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the denomination multiplied, to equal 1 in the next higher. -
Question 1. What is the product of 4 f. 6 s. 5d. 3 qr., multiplied by 32
Illustration.—It was proved in the multiplication of simple numbers, that the multiplicand is placed in the product as many times as the multiplier contains an unit, the additions being performed in the mind. In the multiplication of compound numbers, we obtain a similar result; for every denomination in the multiplicand is a simple number, standing by itself; and by multiplying each denomination by the same multiplier, we place each denomination of the multiplicand in its own product, as many times as there are units in the multiplier; consequently the products of all the denominations will make a compound product, containing the compound multiplicand as many times as the multiplier contain an unit.
In the 3d operation of the last Question, by setting down the multiplicand 3 times, and adding up the several denominations, we obtain a compound number which contains all the denominations of the multiplicand 3 times. In the second operation, when we say, 3 times 3 are 9, 3 times 5 are 15, 3 times 6 are 18, and 3 times 4 are 12, we obtain the same numbers ; for we add each denomination together 3 times in the mind. In the 1st operation, we multiply the same as in the 2d, but as there are 2 pence in the 9 farthings and one farthing over, we set down the 1 farthing, and add the 2 pence to the product of the 5, which makes 17 pence. 12 pence being equal to a shilling, by taking 12 from the 17 pence
and adding 1 shilling to the product of shillings, and setting down 5, the remaining pence, we obtain the same amount of money as we did by the other operations. JNote 1.—From this illustration, it appears that the price of one unit of any quantity should be multiplied by the whole number of units in the quantity, to obtain the price of the whole. It is equally plain, that when the whole weight of several articles, or the whole amount of several things of any kind, is required, the weight, or contents of one, multiplied by the whole number, will give the weight or contents of the whole. 2. Sold 5 barrels of flour for 1 38. 10 s. 6 d. 3 qr, a barrel ; what was the price of the whole * Ans. 7.8. 12 s.9 d. 3 qr. 3. What will 6 gal. of rum come to at 6 s. 3d per gal? Ans. 1 26, 17 s. 6 d.
6. An apothecary wishes to mix 4 quantities of medicine, each weighing 5 lb. 11 oz. 6 dr. 2 sc. 9 gr. What is the weight of the whole 2 Ans. 23 lb. 11 oz. 3 dr. 16 gr.
11. If one side of a square field be 2 fur, 16 ft. in length, what length of fence will it require to inclose said field 2 Ans. 1 M. 3 r. 144 ft. 12. If a man travels 35 M. 7 fur. 3 r. 10 ft. in one day, how far would he travel in 11 days? Ans. 394 M. 5 fur. 39 r. 11 ft.
13. If 8 lots of land measure each i 10 A. 3 R. 21 r. 225 ft. 30 in., how much land in the 8 lots 2 Ans. 887 A. 14 r. 1673 ft. 96 in.
14. How many yards of carpeting, a yard wide,
will it require to cover 12 rooms, each measuring 28 yd. 4 ft. Ans. 341 yd. 3 sq. ft.
.Note 2–In painting, paving, plastering and carpeting, yards are oonsidered the highest denomination.
A Composite Number is a number which is equal to the product of two other numbers; thus, 24 is the composite number of 6 into 4, or 12 into 2, or 8 into 3.
Component Parts are the numbers multiplied together to produce a composite number ; thus, G and 4, 12 and 2, 8 and 3, are the component parts of 24.
H/hen the multiplier exceeds 12, it is generally more convenient to multiply by two numbers.
Rule.—Find two numbers whose product is equal
to the multiplier. Multiply by one of the numbers, and the product by the other, the last product will be the answer. If the multiplier be not a composite number, find the product of the greatest composite numin the multiplier, and add the product of the difference between the composite number and the multiplier, into the multiplicand.
15. If one pile of wood measure 4 C. 76 ft. 1112 in., how much wood in 17 such piles?
C. ft. in.
18 50 992 contents of 4 piles.
73 74 512 contents of 16 piles
78 C. 22 ft. 1624 in. contents of 17 piles.
Illustration.—By the reasoning in the illustration of the first rule, 18 C, 50 ft. 992 in. is what 4 piles contain. By making the product of 4 piles the multiplicand, we place the contents of 4 piles in the next product once for every unit there is in the multiplier, consequently we place the contents of 4 piles, 4 times in the next product; and as 4 times 4 are 16, 73 C. 74 ft. 512 in. must be the contents of 16 piles; and adding the contents of 1 pile to this product we obtain the contents of 17 piles. This method of multiplying will hold true with any other numbers, for in all cases the product of the first figure added together as many times as there are units in the 2d multiplier, must give the product of the whole multiplier, when the product of the two numbers by which we multiply is equal to the given multiplier.
16. How much timber in 26 round sticks, each measuring 1 T. 30 ft. 101 in 7 Ans. 45 T. 21 ft. 898 in. 17. How much timber in 35 square sticks, each measuring 1 T. 20 ft 7 - Ans. 49 T. of TIME,
19. If the moon pass through 12°26" of its orbit in 1 day, how many degrees does it pass through in 15 days? Ans. 180°6' 30".
20. How many yards of cloth in 45 pieces, each measuring 33 yd. 1 na. ? - Ans. 1487 yd. 3 qr. 1 na. 21. How many ells English in 53 pieces of sattinet, each 22 E. E. 2 q1. 3 na. ? Ans. 1195 E. E. 3 na. 22. In 60 pieces of velvet, each 21 ells French 2 nails, how many ells 7 Ans. 1265. 23. In 76 pieces of lace, each 33 E. Fl. 1 qr. 1 na:, how many ells 7 Ans. 2539 E. Fl. 2 qr.
24. How much rum in 84 casks, each containing 108 gal. 1 pt. 3 gl. " Ans. 36 T. 18 gal. 1 qt. 1 pt.
JNote 3--If the multiplier be several hundreds and a part of another hundred, it will be most convenient to find the product of one hundred, and multiply that by the number of hundreds. The H. the remaining part must be added to the product of the Undreds.