8
  69. 2 digits by 3 1/7
  70. 2 digits by 3 1/6
  71. 2 digits by 3.2
  72. 2 digits by 3 2/9
  73. 2 digits by 3 1/4
  74. 2 digits by 3 1/3
  75. 2 digits by 3.4
  76. 2 digits by 3 3/7
  77. 2 digits by 3 4/9
  78. 2 digits by 3 1/2
  79. 2 digits by 3.6
  80. 2 digits by 3 4/7
  81. 2 digits by 3 5/8
  82. 2 digits by 3 2/3
  83. 2 digits by 3.7
  84. 2 digits by 3 5/7
  85. 2 digits by 3 3/4
  86. 2 digits by 3 4/5
  87. 2 digits by 3 6/7
  88. 2 digits by 3 7/8
  89. 2 digits by 3.9
  90. 2 digits by 4.1
  91. 2 digits by 4 1/4
  92. 2 digits by 4 1/7
  93. 2 digits by 4 1/6
  94. 2 digits by 4 1/5
  95. 2 digits by 4 2/7
  96. 2 digits by 4.3
  97. 2 digits by 4.4
  98. 2 digits by 4 3/7
  99. 2 digits by 4 4/9
  100. 2 digits by 4 1/2
  101. 2 digits by 4 5/9
  102. 2 digits by 4.6
  103. 2 digits by 4.7
  104. 2 digits by 4 3/4
  105. 2 digits by 4 4/5
  106. 2 digits by 4 5/6
  107. 2 digits by 4 7/8
  108. 2 digits by 5.1
  109. 2 digits by 5 1/8
  110. 2 digits by 5 1/6
  111. 2 digits by 5.2
  112. 2 digits by 5 1/4
  113. 2 digits by 5.3
  114. 2 digits by 5 4/9
  115. 2 digits by 5 1/2
  116. 2 digits by 5 5/9
  117. 2 digits by 5.6
  118. 2 digits by 5.7
  119. 2 digits by 5 4/7
  120. 2 digits by 5 5/7
  121. 2 digits by 5 4/5
  122. 2 digits by 5 6/7
  123. 2 digits by 5.9
  124. 2 digits by 6.1
  125. 2 digits by 6 1/8
  126. 2 digits by 6 1/5
  127. 2 digits by 6 1/4
  128. 2 digits by 6.3
  129. 2 digits by 6 1/3
  130. 2 digits by 6 3/8
  131. 2 digits by 6.4
  132. 2 digits by 6 4/9
  133. 2 digits by 6 1/2
  134. 2 digits by 6 5/9
  135. 2 digits by 6.6
  136. 2 digits by 6 2/3
  137. 2 digits by 6 7/9
  138. 2 digits by 6 5/6
  139. 2 digits by 6 6/7
  140. 2 digits by 6 8/9
  141. 2 digits by 7.1
  142. 2 digits by 7 1/7
  143. 2 digits by 7.2
  144. 2 digits by 7 1/4
  145. 2 digits by 7.3
  146. 2 digits by 7 2/7
  147. 2 digits by 7.4
  148. 2 digits by 7 1/2
  149. 2 digits by 7 3/5
  150. 2 digits by 7.6
  151. 2 digits by 7.7
  152. 2 digits by 7 3/4
  153. 2 digits by 7 4/5
  154. 2 digits by 8.1
  155. 2 digits by 8 1/6
  156. 2 digits by 8.2
  157. 2 digits by 8 2/7
  158. 2 digits by 8.3
  159. 2 digits by 8 1/3
  160. 2 digits by 8 3/7
  161. 2 digits by 8 4/7
  162. 2 digits by 8 1/2
  163. 2 digits by 8.6
  164. 2 digits by 8 5/8
  165. 2 digits by 8 2/3
  166. 2 digits by 8 5/7
  167. 2 digits by 8 7/9
  168. 2 digits by 8 7/8
  169. 2 digits by 8 8/9
  170. 2 digits by 9.1
  171. 2 digits by 9.2
  172. 2 digits by 9.3
  173. 2 digits by 9 1/3
  174. 2 digits by 9.4
  175. 2 digits by 9 1/2 (four steps)
  176. 2 digits by 9 1/2 (two steps)
  177. 2 digits by 9.6
  178. 2 digits by 9 2/3
  179. 2 digits by 9 5/7
  180. 2 digits by 9.7
  181. 2 digits by 9 3/4
  182. 2 digits by 9 7/9
  183. 2 digits by 9 4/5
  184. 2 digits by 9 5/6
  185. 2 digits by 9 6/7
  186. 2 digits by 9 7/8
  187. 2 digits by 9 8/9
  188. 2 digits by 10.1
  189. 2 digits by 10.4
  190. 2 digits by 10.7
  191. 2 digits by 10 1/2
  192. 2 digits by 11 1/2
  193. 2 digits by 12 1/2
  194. 2 digits by 15
  195. 2,3 digits by 16 2/3
  196. 2 digits by 18
  197. 2 digits by 19 1/2
  198. 2 digits by 20 1/2
  199. 2 digits by 21
