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Back to Calculation Tips & Tricks
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From B. Lee Clay


 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 1/16
  19. 2 digits by 1 1/15
  20. 2 digits by 1.1
  21. 2 digits by 1 1/9
  22. 2 digits by 1 1/8
  23. 2 digits by 1 1/7
  24. 2 digits by 1 1/6
  25. 2 digits by 1 1/5
  26. 2 digits by 1 2/9
  27. 2 digits by 1 1/4
  28. 2 digits by 1 2/7
  29. 2 digits by 1.3
  30. 2 digits by 1 1/3
  31. 2 digits by 1 3/8
  32. 2 digits by 1 2/5
  33. 2 digits by 1 3/7
  34. 2 digits by 1 1/2
  35. 2 digits by 1 4/7
  36. 2 digits by 1 3/5
  37. 2 digits by 1.6
  38. 2,3 digits by 1 2/3
  39. 2 digits by 1.7
  40. 2 digits by 1 5/7
  41. 2 digits by 1 3/4
  42. 2 digits by 1 4/5
  43. 2 digits by 1 5/6
  44. 2 digits by 1 6/7
  45. 2 digits by 1.9
  46. 2 digits by 2.1
  47. 2 digits by 2 1/9
  48. 2 digits by 2 1/7
  49. 2 digits by 2 1/5
  50. 2 digits by 2 2/9
  51. 2 digits by 2 1/4
  52. 2 digits by 2.3
  53. 2 digits by 2 1/3
  54. 2 digits by 2 3/8
  55. 2 digits by 2 2/5
  56. 2 digits by 2.4
  57. 2 digits by 2 4/9
  58. 2, 3 digits by 2 1/2
  59. 2 digits by 2 4/7
  60. 2 digits by 2.6
  61. 2 digits by 2 5/8
  62. 2 digits by 2 2/3
  63. 2 digits by 2.7
  64. 2 digits by 2 5/7
  65. 2 digits by 2 3/4
  66. 2 digits by 2.8
  67. 2 digits by 2 7/9
  68. 2 digits by 2 6/7
  69. 2 digits by 2.9
  70. 2 digits by 3.1
  71. 2 digits by 3 1/8
  72. 2 digits by 3 1/7
  73. 2 digits by 3 1/6
  74. 2 digits by 3.2
  75. 2 digits by 3 2/9
  76. 2 digits by 3 1/4
  77. 2 digits by 3 1/3
  78. 2 digits by 3.4
  79. 2 digits by 3 3/7
  80. 2 digits by 3 4/9
  81. 2 digits by 3 1/2
  82. 2 digits by 3.6
  83. 2 digits by 3 4/7
  84. 2 digits by 3 5/8
  85. 2 digits by 3 2/3
  86. 2 digits by 3.7
  87. 2 digits by 3 5/7
  88. 2 digits by 3 3/4
  89. 2 digits by 3 4/5
  90. 2 digits by 3 6/7
  91. 2 digits by 3 7/8
  92. 2 digits by 3.9
  93. 2 digits by 4.1
  94. 2 digits by 4 1/4
  95. 2 digits by 4 1/7
  96. 2 digits by 4 1/6
  97. 2 digits by 4 1/5
  98. 2 digits by 4 2/7
  99. 2 digits by 4 1/3
  100. 2 digits by 4.3
  101. 2 digits by 4.4
  102. 2 digits by 4 3/7
  103. 2 digits by 4 4/9
  104. 2 digits by 4 1/2
  105. 2 digits by 4 5/9
  106. 2 digits by 4.6
  107. 2 digits by 4 2/3
  108. 2 digits by 4.7
  109. 2 digits by 4 3/4
  110. 2 digits by 4 4/5
  111. 2 digits by 4 5/6
  112. 2 digits by 4 7/8
  113. 2 digits by 4.9
  114. 2 digits by 5.1
  115. 2 digits by 5 1/8
  116. 2 digits by 5 1/6
  117. 2 digits by 5.2
  118. 2 digits by 5 1/4
  119. 2 digits by 5.3
  120. 2 digits by 5 4/9
  121. 2 digits by 5 1/2
  122. 2 digits by 5 5/9
  123. 2 digits by 5.6
  124. 2 digits by 5.7
  125. 2 digits by 5 4/7
  126. 2 digits by 5 5/7
  127. 2 digits by 5 4/5
  128. 2 digits by 5 6/7
  129. 2 digits by 5.9
  130. 2 digits by 6.1
  131. 2 digits by 6 1/8
  132. 2 digits by 6 1/5
  133. 2 digits by 6 1/4
  134. 2 digits by 6.3
  135. 2 digits by 6 1/3
  136. 2 digits by 6 3/8
