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METHOD OF PREDICTION.

25

No. of Integers in Multiplication is 3. 5 - 3=2.
:: No. of places required correct in the Multiplication is 2.

•3114260

8121
311426
62285
3114

2491
7,3 ) 379.318 ( £5.196
1431

3s. 11/d.
701
44

It is obvious that this preliminary determination removes all unnecessary work from the operations.

EXAMPLES. 1. Divide 87391.631 by 39.275 correct to 5 places. 2. Divide 35.8435 by 3978-34 correct to 8 places. 3. Divide 8341.976 by 731.25 correct to 4 places. 4. Divide 39:125678 by 80047.5 correct to 7 places. 5. Divide .00012356 by •967831 correct to 5 places. 6. Divide 93215•6789 by 6345.831 correct to 4 places. 7. Divide 473.87652 by 72:961 correct to 3 places. 8. Divide •00469857 by •043278 correct to 6 places. 9. Divide 9•65784321 by 5136.813 correct to 5 places. 10. Divide •000005678 by 2.1378562 correct to 8 places. 11. Divide £87156. 178. 10}d. by 931. 12. Divide £371. 98. 11 d. by 8047. 13. Divide £8296. 78. 4{d. by 325. 14. Divide £93756. 38. 4 d. by 37-75. 15. Divide £874259. 198. 8{d. by 893-125. 16. Divide £7432. 133. 11/d. by 71235. 17. Divide £310561. 98. 8 d. by 8673. 18. Divide £81. 78. 104d. by 91}. 19. Divide £312. 158. 3{d. by 1394. 20. Divide £8096. 12s. 11d. by 5760. 21. Find Int. on £712. 9s. 5ļd. for 27 days at 4 p.c.

22. Find Int. on £814. 48. 4£d. for 93 days at s} p.c. 23. Find Int. on £857. 58. 64d. for 271 days at 5 p.c. 24. Find Int. on £817. 6s. 3fd. for 89 days at 2 p.c. 25. Find Int. on £1218. 78. 5£d. for 91 days at 1} p.c. 26. Find Int. on £83. 13s. 7{d. for 357 days at 3 p.c. 27. Find Int. on £3765. 98. 8}d. for 183 days at 64 p.c. 28. Find Int. on £1763L. 116. 14d. for 71 days at 5 p.c. 29. Find Int. on £9061. 176. 4}d. for 109 days at 24 p.c. 30. Find Int. on £91. 78. 2d. for 153 days at 2 p.c.

CALCULATION OF PRICES.

27

SECTION II.

THE CALCULATION OF PRICES.

1. Mental or Very Brief Rules.-Applicable to Articles, Weights and Measures.

1°. Given the price of one.
(1) to find price of a dozen-consider price in d.

as 8

(2) to find price of a score-consider price in s. as £. (3) to find price of 48—consider price in f. as 8.

(4) to find price of 96—consider price in eighths of a penny as s.

(5) to find price of a gross-multiply price in f. as s. by 3 or price in d. as s. by 12 or consider price in d. as s. and this again in d. as s.

(6) to find price of 192—consider price in sixteenths of a penny as s.

(7) to find price of 240—consider price in d. as £. (8) to find price of 960—consider price in f. as £.

(9) to find price of 1920—consider price in eighths of a penny as £.

(10) to find price of 3840—consider price in sixteenths of a penny as £.

(11) to find price of any power of 10—decimalise the price into £ and move the point to the right as many places as there are O's in the number.

(12) to find price of any multiple of any of the preceding numbers (including powers of 10)-multiply price changed according to the corresponding rule by the multiple.

(13) to find price of any factor of any of the preceding numbers (including powers of 10)—take the corresponding aliquot of the price changed according to the proper rule.

(14) to find price of any number—find price of nearest multiple of dozens, score, gross, or other of above numbers and add or subtract price of remainder. Examples. 1. 240 articles at 1s. 14d.= £13. 58. Od.

2. 1920 articles at 3 d. =£31. 08. Od.
3. 1000 articles at 2s. 54d.= £121.875= £121.17s.6d.
4. 720 articles at 31d. = £9. 158. Od.
5. 960 articles at 214dm = 1 of £43= £10. 15. Od.
6. 1120 articles at 1s. 2 d.=14 £59= £68. 16s. 8d.
7. 16 doz. at 48.3d. per doz.= £40. 168. Od.
8. 123 articles at 31d. = £1. 158. 101d.
9. 1 gross at 32d.

=12 at 3s. 9d.=45s. Note 1. Variations on the above rules are easily made when prices are quoted by the dozen, score, gross, thousand etc.

Note 2. Which of the above rules is to be used depends on the character of the number or the price.

Note 3. All the above numbers are very useful in the application of Rules (12), (13) and (14).

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Conversely. To find the price of one. (1) given price of a dozen-consider price in s. as d. (2) given price of a score—consider price in £ as s. (3) given price of 48—consider price in s. as f. (4) given price of 96—consider price in s. as eighths

of a penny.

(5) given price of a gross—divide price in s. as d.

MENTAL RULES.

29

(6) given price of 192—consider price in s. as sixteenths of a penny.

(7) given price of 240—consider price in £ as d. (8) given price of 960—consider price in £ as f.

(9) given price of 1920—consider price in £ as eighths of a penny.

(10) given price of 3840—consider price in £ as sixteenths of a penny.

(11) given price of any power of 10—reduce price to pence and mark off as many places as there are O's in the number.

(12) given price of any multiple of the preceding numbers—divide the price changed according to the proper rule by the multiple.

(13) given price of any factor of the preceding numbers--multiply the price changed according to the proper rule by the aliquot denominator corresponding to the factor.

(14) given price of any number-split number into factors and divide the price successively using decimals when advantageous. Examples. 1.

1=5 d. nearly.

1=5}d. 3. 1000 at £15. 108. 7d. 1=3727d. =3 d. nearly.

320 at £3. 78. 6d. 1= $x3}f.=13f.= z'sd.

96 at £2. 38. 7d. 240 at £5. 6s. 8d.

2.

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EXAMPLES. Note. j of a s.=1}d., 1 of a s. = d., } of a £=2s. 6d., is of a £=ls. 3d. 1. Find prices of

(a) i dozen at 24d., 1s. 5 d., 3 d., 9s. 7{d.,
(6) 1 score at 47 d., 28. 94d., 78. 6d., 9:,d.,

(c) 1 gross at 10$d., 18. 3{d. 2. Find prices of 10, 50, 6, 9, 300, dozen at 1s. 13d., 5£d., 3fd., 3s. 11d., 9 d. each.

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