Charles Davies.

School arithmetic. Analytical and practical online

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118. For what is circular measure used? How is every circle sup-
posed to be divided ? Repeat the table.



DENOMINATE NUMBERS. 117

MISCELLANEOUS TABLE.

12 units, or things make 1 dozen.

12 dozen - 1 gross.

12 gross, or 144 dozen ' 1 great gross.

20 things - 1 score.

100 pounds - 1 quintal of fish.

196 pounds 1 barrel of flour.

200 pounds - 1 barrel of pork.

18 inches 1 cubit.

22 inches, nearly - 1 sacred cubit.

14 pounds of iron or lead - 1 stone.

21 J stones - 1 pig.

8 pigs 1 fother.

BOOKS AND PAPER.

The terms, folio, quarto, octavo, duodecimo, &c., indicate
the number of leaves into which a sheet of paper is folded.

A sheet folded in 2 leaves is called a folio.

A sheet folded in 4 leaves " a quarto, or 4to.

A sheet folded in 8 leaves " an octavo, or 8vo

A sheet folded in 12 leaves " a 12mo.

A sheet folded in 16 leaves " a 16mo.

A sheet folded in 18 leaves " an 18mo

A sheet folded in 24 leaves " a 24mo.

A sheet folded in 32 leaves " a 32mo.

24 sheets of paper make 1 quire.

20 quires - - 1 ream.

2 reams - 1 bundle.

5 bundles 1 bale.

MISCELLANEOUS EXAMPLES.

1. How many hours in 344wfc. Qda. llhr. ?

2. In 6 signs, how many minutes ?

3. In 15 tons of hewn timber, how many cubic inches ?

4. In 171360 pence, how many pounds?

5. In 1720320 drams, how many tons?

6. In 55799 grains of laudanum, how many pounds?

7. In 9739 grains, how many pounds Troy?

8. In 59/6. ISpwt. 5grr., how many grains ?

9. In .85 8s., how many guineas ?

10. In 346 E. F., how many Ells English ?

i



118 KEDUCTION OF

11. In 3hhd. ISgal. 2qt., how many half-pints ?

12. In 12 T. Ibcwt. Iqr. 1Mb. 12dr., how many drams?

13. In 40144896 square inches, how many acres?

14. In 5760 grains Troy, how many pounds?

15. In 6 years (of 52 weeks each), 3>2wk. bda. 17/ir., how
many hours ?

16. In 811480", how many signs ?

17. In 2654208 cubic inches, how many cords ?

18. In 18 tons of round timber, how many cubic inches ?

19. In 84 chaldrons of coal, how many pecks?

20. In 302 ells English, how many yards ?

21. In Qihhd. ISgal. 2qt. of molasses, how many gills ?

22. In 76 A IB. 8P., how many square inches?

23. In 15 19s. lid. 3/ar., how many farthings?

24. In 445577 feet, how many miles?

25. In 37444325 square inches, how many acres ?

26. If the entire surface of the earth is found to contain
791300159907840000 square inches, how many square miles
are there ?

27. How many times will a wheel 16 feet and 6 inches in
circumference, turn round in a distance of 84 miles ?

28. What will 28 rods, 129 square feet of land cost at $12
a square foot ?

29. What will be the cost of a pile of wood 36 feet long
6 feet high and 4 feet wide, at 50 cents a cord foot ?

30. A man has a journey to perform of 288 miles. He
travels the distance in 12 days, travelling 6 hours each day :
at what rate does he travel per hour ?

31. How many yards of carpeting 1 yard wide, will carpet
a room 18 feet by 20?

32. If the number of inhabitants in the United States is
24 millions, how long will it take a person to count them,
counting at the rate of 100 a minute ?

33. A merchant wishes to bottle a cask of wine containing
126 gallons, in bottles containing 1 pint each : how many
bottles are necessary ?

34. There is a cube, or square piece of wood, 4 feet each
way : how many small cubes of 1 inch each way, can be
sawed from it, allowing no waste in sawing ?