  137. 2 digits by 6.4
  138. 2 digits by 6 4/9
  139. 2 digits by 6 1/2
  140. 2 digits by 6 5/9
  141. 2 digits by 6.6
  142. 2 digits by 6 2/3
  143. 2 digits by 6 7/9
  144. 2 digits by 6 5/6
  145. 2 digits by 6.8
  146. 2 digits by 6 6/7
  147. 2 digits by 6 8/9
  148. 2 digits by 6.9
  149. 2 digits by 7.1
  150. 2 digits by 7 1/7
  151. 2 digits by 7.2
  152. 2 digits by 7 1/4
  153. 2 digits by 7.3
  154. 2 digits by 7 2/7
  155. 2 digits by 7.4
  156. 2 digits by 7 1/2
  157. 2 digits by 7 3/5
  158. 2 digits by 7.6
  159. 2 digits by 7.7
  160. 2 digits by 7 3/4
  161. 2 digits by 7 4/5
  162. 2 digits by 8.1
  163. 2 digits by 8 1/6
  164. 2 digits by 8.2
  165. 2 digits by 8 2/7
  166. 2 digits by 8.3
  167. 2 digits by 8 1/3
  168. 2 digits by 8 3/7
  169. 2 digits by 8 4/7
  170. 2 digits by 8 1/2
  171. 2 digits by 8.6
  172. 2 digits by 8 5/8
  173. 2 digits by 8 2/3
  174. 2 digits by 8 5/7
  175. 2 digits by 8 7/9
  176. 2 digits by 8.8
  177. 2 digits by 8 7/8
  178. 2 digits by 8 8/9
  179. 2 digits by 8.9
  180. 2 digits by 9.1
  181. 2 digits by 9.2
  182. 2 digits by 9.3
  183. 2 digits by 9 1/3
  184. 2 digits by 9.4
  185. 2 digits by 9 1/2 (four steps)
  186. 2 digits by 9 1/2 (two steps)
  187. 2 digits by 9.6
  188. 2 digits by 9 2/3
  189. 2 digits by 9 5/7
  190. 2 digits by 9.7
  191. 2 digits by 9 3/4
  192. 2 digits by 9 7/9
  193. 2 digits by 9 4/5
  194. 2 digits by 9 5/6
  195. 2 digits by 9 6/7
  196. 2 digits by 9 7/8
  197. 2 digits by 9 8/9
  198. 2 digits by 10.1
  199. 2 digits by 10.4
  200. 2 digits by 10.6
  201. 2 digits by 10.7
  202. 2 digits by 10 1/2
  203. 2 digits by 11 1/2
  204. 2 digits by 12 1/2
  205. 2 digits by 15
  206. 2,3 digits by 16 2/3
  207. 2 digits by 18
  208. 2 digits by 19 1/2
  209. 2 digits by 20 1/2
  210. 2 digits by 21
  211. 2 digits by 22
  212. 2 digits by 23
  213. 2 digits by 24
  214. 2,3 digits by 25
  215. 2 digits by 26
  216. 2 digits by 27
  217. 2 digits by 28
  218. 2 digits by 29
  219. 2 digits by 29 1/2
  220. 2 digits by 30 1/2
  221. 2 digits by 31
  222. 2 digits by 32
  223. 2 digits by 33
  224. 2 digits by 33 1/3
  225. 2 digits by 34
  226. 2 digits by 35
  227. 2 digits by 36
  228. 2 digits by 37
  229. 2 digits by 37 1/2
  230. 2 digits by 38
  231. 2 digits by 39
  232. 2 digits by 39 1/2
  233. 2 digits by 40 1/2
  234. 2 digits by 42
  235. 2 digits by 43
  236. 2 digits by 44
  237. 2 digits by 45
  238. 2 digits by 46
  239. 2 digits by 47
  240. 2 digits by 48
  241. 2 digits by 49 (a)
  242. 2 digits by 49 (b)
  243. 2 digits by 49 1/2
  244. 2 digits by 50 1/2
  245. 2 digits by 51
  246. 2 digits by 52
  247. 2 digits by 53
  248. 2 digits by 54
  249. 2 digits by 55 (a)
  250. 2 digits by 55 (b)
  251. 2 digits by 56
  252. 2 digits by 57
  253. 2 digits by 58
  254. 2 digits by 59
  255. 2 digits by 59 1/2
  256. 2 digits by 60 1/2
  257. 2 digits by 61
  258. 2 digits by 62
  259. 2 digits by 63
  260. 2 digits by 64
  261. 2 digits by 65
  262. 2 digits by 66
