EXAMPLES, Showing the use of Compound Addition and Subtraction. 1. Lent a friend at one time £13 16s. 8d., at another, £35 10s. 6d.; he paid at one time, £10 10s. 11d., at another, £9 3s. 6d.; how much remains due? Ans. £29 12s. 9d. 2. A man had 375 acres 2 roods of land, but one of his sons marrying, he gave him 145 acres; how much had he left? Ans. 230 acres 2 roods. 3. Borrowed $375,50 cts:, paid at one time $95,20 cts., at another $81,10 cts.; how much remains due?. Ans: $199,20 cts. 4. A gentleman paid his 3 labourers as follows, viz.: A he gave £11 13s. 6d.; B he gave 13s. and 6d. more than A; and C he gave as much as A and B both; how much did the gentleman pay out? Ans. £48 1's. 5. James was bound' as an apprentice for 6 years and 7 months; he served 3 years and 9 months, and then bought his time; how much time had he to pay for? Ans. 2-years 10 months. 6. A merchant put in a bin 47 bushels and 3 pecks of corn; ne afterwards sold out 25 bushels and 1 peck; how much had he left in the bin? Ans. 22bu. 2 pk. 7. From a piece of cloth containing 47 yards 2 quarters, a merchant sold four suits, each 6 yards 2 quarters; how much of the piece remains unsold? Ans. 21yds. 2qrs. 8. A gentleman left his son 1005 pounds more than his daughter, whose portion was 4475 pounds 10 shillings; what was the son's portion, and what was the whole estate? Ans. £5480 10s. the son's portion. £9956 the whole estate. 9. From 11 years 6 months 11 days, take 10 years 6 months 29 days? Ans. 11 months 12 days. 10. The revolutionary war broke out between Great Bri tain and the United States, April 19th, 1775, and the treaty of peace was ratified January 20th, 1783; how long did the war last? Ans. 7 years 9 months 1 day. COMPOUND MULTIPLICATION, Is repeating a number of different denominations a certain proposed number of times, or it is the shortest method of performing compound addition where the same number is to be repeated. RULE.-When the quantity does not exceed 12 yards, pounds, &c. set down the price of one, and place the quantity under the right hand denomination for a multiplier. Multiply the right hand denomination, and divide the product by as many as it takes of that denomination to make one in the next at the left; set down the remainder, (if any) under the denomination multiplied, and carry the quotient to the product of the next left hand denomination, and so proceed till you come to the left hand denomination, and there set down the product as in simple multiplication. NOTE. This rule will be found very useful in business; where the price of 1 yard, or I pound, is given, by it, we find the price of a quantity; by multiplying the price of one yard, or one pound, or a unit of any kind, by the quantity, the product will be the price of the quantity. Or if the weight of one hogshead or of one bale is given, we find the weight of the whole by multiplying the weight of one, by the whole number; and in like manner we find the weight of any number of boxes or bags where the weight of one is given. INTRODUCTORY EXAMPLES. £ S. d. 1 3 4 2 Ans. 2 6 8 1. If one yard of broadcloth cost 1 pound 3 shillings and 4 pence; what will two yards cost? Ans. £2 6s. 8d. DEM. It is plain, that the price of one yard multiplied by 2, must give the price of two yards, because it is repeating every denomination expressing the price of one yard by 2; and it will plainly appear by adding, that this is only a short method of performing addition. DEM.-Here, we find by addition the same result is produced; and the same relation exists when we have three, four, five, or any other number for a multiplier, which may clearly be shown by adding the multiplicand as many times as it has been repeated in multiplication. £ s. d. 1 3 4 1 3 4 2 6 8 2. If one Tun of hay cost £2 12s. 8d.; what will three Tuns cost at that rate? £ S. d. 2 12 8 The number of Tuns, 3 Ans. £7 18 0 Ans. £7 18s. Od. DEM. Here, we first multiply 8d, by 3, and we have 24 for the product; we then divide this product by 12, because it takes 12 pence to make 1 shilling; and we have 2 for a quotient and nothing for a remainder, so we set down a cipher under the pence, and then say three times twelve are thirty-six, and add the quotient, two, which we carry from the pence; we then have 38, which we divide by 20, because 20s. make a pound; we find 20 contained in 38 once and 18 over, which we set down under shillings, and carry I pound, which is the quotien, to the product of pounds, by saying three times 2 are 6 and 1 are 7, which we place under pounds, its proper place. This exam ple we will illustrate by addition, so that the student may not mistake the principles of the rule, or the relation which addition and multiplication bear to each other. 