  200. 2 digits by 22
  201. 2 digits by 23
  202. 2 digits by 24
  203. 2,3 digits by 25
  204. 2 digits by 26
  205. 2 digits by 27
  206. 2 digits by 28
  207. 2 digits by 29
  208. 2 digits by 29 1/2
  209. 2 digits by 30 1/2
  210. 2 digits by 31
  211. 2 digits by 32
  212. 2 digits by 33
  213. 2 digits by 33 1/3
  214. 2 digits by 34
  215. 2 digits by 35
  216. 2 digits by 36
  217. 2 digits by 37
  218. 2 digits by 37 1/2
  219. 2 digits by 38
  220. 2 digits by 39
  221. 2 digits by 39 1/2
  222. 2 digits by 40 1/2
  223. 2 digits by 42
  224. 2 digits by 43
  225. 2 digits by 44
  226. 2 digits by 45
  227. 2 digits by 46
  228. 2 digits by 47
  229. 2 digits by 48
  230. 2 digits by 49 (a)
  231. 2 digits by 49 (b)
  232. 2 digits by 49 1/2
  233. 2 digits by 50 1/2
  234. 2 digits by 51
  235. 2 digits by 52
  236. 2 digits by 53
  237. 2 digits by 54
  238. 2 digits by 55 (a)
  239. 2 digits by 55 (b)
  240. 2 digits by 56
  241. 2 digits by 57
  242. 2 digits by 58
  243. 2 digits by 59
  244. 2 digits by 59 1/2
  245. 2 digits by 60 1/2
  246. 2 digits by 61
  247. 2 digits by 62
  248. 2 digits by 63
  249. 2 digits by 64
  250. 2 digits by 65
  251. 2 digits by 66
  252. 2 digits by 67
  253. 2 digits by 68
  254. 2 digits by 69
  255. 2 digits by 69 1/2
  256. 2 digits by 70 1/2
  257. 2 digits by 71
  258. 2 digits by 72
  259. 2 digits by 73
  260. 2 digits by 74
  261. 2,3 digits by 75
  262. 2 digits by 76
  263. 2 digits by 77
  264. 2 digits by 78
  265. 2 digits by 79
  266. 2 digits by 79 1/2
  267. 2 digits by 80 1/2
  268. 2 digits by 81
  269. 2 digits by 82
  270. 2 digits by 83
  271. 2 digits by 84
  272. 2 digits by 85
  273. 2 digits by 86
  274. 2 digits by 87
  275. 2 digits by 88
  276. 2 digits by 89
  277. 2 digits by 89 1/2
  278. 2 digits by 90 1/2
  279. 2 digits by 91
  280. 2 digits by 92
  281. 2 digits by 93
  282. 2 digits by 94
  283. 2 digits by 97
  284. 2 digits by 99
  285. 3 digits by 99
  286. 2,3 digits by 101
  287. 2 digits by 102 + 11
  288. 2 digits by 103 + 12
  289. 2 digits by 125
  290. 3 digits by 143
  291. 2 digits by 166 2/3
  292. 2 digits by 198
  293. 2 digits by 201 + 11
  294. 2 digits by 202 + 11
  295. 2 digits by 250
  296. 2 digits by 297
  297. 2 digits by 375
  298. 2 digits by 396
  299. 2 digits by 495
  300. 2 digits by 594
  301. 2 digits by 625
  302. 2 digits by 693
  303. 2 digits by 792
  304. 2 digits by 875
  305. 2 digits by 891
  306. 2 digits by 999
  307. 2,3 digits by 1001 + 21,201
  308. 2-4 digits by 1000, + 21, 201, 2001
  309. 2-5 digits by 100001
  310. 1 rep. by 9 rep.
  311. 1 rep. by 12 rep.
  312. 1 rep. by 13 rep.
  313. 1 rep. by 14 rep.
  314. 1 rep. by 15 rep.
  315. 1 rep. by 16 rep.
  316. 1 rep. by 17 rep.
  317. 1 rep. by 18 rep.
  318. 1 rep. by 19 rep.
  319. 1 rep. by 21
  320. 1 rep. by 22
  321. 1 rep. by 23
  322. 1 rep. by 24
  323. 1 rep. by 25
  324. 1 rep. by 26
  325. 1 rep. by 27
  326. 1 rep. by 29
  327. 1 rep. by 33
  328. 1 rep. by 41
  329. 1 rep. by 44
  330. 1 rep. by 45
  331. 1 rep. by 55
  332. 1 rep. by 66
  333. 1 rep. by 77
  334. 1 rep. by 88
  335. 1 rep. by 99
  336. 1 rep. by 222
  337. 1 rep. by 333
  338. 2 rep. by 5 rep.
