COMPOUND MULTIPLICATION.
1. If the multiplier do not exceed 12, the operation is performed at once, be ginning at the lowest place, arid carrying according to the value of the place.
Examples.
L. 8. d. cwt. qr. lb.
13 .. 6 .. 12 .. 2 .. 8 9 5119 .. 19 .. 3 62 3 .. 12 1. R. I'. lb. oz. (hot.
13 .. 3 .. 18 7 .. 5 .. 9 6 1283 .. 0 ,. 28 89 .. 5 .. 8 II. If the multiplier be a composite number, whose component parts do not exceed 12, multiply first by one of these parts, then multiply the product by the other. Proceed in the same manner, if there be more than two.
L. 8. d.
Er. 1. 256 .. 4 .. 73 X by 72 12 x 6 12 3074 .. 15 .. 6 6 Ans. 18448 .. 13 .. 0 .L s. d.
Es. 2. 355 .. 13 ..74 X 180 =12X 5 X3 12 4268 .. 3 .. 9 5 2134U .. 18 .. 9 3 Ans. 64022 .. 16 .. 3 The component parts will answer in any order ; it is best, however, when it can be done, to take them in such order as may dear off some of the lower places in the first multiplication, as is done in both the examples. The operation may be proved by taking the component parts in a different order, or by dividing the multiplier in a different manner.
III. If the multiplier be a prime num ber, multiply first by the composite num ber next lower, then by the difference, and add the products.
Here we multiply the given sum by 12 and 7, because 12 x 7 = 84, the answer is 48404/. 2s. 6d. we then multiply the given sum by 3, which gives 1728/ 14s. 43cL these sums added together give the true answer.
IV. If there be a composite number a little larger than the multiplier, we may multiply by that number, and by the dif ference, and subtract the second product from the first.
L. s. d.
.Er. 3276 .. 10 .. 43 X 34 = 5 X 6-2 6 23861 .. 2 .. 3 6 143166 .. 13 .. 6 7953 0 .. 9 Ans.135213 .. 12 .. 9 • We multiply the given sum by 6 and 6, because 6 x 6 = 36 ; the answer is 1431661. 13s. 6d. we then multiply the sum by 2, and subtracting that product from the former, we get the true answer.
V. If the multiplier be large, multiply by 10, and multiply the product again by 10; by which means you obtain an hun dred times the given number. If the multiplier exceed 1000, multiply by 10 again, and continue it farther, if the multi plier require it ; then multiply the given number by the unit place of the multi plier; the first product by ten place, the second product by the hundred place, and so on. Add the products thus obtained
together.
The following examples will furnish the learner with practice.
1. 21 ells of Rolland, at."7.2. 8i-d. per ell. .3ns. L8 .. 1 101.
2. 35 firkins of butter, at 15s. 31d. per firkin. ..Rns. L26 .. 15 .. 21 3. 75 lb. of nutmegs, at 7s. 2id. per lb. Ans. L27 .. 2 .. 21.
4. 37 yards of tabby, at 9s. 7d. per yard. .12ns. L17 .. 14 .. 7.
5. 97 cwt of cheese, at 1?. 5s. 3d. per cwt. Ans. L122 .. 9 3.
6. 43 dozen of candles, at 6s. 4d. per doz. Ans. L13 .. 12 .. 4.
7. 127 lb. of bohea tea, at 12s. 3d. per lb. .Rns. L77 .. 15 .. 9.
3. 135 gallons of rum, at 7s. 5d. per gal lon. .ans. L50 .. 1 .. 3.
9. 74 ells of diaper, at ls. 4id per ell.
A718. L5 .. 1 .. 9.
The use of multiplication is to compute the amount of any number of equal arti cles, either in respect of measure, weight, value, or any other consideration. The multiplicand expresses how much is to be reckoned for each article, and the multiplier expresses how many times that is to be reckoned. As the multiplier points out the number of articles to be added, it is always an abstract number, and has no reference to any value or mea sure whatever. It is therefore quite im proper to attempt the multiplication of shillings by shillings, or to consider the multiplier as expressive of any denomi nation. The most common instances, in which the practice of this operation is required, are to find the amount of any number of parcels, to find the value of any number of articles, to find the weight or measure of a number of articles, &c. This computation for changing any sum of money, weight or measure, into a dif ferent kind, is called Reduction. When the quantity given is expressed in differ entdenominations, we reduce the highest to the next lower, and add thereto the given number of that denomination ; and proceed in like manner till we have re duced it to the lowest denomination.
Er. Reduce 58/. 48. 21d. into farthings. 58 .. 4 .. 2i 20 1164 = shillings in L58 .. 4.
12 13970 = pence in L58 4 .. 2. 4 Ans.55882 = farthings in L58 .. 4 .. 21