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



DENOMINATE NUMBERS 119

36. How many times will the wheel of a car, 10 feet and
6 inches in circumference, turn round in going from Hartford
to New Haven, a distance of 34 miles ?

37. How many seconds old is a man who has lived 32
years and 40 days ?

38. There are 15713280 inches in the distance from New
York to Boston, how many miles ?

39. What will be the cost of 3 loads of hay, each weighing
IScwt. 3qr. 24/6., at 7 mills a pound?

ADDITION OF DENOMINATE NUMBERS.

119. Addition of denominate numbers is the operation of
finding a single number equivalent in value to two or more
given numbers. Such single number is called the sum.

How many pounds, shillings, and pence in 4 8s. 9c?.,
27 14s. lid., and 156 17s. lOd. ?

ANALYSIS. We write the units of the same OPERATION.

name in the same column. Add the column . s. d.

of pence ; then 30 pence are equal to 2 shil- 489

lings and 6 pence : writing down the 6, carrying 9 * -. - , ,

the two to the shillings. Find the sum of the JJ 1 J iL
shillings, which is 41 ; that is, 2 pounds and 1

shilling over. Write down 1*. ; then, carrying ^189 l s< g^
the 2 to the column of pounds, we find the
sum to be 189 Is. 6d.

NOTE. In simple numbers, the number of units of the scale,
at any place, is always 10. Hence, we carry 1 for every 10. In
denominate numbers, the scale varies. The number of units, in
passing from pence to shillings, is 12 ; hence, we carry one for
every 12. In passing from shillings to pounds, it is 20 ; hence, we
carry one for every 20. In passing from one denomination to
another, we carry 1 for so many units as are contained in the scale
at that place. Hence, for the addition of denominate numbers, we
have the following

RULE. I. Set down the numbers so that units of the
same name shall stand in the same column ;

II. Add as in simple numbers, and carry from one de-
nomination to another according to the scale.
PROOF. The same as in simple numbers.

119. What is addition of denominate numbers? How do .you set
down the numbers for addition ? How do you add ? How do you
prove addition ? ^-



ADDITION OF



( 8 }
173 13

87 17
75 18


d.
5

7*


EXAMPLES.

(2.)
s d
705 17 3J
354 17 2j
175 17 3|


(3.;

s.
104 18
404 17
467 11


I
d.
9|

'4


25


17


4




87


19 71


597 14


*i


10


10


ii




52


12 7|




22 18


5


373


18


3










18 6


5


TROY WEIGHT.


(4.)


(5.)




Ib.


oz.


pwt.


gr.


Ib.


oz.


pwt.


gr.


Ldd


100


10


19


20


171


6


13


14




432


6





5


391


11


9


12




80


3


2


1


230


6


6


13




7








9


94


7


3


18







11


10


23


42


10


15


20










8


9


31








21



APOTHECARIES' WEIGHT.

(6.) (7.) (8.)

ft) ! 3 3 gr. I 3 3 gr. 33 gr.

24 7 2 1 16 11 2 1 17 3 2 15

17 It 7 2 19 7 4 2 14 1 13

36 6 5 7 4 1 19 2 2 11

15 9 7 1 13 2 5 2 11 7 17

93419 10 1 2 16 5 2 14

AVOIRDUPOIS WEIGHT.

(9.) (10.)

cwt. qr. Ib. oz. dr. T. cwt. qr. Ib. oz.

14 2 14 9 15 12 1 10 10

13 2 20 1 15 71 8 2 6

93673 83 19 3 15 5

10 18 12 11 36 7 20 14

73232 47 11 2 2 11

6 1 19 8 1 63 5 2 19 7

4 , 3 15 5 12 13 1 14 9

12 2 13 9 7 5 10



DENOMINATE NUMBERS. 121

11. A merchant bought 4 barrels of potash of the following
weights, viz. : 1st, 3cwt. 2qr. Mb. 12oz. 3dr. ; 2d, cwt. Iqr.
21/6. 4oz. ; 3d, cwt ; 4th, icwt. Qqr. 2/6. 15oz. 15dr. :
what was the entire weight of the four barrels ?