  263. 2 digits by 67
  264. 2 digits by 68
  265. 2 digits by 69
  266. 2 digits by 69 1/2
  267. 2 digits by 70 1/2
  268. 2 digits by 71
  269. 2 digits by 72
  270. 2 digits by 73
  271. 2 digits by 74
  272. 2,3 digits by 75
  273. 2 digits by 76
  274. 2 digits by 77
  275. 2 digits by 78
  276. 2 digits by 79
  277. 2 digits by 79 1/2
  278. 2 digits by 80 1/2
  279. 2 digits by 81
  280. 2 digits by 82
  281. 2 digits by 83
  282. 2 digits by 84
  283. 2 digits by 85
  284. 2 digits by 86
  285. 2 digits by 87
  286. 2 digits by 88
  287. 2 digits by 89
  288. 2 digits by 89 1/2
  289. 2 digits by 90 1/2
  290. 2 digits by 91
  291. 2 digits by 92
  292. 2 digits by 93
  293. 2 digits by 94
  294. 2 digits by 95
  295. 2 digits by 97
  296. 2 digits by 98
  297. 2 digits by 99
  298. 3 digits by 99
  299. 2,3 digits by 101
  300. 2 digits by 102 + 11
  301. 2 digits by 103 + 12
  302. 2 digits by 125
  303. 3 digits by 143
  304. 2 digits by 166 2/3
  305. 2 digits by 198
  306. 2 digits by 201 + 11
  307. 2 digits by 202 + 11
  308. 2 digits by 250
  309. 2 digits by 297
  310. 2 digits by 375
  311. 2 digits by 396
  312. 2 digits by 495
  313. 2 digits by 594
  314. 2 digits by 625
  315. 2 digits by 693
  316. 2 digits by 792
  317. 2 digits by 875
  318. 2 digits by 891
  319. 2 digits by 999
  320. 2,3 digits by 1001 + 21,201
  321. 2-4 digits by 1000, + 21, 201, 2001
  322. 2-5 digits by 100001
  323. 1 rep. by 9 rep.
  324. 1 rep. by 12 rep.
  325. 1 rep. by 13 rep.
  326. 1 rep. by 14 rep.
  327. 1 rep. by 15 rep.
  328. 1 rep. by 16 rep.
  329. 1 rep. by 17 rep.
  330. 1 rep. by 18 rep.
  331. 1 rep. by 19 rep.
  332. 1 rep. by 21
  333. 1 rep. by 22
  334. 1 rep. by 23
  335. 1 rep. by 24
  336. 1 rep. by 25
  337. 1 rep. by 26
  338. 1 rep. by 27
  339. 1 rep. by 29
  340. 1 rep. by 33
  341. 1 rep. by 41
  342. 1 rep. by 44
  343. 1 rep. by 45
  344. 1 rep. by 55
  345. 1 rep. by 66
  346. 1 rep. by 77
  347. 1 rep. by 88
  348. 1 rep. by 99
  349. 1 rep. by 222
  350. 1 rep. by 333
  351. 2 rep. by 5 rep.
  352. 2 rep. by 9 rep.
  353. 2 rep. by 12
  354. 2 rep. by 13
  355. 2 rep. by 14
  356. 2 rep. by 15
  357. 2 rep. by 16
  358. 2 rep. by 17
  359. 2 rep. by 22
  360. 2 rep. by 24
  361. 2 rep. by 28
  362. 2 rep. by 29
  363. 2 rep. by 33
  364. 2 rep. by 44
  365. 2 rep. by 45
  366. 2 rep. by 55
  367. 2 rep. by 66
  368. 2 rep. by 77
  369. 2 rep. by 88
  370. 2 rep. by 99
  371. 3 rep. by 6 rep.
  372. 3 rep. by 9 rep.
  373. 3 rep. by 13
  374. 3 rep. by 14
  375. 3 rep. by 15
  376. 3 rep. by 22
  377. 3 rep. by 23
  378. 3 rep. by 24
  379. 3 rep. by 35
  380. 3 rep. by 55
  381. 3 rep. by 66
  382. 3 rep. by 77
  383. 3 rep. by 88
  384. 3 rep. by 99
  385. 4 rep. by 13
  386. 4 rep. by 14
  387. 4 rep. by 15
  388. 4 rep. by 17
  389. 4 rep. by 22
  390. 4 rep. by 24
  391. 4 rep. by 28
  392. 4 rep. by 31
  393. 4 rep. by 36
  394. 4 rep. by 42
  395. 4 rep. by 44
  396. 4 rep. by 55
  397. 4 rep. by 66
  398. 4 rep. by 88
  399. 4 rep. by 99
