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much grain had he in all, and how much more wheat than rye?
In all 1374bu. 3pk. 6qt.
Wheat more than rye 198bu. 7qt. 9. A father was born on the 8th of December 1759, his first son on the 4th of June 1795 : what was the difference of their ages ?
Ans. 35yr. 5mo. 27da. 10. A merchant has a bill to pay of £600. He has £250 198 8d in cash, a good note against A for £75 108 6d and a note against B for £37 11s od: how much inoney does he want to make the payment? Ans. £
S d. 11. A tailor requires lyd. 3qr. 3na. of cloth for a father's coat, and lyd. lqr. 2na. for each of two sons: the father buys 6 yards, does he buy too much or too little ?
Ans. lyd. lqr. Ina. too much.
MULTIPLICATION OF DENOMINATE NUMBERS.
1. Charles pays 6d for a pencil : How much will buy two pencils? How much will buy 3 pencils ? 4 pencils 5 pencils ? 6 pencils ?
2. James puts 1 quart and 1 pint into a measure: How much could he put in a measure of twice the size? In a measure of three times the size? 4 times the size? 5 times the size ? 6 times the size ?
3. What is the product of 2s 4d multiplied by 2? by 3 ? by 4? by 5? by 6? by 7? by 8 ? by 9?
4. What is the product of lyd. Iqr. multiplied by 2? by 3? by 4? by 5 by 6? by 7 ? by 8? by 9 ?
5. Multiply E3 9s 10d by 4 ?
In this example we say, 4 times 10d are 40d, equal to 38 and 4d. Set down £ d the 4d in the lower line. Then 4 times
3 9 10 9s are 36s and 3s to carry make 39s,
4 equal to £1 and 19s over: set down £12 363 400 the 19s. Then 4 times £3 are £12 £13 19s 4d and £i'to carry make £13.
We may conclude from the examples that, to multiply a denominate number by a simple one, is to repeat the denominate number as many times as there are units in the multiplier.
§ 73. When the simple number does not exceed 12.
I. Write down the denominate number and set the multiplier under the lowest denomination.
II. Multiply the lowest denomination by the multiplier, and see how many units of the next higher denomination are contained in the product, and set down the excess as in addition.
III. Multiply the next higher denomination by the multiplier and add the units to be carried from the last product; then reduce the sum to units of the next higher denomination, write down the excess and proceed in the same way for all the denominations, setting down the entire product when you come to the last.
Q. What is required when you multiply a denominate number by a simple one ? When the simple number does not exceed 12, how do you write it down? How do you begin to multiply? How do you carry ?
(2.) 3 d
T.cwt. qr. lb. oz. 17 15 9
9 3 27. 12 6
7 106 14 6
3 9 3 26 4 3. Multiply 9s 6d by 3?
Ans. £1 8s 6d. 4. What will 12 gallons of brandy cost at 9s 6d per gallon?
Ans. £5 14s. 5. What will 9cwt. of butter cost at £1 11s 5d per cwt.
Ans. £14 2s 9d,
1. What is the cost of 4 yards of cloth at £1 3s 6d
The amount per yard multiplied by the number of yards will evidently give the entire cost.
OPERATION. £1 38 6d
£4 14s Od Ans.
2. What will be the cost of 9 hats, at 9s 9d each?
Ans. £4 7s 9d. 3. A farmer has 11 bags of corn each containing 2bu. 1 pk. 3qt.: how much corn in all the bags ?
Ans. 25bu. 3pk Iqt. 4. What is the cost of 12 bushels of wheat at 9s 6d per bushel ?
Ans. £ s. 5. How much sugar in 12 barrels, each containing 3cwt. 2gr. 2716.?
Ans. 2 T. 4cwt. 3qr. 161b. 6. In 7 loads of wood, each containing 1 cord and 2 cord feet, how many cords ? Ans. 8 cords 6 cord feet.
CASE II. $ 74. When the simple number is greater than 12 and a composite number.
RULE. Multiply the denominate number by one of the component parts, or factors, and then multiply the product by the other factors in succession : the last product is the one required.
EXAMPLES. 1. Multiply £6 2s 9d by 48=6X8. Ans. £294 12s.
2. What will 24 barrels of flour cost, at £2 lls 8d per barrel ?
Ans. £62. 3. What is the cost of 42cwt. of tallow, at £1 14s 6d per cwt?
4. What is the cost of 120 dozen of candles at 5s 9d per dozen ?
Ans. £34 10s. 5. How much water will be contained in 96 hogsheads, each containing 62gal. 1qt. 1 pt. lgi.? Ans. 5991 gallons.
CASE III. § 75. When the simple number exceeds 12 and is not a composite number.
RULE. Multiply the simple number by each of the denominations separately, and reduce each product to the highest denomination named. Then add the several products together, and their sum will be the answer sought.
EXAMPLES. 1. Multiply £5 3s 8d by 13. 13
13 £5 £65
2. Multiply £6 8s 9d by 139.
139 x9d = 1251d=£ 5 4s 3d
Ans. £894 16s 3d.
3. Multiply £0 2s 4d by 195.
Ans. £22 158. 4. What is the cost of 46 bushels of wheat at 4s 710 per
bushel ? 5. What is the cost of 117cut. of raisins at £1 2s 3d per cwt. ?
Ans. £130 3s 3d.
Q. How do you multiply when the simple number is greater than 12 and a composite number? How do you multiply when the simple number exceeds 12 and is not a composite number?
BILLS OF PARCELS.
A Hosier's BILL.
Jan. 4. 1837. Mr. Thomas Williams,
Bought of Richard Simpson
d. 8 Pair of worsted stockings, at 4 6 per pair 5 Pair of thread ditto,
at 3 2 5 Pair of black silk ditto, at 14 0 6 Pair of black worsted ditto, at 4 2 4 Pair of cotton ditto,
at 7 6 2 Yards of fine flannel,
8 per yard. Total cost £9 Os 2d.
A GROCER'S BILL.
Aug. 6, 1837. Mr. Nathaniel Parsons,
Bought of William Smith.
d. 24 lb. of royal green tea,
16. 24 lb. of imperial tea,
0 35 lb. of best bohea,
at 13 10 1776. of coffee,
at 5 4 25 lb. of double refined sugar,
at 1 11 9 Sugar loaves, weighing 1371b. at 0 77
Total cost £85 188 111d.
DIVISION OF DENOMINATE NUMBERS. 1. Charles has 3s and wishes to divide it equally between himself and two brothers : how much must he give to each ? If he divides 2s 6d, how much? If he divides 2s, how much? If he divides 1s 6d, how much? If he divides ls, how much?
2. John has a bushel of nuts and wishes to divide them equally among himself and three brothers : how much will each have? If he divides 3pks., how much? If he divides 2pks. 4 qt.? If he divides 1pk.? If he divides 2qt. ? If he divides 1qt. ?