LONG MEASURE.


L.
16


.<"<
mi. fur.

2 7


i
rd. yd. ft.
39 9 2




rd.
16


yd. ft.

9 2


171.
11


327


1


2


20 7 1




12


11


1


9


87





1


15 6 1




18


14





7


1


1


1


1 2 2




19


15


2


1


CLOTH MEASURE.


(14.)
E. Fl qr.
126 4


na.
4


(15.)
yd. qr.
4 3


na.
2


E.E.

128


(16.)
qr. na.
5 1


in.
3


65


3


1


5 4


1


20


3


1


2


72


1


3


6 1





19


1


4


1


157


2


3


25 2


2


15


3


1


2



LAND OR SQUARE MEASURE.

(17.) (18.)

Sq. yd. Sq.ft. Sq. in. M. A. R. P. Sq.yd

97 4 104 2 60 3 37 25

22 3 27 6 375 2 25 21

105 8 2 7 450 1 31 20

37 7 127 11 30 25 19

19. There are 4 fields, the 1st contains 12A 2P. 38P. ;
the 2d, 4: A. IR. 26P. ; the 3d, 85 A QR. 19P. ; arid the
4th, 57 A IR. 2P. : how many acres in the four fields ?

CUBIC MEASURE.

(20.) (21.) (22.)

Cu.yd. Cu.ft. Cu.in. C. S.ft. C. Cord ft.

65 25 1129 16 127 87 9

37 26 132 17 12 26 7

50 1 1064 18 119 16 6

22 19 17 37 104 19 5



122 ADDITION OF

WINE OR LIQUID MEASURE.

(23.) (24.)

hhd. gal. qt. pt. tun. pi. hhd. gal. qt.

127 65 3 2 14 2 1 27 3

12 60 2 3 15 1 2 25 2

450 29 1 4 2 1 27 1

21 023 501 62 3

14 39 1 2 7 1 2 21 2



DRY MEASURE.

(25.) (26.)

ch. bu. pk. qt. pt. ch. bu. pk. qt. pt.

27 25 3 7 1 141 36 3 7 2

59 21 2 6 3 21 32 2 4 1

21271 85 9103

5 9182 10 4413

TIME.

(27.) (28.)

yr. mo. wk. da. hr. wk. da. hr. m. sec.

* 4 11 3 6 20 8 8 14 55 57

3 10 2 5 21 10 7 23 57 49

5 8 1 4 19 20 6 14 42 01

101 9 3 7 23 6 5 23 19 59

55 8 4 6 17 2 2 20 45 48



CIRCULAR MEASURE OR MOTION.

(29.) (30.)

s. ' " s. ' "

5 17 36 29 6 29 27 49

7 25 41 21 8 18 29 16

8 15 16 09 7 09 04 58



NOTE. Since 12 signs make a circumference of a circle, we
write down only the excess over exact 12's.

APPLICATIONS IN ADDITION.

1. Add 46/6. 9oz. Ifywot. 16<?r., 87/6. lOoz. Gpwt. Ugr.,
100/6. lOoz Wpwt. 10#r., and 56/6. Zpwt. 6gr. together.



DENOMINATE NUMBERS. 123

2. What is the weight of forty-six pounds, eight ounces,
thirteen pennyweights, fourteen grains ; ninety-seven pounds,
three ounces ; and one hundred pounds, five ounces, ten pen-
nyweights and thirteen grains ?

3, Add the following together: 29 T. Ibcwt. Iqr. 14/6.
12oz. Mr., IScwt. 3?r, lib., 50 1 7 . 3?r 4oz., and 2T. Iqr.



4 What is the weight of 39 T. Wcwt. 2?r. 2/6. 15oz. I2dr.,
llcwt. 6/6., I2cwt. 3?r., and 2?r. Sib. Mr.l

5. What is the sum of the following : 314^4. 2E. 39P.
200s7. ft- 136s?. in., UA. IE. 20P. 10s?. ft., BE. 36P.
and 4 A. IE. 16P.?

