of it for £59 135. 10d. How much will he have left, and what will it cost him? (7) A person bought 17 cwt. 3 qrs. 13 lbs. of sugar for £35 9s. 8d., and he sold 9 cwt. 3 qrs. 18 lbs. for £29 5s. 6d. How much sugar will he have left, and what will it cost him? (8) An auctioneer offered the following pieces of land for sale:-Lot 1, containing 5 a. 3 r. 26 p. ; lot 2, 6 a. 2 r. 18 p.; lot 3, 5 a. 2 r. 14 p.; and lot 4, 6 a. 3 r. 26 p. He only sold three lots, making in all 18 a. 1 r. 26 p. Which lot remained unsold? (9) A grocer paid £9 19s. 8d. for a cask of sugar weighing 5 cwt. 3 qrs. 11 lbs., of which the cask weighed 1 qr. 16 lbs. He sold 2 cwt. 1 qr. 25 lbs. for £5 35. 10d. how much sugar had he left, and what did it stand him in? : (1) Three boxes weighed 9 cwt. 2 lbs. ; the first and second weighed 6 cwt. 2 qrs. 7 lbs., and the second and third 6 cwt. 23 lbs. Find the weight of each, CHAPTER V. COMPOUND MULTIPLICATION.-SECTION I. COMPOUND MULTIPLICATION is the process of finding the amount of a compound quantity repeated any given number of times. The number of times the quantity is repeated is called the multiplier, and it must necessarily be an abstract number, because we can attach no meaning to a compound quantity such as £45 17s. 9d. repeated 3 pence times, 2s. 6d. times, or 5 yards times. The amount, however, of £45 175. 93d., repeated three times, may be obtained by Compound Addition, or by an abbreviated method of performing the same operation called Compound Multiplication. Example. Multiply £45 175. 9åd. by 3. £45 17 9 45 17 9 Explanation.-Setting down the given quantity three times, as in 45 17 9 Compound Addition, the sum of the £137 13 51 farthings is 9 farthings, or 24d.; set £137 13 54 down d. and carry 2. The sum of the pence column is 27, and with the 2 carried 29 pence, or 25. 5d.; set down 5d. and carry 2. The sum of the units' column of the shillings is 21, and with the two carried 23; set down 3 and carry 2 to the tens' column, the sum of which is 3, and with the 2 carried 5. Dividing 5 by 2 (see Compound Addition, page 31), or, which is the same thing, taking the half of five, the result is 2, with a remainder ; set down I and carry 2 to the pounds. The sum of the units' column is 15, and with the 2 carried 17; set down 7 and carry 1. Lastly, the sum of the tens' column is 12, and with the carried 13, which must be set down. Therefore, £45 17s. 9 d., repeated three times, is £137 138. 54d. We now proceed to obtain the result by Compound Multiplication, and the pupil should compare the process, step by step, with the method just employed. Explanation. Multiplying the farthings by 3, we get three times 3 or 9 farthings, that is 21d.; set down. d. and carry 2. Three times 9 is 27, and 2 are 29; 29 pence are 25. 5d.; set down 5 and carry 2. Next, three times 7 is 21 and 2 are 23; set down 3 and carry 2. Three times I is 3 and 2 are 5; the half of 5 is 2 and 1 over; set down I and carry 2. Then, three times 5 is 15 and 2 are 17, 7 and carry 1; three times 4 is 12 and 1 are 13, which must be set down. Hence the following Rule. To multiply by a number not greater than 12, begin with the lowest denomination and multiply each denomination, successively, from the lowest to the highest, carrying from lower denominations to higher according to the ascending scale of the multiplicand, as in Compound Addition. (7) 243 11 7 × 7. (8) 187 914 × 8. 19386 11 12 × 9. (10) 478 79 x 10.369 10 13 x 11. (12)748 bar. gal. qts. bar. gal. qts. F439 24 3 × 5. (2)567 28 2 × 6. (4)586 19 1 × 8.5439 32 3 × 9. dys. hrs. min. (7)79 23 19 × 7. (10) 47 18 53 x 10. 43687 131061 (a) 262122 dys. hrs. min. 915 × 12. bar. gal. qts. (3678 26 3 × 7. (789 35 2 × 10. dys. hrs. min. 8.958 21 48 × 9. ()59 23 39 × 11. (1969 19 47 x 12. SECTION 11. To multiply a compound quantity by 100, 1000, &c. It has been explained in simple multiplication that the partial products (a), (b), (c), are obtained by multiplying by the local values of the figures in the multiplier, namely by 3, 60, 400, or, (b) which is the same thing, by 3, 6 (c) times 10, and 4 times 100; the multiplication by 10, 100, &c., being effected by placing the first figure of the partial product in the tens', hundreds', &c., columns, and omitting the noughts arising from such multiplication. 174748 20227081 The same principle is employed in Compound Multiplication, the product of £89 17s. 5d. by 463, for example, being obtained by adding together the partial products arising from the multiplication by 3, 60, 400. But since the several denominations of a compound quantity are connected by a varying scale, the multiplication by 10, 100, &c., cannot be effected, as in the case of a simple number, by placing one, two, &c., noughts after the given quantity. Hence it is necessary to find the tens, hundreds, &c., of a compound quantity by actual multiplication, and then the partial products may be obtained by multiplying these results by the number of tens, hundreds, &c., in the multiplier. The multiplication by 10, therefore, occurs very frequently in Compound Multiplication, and the pupil should make himself thoroughly acquainted with the following easy method of performing the operation. To multiply a compound quantity by 10, imagine a nought to be placed after the first number to be multiplied, and divide by the number which connects the denomination of the result with the next higher denomination. Set down the remainder, and imagine the carrying figure. to be placed after the number next to be multiplied. Proceed in the same way with all the figures. Examples. Multiply £789 13s. 5 d. by 10. £789 135 ΙΟ £7896 14 9 Explanation.-Ten times 3 farthings is 7d.; set down d., and imagine the 7 to be placed after the 5; the result is 57d., or |