  339. 2 rep. by 9 rep.
  340. 2 rep. by 12
  341. 2 rep. by 13
  342. 2 rep. by 14
  343. 2 rep. by 15
  344. 2 rep. by 16
  345. 2 rep. by 17
  346. 2 rep. by 22
  347. 2 rep. by 24
  348. 2 rep. by 28
  349. 2 rep. by 33
  350. 2 rep. by 44
  351. 2 rep. by 45
  352. 2 rep. by 55
  353. 2 rep. by 66
  354. 2 rep. by 77
  355. 2 rep. by 88
  356. 2 rep. by 99
  357. 3 rep. by 6 rep.
  358. 3 rep. by 9 rep.
  359. 3 rep. by 13
  360. 3 rep. by 15
  361. 3 rep. by 23
  362. 3 rep. by 35
  363. 3 rep. by 55
  364. 3 rep. by 66
  365. 3 rep. by 77
  366. 3 rep. by 88
  367. 3 rep. by 99
  368. 4 rep. by 15
  369. 4 rep. by 17
  370. 4 rep. by 22
  371. 4 rep. by 24
  372. 4 rep. by 28
  373. 4 rep. by 31
  374. 4 rep. by 36
  375. 4 rep. by 42
  376. 4 rep. by 44
  377. 4 rep. by 55
  378. 4 rep. by 88
  379. 4 rep. by 3 rep.
  380. 4 rep. by 5 rep.
  381. 4 rep. by 9 rep.
  382. 5 rep. by 25
  383. 5 rep. by 28
  384. 5 rep. by 33
  385. 5 rep. by 55
  386. 5 rep. by 66
  387. 5 rep. by 88
  388. 5 rep. by 9 rep.
  389. 6 rep. by 9 rep.
  390. 6 rep. by 12
  391. 6 rep. by 16
  392. 6 rep. by 22
  393. 6 rep. by 31
  394. 6 rep. by 32
  395. 6 rep. by 33
  396. 6 rep. by 43
  397. 6 rep. by 66
  398. 6 rep. by 77
  399. 6 rep. by 88
  400. 6 rep. by 444
  401. 6 rep. by 888
  402. 7 rep. by 9 rep.
  403. 7 rep. by 17
  404. 7 rep. by 32
  405. 7 rep. by 33
  406. 7 rep. by 42
  407. 7 rep. by 44
  408. 7 rep. by 55
  409. 7 rep. by 88
  410. 8 rep. by 9 rep.
  411. 8 rep. by 22
  412. 8 rep. by 23
  413. 8 rep. by 29
  414. 8 rep. by 36
  415. 8 rep. by 44
  416. 8 rep. by 55
  417. 8 rep. by 66
  418. 8 rep. by 88
  419. 9 rep. by 14
  420. 9 rep. by 22
  421. 9 rep. by 25
  422. 9 rep. by 27
  423. 9 rep. by 33
  424. 9 rep. by 44
  425. 9 rep. by 55
  426. 9 rep. by 77
  427. 9 rep. by 99
  428. 3 repeating by 2, /37
  429. 3 repeating by 5, /37
  430. 9 rep. by 3, /12345679
  431. multi-digits by 8 + last digit
  432. by 8, add number, - 20
  433. integer + 1/2 times, + 1
  434. sum,difference of 2,1 digits
  435. two mixed numbers
  436. two mixed numbers,fractions
  437. 4 digits by 99
  438. 4 digits by 137, then 73; -1200
  439. 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
            (difference of 1)

  1. Choose a 2-digit number.
  2. Select a number either 1 smaller or 1 larger.
  3. Square the larger number (multiply it by itself).
  4. Subtract the larger number from the product.
    OR
  5. Square the smaller number (multiply it by itself).
  6. Add the smaller number to the product. Pick the easier one to square.

   Example:

  1. If the first number is 76, choose 75 as the second number.
  2. 75 × 75 = 5625 (square the smaller). Remember how to square a two-digit number ending in 5?
  3. 5625 + 75 = 5700 (add the smaller).
  4. So 76 × 75 = 5700.

   See the pattern?

  1. If the first number is 32, choose 31 as the second number.
  2. 32 × 32 = 1024 (square the larger). Remember how to square a two-digit number ending in 2?
  3. 1024 - 32 = 992 (subtract the larger).
  4. So 32 × 31 = 992.


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14 January 1996
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