6. What is the solid content of 64fons 33/2. 800m., Qtons
1200m., 25/35., 700m., and 95tes 31/fc 1500m.

7. Add together, 966u. 3p&. 2qt. Ipt., 466w. 3pfc. 1?. Ipt.,
2pk. Iqt. Ipt. and 236w. 3p&. 4?. lp.

8. What is the area of the four following pieces of land ;
the first containing 20 A. BE. 15P. 250s?. ft. 116s?. in. ; the
second, 19A IE. 39P. ; the third, 2P. 10P. 60s?, ft. ; and
the fourth, 5 A. 6P. 50s?. in. ?

9. A farmer raised from one field 37Zw. Ipk. 3qt. of wheat ;
from a second, 416w. 2pk. 5?. of barley ; from a third, 356w.
Ipk. 3qt. of rye ; from a fourth, 436w. 3pk. Iqt. of oats ; how
much grain did he raise in all ?

10. A grocer received an invoice of 4hhd. of sugar ; the
first weighed llcwt. 15/6. ; the second, 12cwt. 3?r. 15/6. ; the
third, Scwt. Iqr. 16/6. ; the fourth, I2cwt. Iqr. : how much
did the four weigh ?

11. A lady purchased 32?/ds. 3?rs. of sheeting ; 31yds. Iqr.
of shirting ; llyds. 2?rs. of linen ; and Qyds. 2??*s. of cambric :
what was the whole number of yards purchased ?

12. Purchased a silver teapot weighing 23oz. llpivt. llgr. ;
a sugar bowl, weighing 8oz. ISpwt. l$gr. a cream pitcher,
weighing 5oz. ll^r. : what was the weight of the whole ?

13. A stage goes one day, 87m. Qfur. 24rd. ? the next, 75??i.
3/wr. 17r^. ; the third, 80m. Ifur. Wrd. ; the fourth, 78m.
5/*wr. : how far does it go in the four days ?

14. Bought three pieces of land ; the first contained 17
acres IE. 35?'rf. ; the second, 36 acres 2E. 2lrd. ; and the
third, 46 acres QE. 37rd. : how much land did I purchase ?



124: SUBTRACTION OF



SUBTRACTION OF DENOMINATE NUMBERS.

120. The difference between two denominate numbers is
such a number as added to the less will give the greater.
SUBTRACTION is the operation of finding this difference.

I. What is the difference between 27 16s Sd and 19
17s. 9df.?

ANALYSIS. We cannot take 9rf. from Sd. ; OPERATION.
we therefore add to the upper number as many 20 12

units as are contained in the scale, and at the x** IDS. 8a.
same time add 1, mentally, to the next higher 19 17 9

denomination of the subtrahend. We then say, To rr~

9 from 20 leaves 11. Then, as we cannot sub-
tract 18 from 1C,' we add 20 and say, 18 from 36 leaves 18. Now,
as we have taken 1 pound=20 shillings, from the pounds, and
added it to the shillings, there are but 26 pounds left. We may
then say, 19 from 26 leaves 7, or 20 from 27 leaves 7. The lat-
ter is the easiest in practice.

The first step is called borrowing, the second, carrying : hence,

RULE. I. Set down the less number under the greater,
placing units of the same value in the same column.

II. Begin with the lowest denomination, and subtract as in
simple numbers, borrowing and carrying for each operation
according to the scale.

PROOF. The same as in simple numbers.
EXAMPLES.

(1.) (2-)

A. E. P. T. cwt. qr. Ib.

From - 18 3 28 4 12 3 20

Take - 15 2 30 ) 2 18 _ 3 1)

Remainder ~3 (T~38 ) 1 14 19 )

Proof - liTir~28 4 12 3 20

(3.) (4 )

Ib. oz. pwt. gr. Ib. oz. pwt. gr.

From - 273 18 9 10

Take - 98 10 18 21 9 10 15 20
Remainder



DENOMINATE NUMBERS.



