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2. In 2 circles, how many

seconds ?

Ans. 2592000". 3. In 32295 minutes how many circles ?

Ans. 1c. 5s. 28o. 15'. 4. In 27894 seconds, how many degrees?

Ans. 70. 44'. 54". 991. The following denominations of things are not included in the Tables.

12 things make 1 dozen.
12 dozen
12 gross, or 144 dozen 1

great gross.

1 gross.

ALSO 20 things

make 1 score. 112 pounds

1 quintal of fish. 24 sheets of paper

1 quire. 20 quires

1 ream. QUESTIONS. $ 90. For what is circular measure used? How is every circle supposed to be divided ? Repeat the Table.

91. How many things make a dozen? How many do. zen a gross? How many gross a great gross? How many things make a score ? How many pounds a quintal of fish? How many sheets a quire of paper ? How many quires a

ream ?

APPLICATIONS IN REDUCTION. 1. In 6169 pence, how many pounds ?

Ans. £25. 14s. ld. 2. In 5926. 13pwt. 5gr., how many grains ?

Ans. 340157. 3. In £85 8s how many guineas ?

Ans. 81 guineas 7s. 4. How many strokes does a regular clock strike in a year of 365 days, striking once at one, twice at two, &c. for the 24 hours in the day?

Ans. 56940.

5. In 757 boxes of sugar containing 2816. each, how many tons ?

Ans. Stons, 9cut. lqr. 6. How many cords are there in a pile of wood that is 36 feet long, 6 feet high, and 4 feet wide ?

Ans. 6 cords, and 6 cord feet. 7. A man has a journey to perform of 288 miles ; supposing him to travel 12 hours each day for 6 days in succession, at what rate must he travel

per

hour to accomplish it in that time?

Ans. 4 miles. 8. How many yards of carpeting which is one yard in width, will be required to carpet a room 18 feet wide and 20 feet long?

Ans. 40 yards. 9. Reduce 346 Ells Flemish, to Ells English.

Ans. 207} Ells Eng. 10. Suppose the number of inhabitants in the United States to be 12 millions, how long would it take to count them, counting at the rate of 50 in a minute ?

Ans. 166 days 16 hours. 11. A merchant wishes to bottle a cask of wine containing 63 gallons, into bottles containing one pint each: how many bottles are necessary ?

Ans. 504. 12. There is a cube, or square piece of wood 2 feet, or 24 inches each way: how many small cubes of one inch each way can be şawed from it, allowing no waste in sawing ?

Ans. 13824. 13. A merchant wishes to ship 285 bushels of flax seed, in casks containing 7 bushels 2 pecks each : what number of casks are required ?

Ans. 38.

ADDITION OF DENOMINATE NUMBERS.

92. Addition of denominate numbers, like that of simple numbers, teaches how to express the value of several numbers by a single one, which is called their sum.

RULE. I. Set doren the numbers to be added so that all the denominations of the saine kind shall stand in the same column.

II. Begin with the column of the lowest denomination, and add it up as in whole numbers.

III. Then consider how many units of this denomination make one unit of the next higher, and divide the sum by this number. Write down the remainder under the units of its kind, and carry the quotient to the next column, as in addition of simple numbers.

IV. Proceed in the same way for all the columns to the last, and set down the entire sum of the last column.

§ 93. The proof is the same as in the addition of simple numbers.

EXAMPLES ENGLISH MONEY. £ S

d 4 8 9 27 14 11

156 17 10 Sum £189 1s 6d

184 12 9 Proof

189 1 6 Ve find the sum in the column of pence to be 30; 9. 2 shillings and 6 pence: setting down the 6

pence and carrying 2 to the shillings, we find 41 in the column of shillings; that is, £2 and 1 shilling. Set down 1 shilling, and carry the 2 to the pounds; their sum is 189.

$94. Note.-In simple numbers 10 units of any
one of the columns, make one unit of the next left
hand column, $ 10. We therefore carry one for every
10. But in denominate numbers the higher de-
nominations are formed differently. For example,
12 pence make 1 shilling, the unit of the next high.
er denomination; and 20 shillings make 1 pound.
In passing from pence to shillings, we must there.
fore carry 1 for every 12, and one for every 20 in
passing from shillings to pounds. And in general,
we must carry 1 for so many units of the lower de.
nomination, as make one unit of the next higher.
£

d
£

d
173 13

705 17 31
17 7

354 17 21
75
18
71
175

17 34
25 17 87 87 19 71
10
10 104

52 12 73
5 7

27 10 51 Sum 376 3 10 1404

14 61 202 10 5 698 17 3 Proof 376 3 10 1404 14 6

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QUESTIONS. 92. What is addition of denominate numbers ? How do you set down the numbers for addition ? Where do you be. gin to add ? How do you add the several columns ?

$93. How do you prove addition?

$ 94. Why do you carry one for every ten in addition of simple numbers ? For how many do you carry one in passing from pence to shillings ?~from shillings to pounds ? In general, for how many do you carry one ?

TROY WEIGHT.

1b. OZ. pwt. gr.

11 8 18 19 Add together 114 9 6 16

223 10 17 12 Sum 350 5 2 23

Adding up the grains, we find their sum to be 47; that is, 1 pwt. and 23 gr. : setting down 23, and carrying 1 to the pennyweights, we find their sum to be 42: that is, 2 oz. and 2 pwt. Carrying 2 to the ounces, we find their sum to be 29; that is, 2 lb. and 5 oz.: carrying 2 to the pounds and adding, we find their sum to be 350.

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