COMPOUND SUBTRACTION.

COMPOUND SUBTRACTION is the method of deducting one Compound Number from another.

RULE.-1. Place the less number under the greater, in such a way that the numbers of the same denomination shall be below each other-pounds under pounds, shillings under shillings; and so on.

2. Beginning at the lowest denomination, subtract the under from the upper figures, and place the remainder directly below: then subtract the under from the upper figures of the next denomination; and so on with all the others, writing the remainders in each case below their respective denominations. The subtracting of the highest denomination is performed as in Simple Subtraction.

3. When the under number of any denomination is greater than the upper, add to the upper number the value of one of the next higher denomination, and then go on with the subtraction. As an equivalent, however, for this, the under figure of the next higher denomination must be considered as having had 1 added to it before it is deducted from the figure above, on the same principle as in Simple Subtraction.

Example.-From £36, 14s. 51d. take £27, 17s. 83d.

£ S. d. 36 14 5

27 17 83 £8 16 83

Commencing at the lowest term, we have 3 farthings to take from 2, but as we cannot do this, we borrow from the pence 1 penny, or 4 farthings, which, added to the 2 farthings, make 6; then 3 from 6 and 3 remain, which are written under the farthings. We now repay the penny borrowed by carrying 1 to the 8 pence in the lower line; there is thus 9 pence to subtract from 5, but as this cannot be done, we borrow a shilling, or 12 pence, which, added to the 5, make 17, then 9 from 17 and 8 remains, which is placed under the pence. The borrowed shilling is repaid by adding 1 to the 17, making 18 to be taken from 14, but as we cannot do this, we borrow 1 pound, or 20s., which being added to 14, make 34; then 18 from 34 and 16 remain, which are placed under the shillings. The £1 borrowed is carried to the £27, which are subtracted, as in Simple Subtraction.

19. 5 tons 14 cwts. 21 lbs. 10 oz. 27. 194 acres 2 roods 32 per.

Miscellaneous Exercises.

1. If £1750, 12s. 6d. be taken from £2000, how much will remain ? Ans. £249, 7s. 6d.

2. Lent a friend £37, 15s., of which he has repaid me £23, 12s. 9d. How much is he still due me? Ans. £14, 2s. 3d. 3. A merchant bought goods to the amount of £371, 15s. 9d., and sold them for £430, 8s. 6d. What profit did he make on his purchase? Ans. £58, 12s. 9d. 4. Made purchases in a grocer's shop to the amount of £3, 14s. 7 d., and gave a £5 note in payment. How much should Í get back? Ans. £1, 5s. 4d. 5. Went to market with £2, 13s. 6d. in my purse; laid out on butcher meat, 11s. 9d.; poultry, 5s. 3d.; fish, 3s. 7d.; vegetables, 1s. 10d.; cheese, 7s. 84d.; butter and eggs, 3s. 5d.; and on tea and sugar, 15s. 7d. How much should I have over? Ans. 4s. 4d. 6. A merchant borrowed £500, of which he repaid in April £63, 15s.; in June, £113, 12s. 8d.; in August, £87, 4s. 5d.; and in December, £173, 17s. 10d. How much, then, remained to be paid? Ans. £61, 10s. 1d.

7. The gross weight of a hogshead of sugar is 14 cwts. 2 qrs. 7 lbs. What is the net weight, allowing 3 qrs. 18 lbs. as the weight of the cask? Ans. 13 cwts. 2 qrs. 17 lbs. 8. A silversmith received an ingot of silver weighing 3 lbs. 8 oz. 12 dwts., of which he was to make 1 dozen table and 1 dozen tea spoons. The table-spoons weighed 1 lb. 11 oz. and 12 dwts.; the tea-spoons, 8 oz. 15 dwts. How much of the silver remained? Ans. 1 lb. 0 oz. 5 dwts. 9. From London to Newcastle, by way of York, is 276 miles 4 furlongs, and from York to Newcastle it is 82 miles 5 furlongs. How far is it from London to York? Ans. 193 miles 7 furlongs.