125



(5.)

T, cwt. qr. Ib. oz.

From - 7 14 1 3 6

Take - 2 6 3 4 11
Remainder

T. hhd. gal. qt. pt.

From - 151 3 50 3 2

Take - 27 2 54 3 2
Remainder



(6.)

cwt. qr. Ib. oz. dr.

14 2 12 10 8

6 3 16 15 3



(8.)

yr. wk. da. hr. '
95 25 4 20 45 50
80 30 6 23 46 56



TIME BETWEEN DATES.
121. To find the time between any two dates.

1. What time elapsed between July 5th, 1848, and August
8th., 1850 ?



OPERATION.

yr. mo. da.
1850 8 8
1848 7 5
213



NOTE. In the first date, the number of
the year is 1848 ; the number of the month
7, and the number of the day, 5. In the
second date, the number of the year is 1850,
the number of the month 8, and the number
of the day, 8.

Hence, to find the time between two dates :

Write the numbers of the earlier date under those of the
later, and subtract according to the preceding rule.

NOTE. 1. In finding the difference between dates, as in casting
interest, the month is regarded as the twelfth part of a year, and
as containing 30 days.

2. The civil day begins and ends at 12 o'clock at night.

2. What is the difference of time between March 2d,
1847, and July 4th, 1856?

3. What is the difference of time between April 28th, 1834,
and February 3d, 1856 ?

4. What time elapsed between November 29th, 1836, and
January 2d, 1854 ?



120. What is the difference between two denominate numbers?
Give the rule for subtraction. How do you prove subtraction ?

131. Give the rule for finding the difference between two date*- How
is the month reckoned ? At what time docs a civil day begin ?



126 SUBTRACTION OF

5. What time elapsed between November 8th, at 1 1 o'clock
A.M., 1847, and December 16th, at 4 o'clock, P.M., 1850 ?

OPERATION.

ANALYSIS. The hours are numbered 1/r vnn fj n i> r

_ y / //tC/. tit/. /If .

from 12 at night, when the civil day begins. 1359 10 IA i/
The numbers of the years, months, days 184 *
and hours are used.

3185

6. What time elapsed between October 9th, at 11 P.M.,
1840, and February 6th, at 9 P.M., 1853 ?

7. Mr. Johnson was born September 6th, 1771, at 9 o'clock
A.M., and his first child November 5th, 1801, at 9 o'clock
P.M. : what was the difference of their ages ?

APPLICATIONS IN ADDITION AND SUBTRACTION.

1. From 38mo. 2wk. Zda. 7/ir. 10m., take lOmo. Zwk.
2da. Whr. 50m.

2. From 176t/r. 8mo. 3wh 4da., take 91yr. 9mo.



3. From 3, take 3s.

4. From 2/6. take 20#r. Troy.

5. From 8R, take lft> 1 3 23 23.

6. From 9T. r take IT. lewt. 2qr. 20/6. 15o2.

7. From 3 miles, take 3/wr. 19rd.

8. The revolution commenced April 19th, 1775, and a
general peace took place January 20, 1783 : how long did
the war continue ?

9. America was discovered by Columbus, October 11,
1492 : what was the length of time to July 25, 1855 ?

10. I purchased 167/6. 8oz. IGpwt. lOgrr. of silver, and
sold 98/6. lOoz. I2frwt. Wgr. : how much had I left?

11. I bought 19T. llcwt. Zqr. 2/6. 12oz., 12c?r. of old
,'ron, and sold 17 T. IScwt. 2^r. 19/6. 14oz. lOc^r. : what had

I left ?

12. I purchased lOlIbll? ^3 23 19pr. of medicine,
and sold 17ft>2333 1& bgr.: how much remained un-
sold?

13. From 46?/d. Iqr. 3na., take 42^. 3qr. Ina. 2m.

14. Bought 7 cords of wood, and 2 cords 78 feet having
been stolen, how much remained ?



DENOMINATE NUMBERS. 157

.5. A owes B 100 : what will remain due after he has
paid him 25 3s. 6J<*. ?