  400. 4 rep. by 3 rep.
  401. 4 rep. by 5 rep.
  402. 4 rep. by 9 rep.
  403. 5 rep. by 15
  404. 5 rep. by 25
  405. 5 rep. by 28
  406. 5 rep. by 33
  407. 5 rep. by 55
  408. 5 rep. by 66
  409. 5 rep. by 77
  410. 5 rep. by 88
  411. 5 rep. by 99
  412. 5 rep. by 9 rep.
  413. 6 rep. by 9 rep.
  414. 6 rep. by 12
  415. 6 rep. by 15
  416. 6 rep. by 16
  417. 6 rep. by 22
  418. 6 rep. by 31
  419. 6 rep. by 32
  420. 6 rep. by 33
  421. 6 rep. by 43
  422. 6 rep. by 55
  423. 6 rep. by 66
  424. 6 rep. by 77
  425. 6 rep. by 88
  426. 6 rep. by 444
  427. 6 rep. by 888
  428. 7 rep. by 9 rep.
  429. 7 rep. by 15
  430. 7 rep. by 17
  431. 7 rep. by 32
  432. 7 rep. by 33
  433. 7 rep. by 42
  434. 7 rep. by 44
  435. 7 rep. by 55
  436. 7 rep. by 66
  437. 7 rep. by 77
  438. 7 rep. by 88
  439. 7 rep. by 99
  440. 8 rep. by 9 rep.
  441. 8 rep. by 22
  442. 8 rep. by 23
  443. 8 rep. by 24
  444. 8 rep. by 29
  445. 8 rep. by 36
  446. 8 rep. by 44
  447. 8 rep. by 55
  448. 8 rep. by 66
  449. 8 rep. by 88
  450. 9 rep. by 14
  451. 9 rep. by 22
  452. 9 rep. by 25
  453. 9 rep. by 27
  454. 9 rep. by 33
  455. 9 rep. by 44
  456. 9 rep. by 55
  457. 9 rep. by 77
  458. 9 rep. by 88
  459. 9 rep. by 99
  460. 3 repeating by 2, /37
  461. 3 repeating by 5, /37
  462. 9 rep. by 3, /12345679
  463. multi-digits by 8 + last digit
  464. by 8, add number, - 20
  465. integer + 1/2 times, + 1
  466. sum,difference of 2,1 digits
  467. two mixed numbers
  468. two mixed numbers,fractions
  469. 4 digits by 99
  470. 4 digits by 137, then 73; -1200
  471. 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, 2nd digits sum to 10)

  1. Both numbers should have the same first digit.
  2. Choose second digits whose sum is 10.
  3. Multiply the first digit by one number greater than itself; this number will be the first part of the answer:
    X X _ _.
  4. Multiply the two second digits together; the product
    will be the last part of the answer: _ _ X X.

Note: If the two second digits are 1 and 9 (or, more generally, have a product that is less than ten), insert a 0 (zero) for the first X in step 4.

(Thanks to Michael Richardson, age 10, for this note.)

   Example:

  1. If the first number is 47, choose 43 as the second number (same first digit, second digits add to 10).
  2. 4 × 5 = 20 (multiply the first digit by one number greater than itself): the first part of the answer is
    2 0 _ _.
  3. 7 × 3 = 21 (multiply the two second digits together); the last part of the answer is _ _ 2 1.
  4. So 47 × 43 = 2021.

   See the pattern?

  1. If the first number is 62, choose 68 as the second number (same first digit, second digits add to 10).
  2. 6 × 7 = 42 (multiply the first digit by one greater), the first part of the answer is 4 2 _ _.
  3. 2 × 8 = 16 (multiply the two second digits together); the last part of the answer is _ _ 1 6.
  4. So 62 × 68 = 4216.


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14 January 1996
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