£
984 price at£1.
Price of 984 yds. at £2 „ 15 „ 6.1968£2.
49210s.
2465s.
24„ 126d.
2730„ 12at £2 „ 15 „ 6

Approximations.Approximate methods should be practised, and for this reason it is well to get the habit of multiplying by the larger number first.

Suppose we want a sum accurate, say to 3 decimal places. We remove the point from one of the factors, pushing it, of course, an equal distance in the other. We make the whole number reversed the multiplier, and begin with the fourth decimal figure (one beyond the one we need). This will give the fourth place as the first number, since we are multiplying by units. In the next row we must take in the fifth decimal, since we are multiplying by 10, and so on. Here is a sum worked out at length and an abbreviated one:—

Find correct to 3 places of decimals 3·45 × ·00059692:

3·45 × ·00059692 = 345 × ·059692
·059692·059692
      345    543
17907600   2984
2387680  23876
   298460 179076
20·59374020·5936

In division we approximate by cutting off a figure each time from the divisor as soon as we have come to the number which is one less than the number of digits still to be found. Get correct to five places.

454523)145367·9(·31982
1363569
901100
454523
446577
409068
37509
36360
1149
908
241

Summary.I might summarise the order of teaching fractions thus:—

What a fraction is—mixed numbers, improper fractions.

Effect of increasing or diminishing numerator or denominator.