1 d. 12 8 £ S. 2 2 12 8 2 Ans. 7 Here we again see that the same result is produced by adding the price of one yard instead of multiplying. The student will perceive that we carry in both cases the same; when we multiply the 8 pence by 3, the product is 24 pence, that is 2 shillings, conse18 0 quently 2 shillings may be added to the prodact of shillings; and in addition we have 24 pence, that is, 2 shillings which may be added to the shillings, and in multiplying the 12 shillings the product is 36 shillings, and the 2 shillings to carry make 38 shillings, that is, I pound and 18 shillings, consequently we set down the 18 shillings and carry the pound to the product of pounds; and by addition we obtain 38 shillings the same as in multiplication, that is, 1 pound and 18 shillings; consequently we set down the 18 shillings and carry the 1 pound, and by adding we obtain 7 pounds, and the same number by multiplying. 3. What will 4 yards of cloth come to, at 3s. 4d. per yard? Ans. 13s. 4d. 4. What cost 5 yards of calico, at 3s. 9d. per yard? Ans. 18s. 9d. 5. What will 6 tuns of hay cost, at £2 3s. 6d. per tun? Ans. £13 1s. Od. 6. A man bought 7 sheep at 9s. 6d. per head; what did they cost him? Ans. £3 6s. 6d. 7. A man bought 8 bushels of apples, at 2s. 6d. per bushel; what did they cost him? Ans. £t. 8. Bought 9 pieces of shirting, each containing 28yds. 2qrs. 2na.; how many yards in the 9 pieces? Ans. 257yds. 2qrs. 2na. 9. Bought 10 cwt. of beef at £1 18s. 6d. per cwt.; what did the whole cost? Ans. £19 5s. 10. What must a merchant pay you for 11cwt. of pork, at £2 1s. 6d. per cwt.? Ans. £22 16s. 6d. 11. What will twelve horses come to, at £29 16s. 8d. each? Ans. £358. CASE II When the multiplier exceeds 12, and is a composite number, produced by multiplying together any two fi gures in the multiplication table, it will often be found more convenient, first, to multiply by one of the component figures, and then that product by the other; the last product will be the answer. EXAMPLES. 1. What will 16 yards of broadcloth come to, at £2 3s. 3d. Ans. £34 12s. per yard? £ S. d. 2 3 3 4 8 13 4 Ans. 34 12 0 0 DEM.-When we multiply the price of one yard by 4, we obtain the price of four yards; because it is the same as adding the price of one yard 4 times; and when we multiply the price of four yards by 4, it must give the price of sixteen yards, because 4 times 4 are 16; and when we multiply the price of four yards by 4, it is the same as adding as many times, because if we should add the price of four yards to itself once, we would have the price of eight yards, because 2 times 4 are 8; and if we add the price of four twice to itself, we must have the price of twelve, because 3 times 4 are 12, or 4 and 4 are 8 and 4 are 12; then if we multiply the price of four by 4 we have the price of sixteen, because it is the same as adding the price of four 3 times to itself; thus, 4 once added to 4 make 8, and 4 added to 8 make 12, and 4 again added make 16, that is, adding the price of four, 3 times to itself, or putting down the price of four, 4 times and adding. NOTE. It will be recollected that 4 and 4 are the component parts of 16, because 4 times 4 are 16. 2. What will 20 calves come to, at £1 6s. 3d. each? Ans. £26 5s. 3. If one yard of calico cost 2s. 6d.; what will 24 yards cost? Ans. £3. 4. What will 28 pounds of beef come to, at 4 pence per pound? Ans. 9s. 4d. 5. What must a man pay for 36 sheep, at 9 shillings 4 pence each? Ans. £16 16s. 6. What is the weight of 48 pipes of wine, each weighing 18cwt. 2qrs. 14lb. Ans. 894cwt., or 44T. 14cwt. 7. What is the weight of 72 boxes, each weighing 1 quar ter 14 pounds? Ans. 27cwt. 8. In 21 pieces of cloth, each containing 24yds. 2qrs. 3n.; how many yards? Ans. 518yds. 1qr. 3na. 9. What will 63 yards of calico come to, at 3 shillings 1 penny per yard? Ans. £9 14s. 3d. 10. What will 56 bushels of corn come to, at 3 shillings 9 pence per bushel? Ans. £10 10s. CASE III-When the multiplier is not the exact product of any two figures in the multiplication table, and is above. 12. |