16. A farmer raised 136 bushels of wheat ; if he sells
496w. 2p. Iqt. Ipt., how much will he have left?

17. From 174/iM. Wgal. Iqt. Ipt. of beer, take SQhhd.
17 gals. 2qt. Ipt. *

18. A farmer had 5766w. Ipk. %qt. of wheat ; he sold
1396w. 2p&. 3qt. Ipt. : how much remaiued unsold?

19. A merchant bought Vlcwt. 2qr. 14/6. of sugar, of
which he sold at one time 3cwt. Zqr. 20/6. ; at another Qcwt.
Iqr. 5/6. : how much remained unsold ?

20. Sold a merchant one quarter of beef for 2 7s. 9d ;
one cheese for 9s Id. ; 20 bushels of corn for 4 10s. lid. ;
and 40 bushels of wheat for 19 12s. 8Jd. : how much did
the whole come to ?

21. Bought of a silversmith a teapot, weighing 3/6. 4oz.
Qpivt. 2lgr. ; one dozen of silver spoons, weighing 2/6. loz.
Ipwt. ; 2 dishes weighing 16/6. lOoz. ISpwt. IQgr. : how
much did the whole weigh ?

22. Bought one hogshead of sugar weighing $cwt. 3qr. 2/6.
14oz. ; one barrel weighing 3cwt. Iqr. 2/6., and a second
barrel weighing Scwt. Qqr. lib. 4oz. : how much did the
whole weigh?

23. A merchant buys two hogsheads of sugar, one weigh-
ing Scwt. 3qr. 21/6., the other 9cwt. 2qr. 6/6. ; he sells two
barrels, one weighing 3cwt. Iqr. 12/6. 14oz., the other, Zcwt.
Bqr. 15/6. 6oz. : how much remains on hand ?

24. A man sets out upon a journey and has 200 miles to
travel ; the first day he traveled 9 leagues 2 miles 7 furlongs
30 rods ; the second day 12 leagues 1 mile 1 furlong ; the
third day 14 leagues ; the fourth day 15 leagues 2 miles ^
5 furlongs 35 rods : how far had he then to travel ?

25. A farmer has two meadows, one containing A. ZR.
37P., the other contains 10A 2R. 25P. ; also three pas- ,
tures, the first containing 12^4. IE. IP. ; the second con-'
taining 13A BE., and the third &A. IE. 39P. : by how
many acres does the pasture exceed the meadow land ?

26. Supposing the Declaration of Independence to have
been published at precisely 12 o'clock on the 4th of July,
1776, how much time elapsed to the 1st of January, 1833,
at 25 minutes past 3, T.M. ?



128 MULTIPLICATION OF



MULTIPLICATION OF DENOMINATE NUMBERS.

122. MULTIPLICATION of denominate numbers is the opera-
tion of multiplying a denominate number by an abstract number.

I. A tailor has 5 pieces of cloth each containing 6yd~
%qr. 3na. : how many yards are there in all ?

ANALYSIS. In all the pieces there are 5 OPERATION.
times as much as there is in 1 piece. If in yd. or. na.
1 piece each denomination be taken 5 times, it o 3
the result will be 5 times as great as the multi-
plicand. Taking each denomination 5 times,

we have 30#d. lO^r. 15?ia. 30 10 15"

But, instead of writing the separate products, 33 1 3
we begin with the lowest denomination and
say, 5 times 3na. are 15na. ; divide by 4, the units of the scale, write
down the remainder 3fta., and reserve the quotient Sgr. for the
next product. Then say, 5 times 2qr. are 10r., to which add the
%qr. making 13gr. Then divide by 4, write down the remainder
1, and reserve the quotient 3 for the next product. Then say, 5
times 6 are 30, and 3 to carry are 33 yards : hence,

RULE. I. Write down the denominate number and set
the multiplier under the lowest denomination.

II. Multiply as in simple numbers, and in passing from one
denomination to another, divide by the units of the scale, set
down the remainder and carry the quotient to the next product.