10. From a piece of cloth, measuring 57 yards 2 quarters, a draper sold to one person 5 yds. 3 qrs. 2 nails; to another, 7 yds. 1 qr. 3 nails; to a third, 6 yds. 2 qrs.; and to a fourth, 11 yds. 1 qr. 2 nails. How much of the piece then remained?

Ans. 26 yds. 1 qr. 1 nail. 11. A farmer laid out a piece of ground, consisting of 5 acres 2 roods 12 perches, for a fruit and vegetable garden. The vegetable-garden occupied 3 acres 1 rood 29 perches. What was the size of the fruit-garden? Ans. 2 acres 0 roods 23 per.

12. A farmer brought 8 quarters 3 bushels 2 pecks of wheat to market. He sold 6 quarters 5 bushels 3 pecks. How much did he return with? Ans. 1 qr. 5 bush. 3 pecks. 13. A wine-merchant drew off at one time 23 gals. 2 qts., and at another, 16 gals. 3 qts. 2 pts., from a cask containing 87 gals. port. What quantity then remained in the cask? Ans. 46 gals. 2 qts.

14. If it take 26 hours and 35 minutes to go to a certain town by the stage-coach, and 7 hours 45 minutes 30 seconds by railway; how much time is saved by taking the latter mode of conveyance? Ans. 18 hours 49 min. 30 sec.

COMPOUND MULTIPLICATION.

COMPOUND MULTIPLICATION is the method of multiplying a compound number by a simple number.

RULES.

I. WHEN THE MULTIPLIER DOES NOT EXCEED 12.

RULE.-1. Write the multiplier below the right-hand figures of the multiplicand.

2. Multiply the lowest denomination of the latter by the multiplier; find how many of the next higher denomination is contained in the product, and carry the number of times to that denomination, writing any remainder below the number just multiplied.

3. Multiply the next higher denomination in the same way, writing down any remainder, and carrying to the denomination above it, as before; and so on till all the denominations have been multiplied in succession: the highest denomination is multiplied as in Simple Multiplication.

Example.-Multiply £37, 15s. 8d. by 6.

£ S. d.

37 15 82 6

£226 14 4

Here the multiplier, 6, is placed under the pence (the farthings being considered merely as a fraction of the pence), and beginning with the farthings we have 6 times 3, which make 18 farthings, and these being converted into pence, give 43 pence. The is placed under the farthings, and the 4 carried to the pence. Multiplying the pence, we have 6 times 8 making 48, and the 4 from the farthings make 52 pence, or 4 shillings and 4 pence. The 4d. is put under the pence, and the 4s. are carried to the shillings: then 6 times 15 are 90, and 4 are 94s. ; that is, 4 pounds and 14 shillings over. The 14s. are marked under the shillings, and the £4 carried to the pounds: then multiply the £37, as in Simple Multiplication, and include the £4 from the shillings; the product, 226, is written under the pounds.

NOTE. In multiplying the shillings, the following is the most convenient method:-First multiply the units, take the tens out of the product and carry them to the tens, writing any remainder below the units; next multiply the tens, and having added those brought from the units, halve the product; carry the half to the pounds, and if there is a remainder of 1, write 1 below the tens; if there is no remainder, there is nothing written below the tens of the shillings. The halving of the product of the tens is merely a short way of dividing it by 20, to convert it into pounds.

In the above example we first multiply the units of the shillings6 times 5 are 30, and 4 from the pence are 34: write 4 below the units, and carrying 3 to the tens, 6 times 1 are 6, and 3 are 9; then halving this, write the remainder, 1, below the tens, and carry the half, 4, to the pounds, which are multiplied as before.

D

II. WHEN THE MULTIPLIER IS THE PRODUCT OF TWO NUMBERS, NEITHER OF WHICH EXCEEDS 12.

RULE. Find the factors or numbers that produce the multiplier, then multiply the given quantity by the one factor, and the product by the other: the last product is the answer.

Examples.-Multiply £1, 2s. 6d. by 14.

Here the multiplier, 14, is the product of the two numbers, 7 and 2; we therefore first multiply the given sum by 7, and then the product by 2.

Exercises.