PROOF. The same as in simple numbers.




17


CM.

s. d

15 9


.far.
6


EXAMPLES.
T.


c?r/.
10


(2.
*


:>*

2


oz.
12

7


106 14 10

(3.)
m.fur. rd.
9 3 20


2 3

*?

6


10

8.

9






9


19

(4.)

27


4

35
3





132. What is multiplication of denominate numbers? Give the rule.
How do you prove multiplication ?



DENOMINATE NUMBERS. 129

(5.) (6.)

yr. mo. da. hr. T. cwt. qr. Ib. oz. dr.

6 5 15 18 6 12 3 20 12 9
5 8



7. A farmer has 11 bags of corn, each containing 26w. Ipk.
3qt. : how much corn in all the bags ?

8. How much sugar in 12 barrels, each containing 3cw
3qr. 2/6. ?

9. In 7 loads of wood, each containing 1 cord and 2 cord
feet, how many cords ?

10. A bond was given 21st of May, 1825, and was taken
up the 12th of March, 1831 ; what will be the product, if
the time which elapsed from the date of the bond till the day
it was taken up, be multiplied by 3 ?

11. What is the weight of'l dozen silver spoons, each
weighing 3oz. Spwt. ?

12. What is the weight of 7 tierces of rice, each weighing
5cwt. 2qr. 16/6.? '

13. Bought 4 packages of medicine, each containing 3fi>
4^ 63 13 16#r. : what is the weight of all ?

14. How far will a man travel in 5 days at the rate of
24mi. 4/ur. krd. per day ?

15. How much land is there in 9 fields, each field contain-
ing 12^. IK 25P.?

16. How many yards in 9 pieces, each 29 yd. 2qr. 3na. ?

17. If a vessel sails 5L. 2>mi. 6fur. SQrd. in one day,
how far will it sail in 8 days ?

18. How much water will be contained in 96 hogsheads,
each containing QZgal. Iqt. Ipt. Igi. ?

NOTE. When the multiplier is a composite number, and the
factors do not exceed 12, multiply by the factors in succession.
In the last example 96=12 x 8.

19. If one spoon weighs 3oz. 5pwt. 15<?r. what is the
weight of 120 spoons? i

20. If a man travel 249m. 7/itr. 4rd. in one day, how far
will he go in one month of 30 days?

21. If the earth revolve 15' of space per minute of tune,
how far does it revolve per hour ?

22. Bought 90/i/id. of sugar, each weighing IZcwt. Zqr.
. : what was the weight of the whole?



130 DIVISION OF

23. What is the cost of 18 sheep, at 5s. 9|d. apiece ?

24. How much molasses is contained in 2bhhd. each hogs-
head having ftlgal. \qt. Ipt. ?

25. How many yards of cloth in 36 pieces, each piece con-
taining %5yd. 3qr. ?

26. A farmer has 18 lots, and each lot contains 41 A 2#.
IIP. : how many acres does he own?

21. There are three men whose mutual ages are 14 times
2Qyr. 5mo. 3wk. Qda. : what is the sum of their ages?

28. Bought 90/i/id. of sugar, each weighing 12cwt. 2qr.
14lb. ; what is the weight of the whole ?

29. If a vessel sail 49ml Qfur. 8rd. in one day, how far
will she sail in one month of 30 days ?

30. Suppose each of 50 farmers to raise 125m. 3pk. 6qt. of
grain : how much do they all raise ?

31. If a steam ship, in crossing the Atlantic, goes 211mi.
4/wr. 32rd. a day, how far will she go in 15 days?

32. If 1 horse consume 2 tons Iqr. 20/6. of hay in a winter,
how much will 36 horses consume?

33. How much cloth will clothe a company of 48 men, if
it takes 5yd. 3qr. 2na. to clothe one man ?

NOTE. Each denomination may Be multiplied by the multiplier,
separately, and the results reduced and added.



DIVISION OF DENOMINATE NUMBERS.

123. DIVISION of denominate numbers is the operation of
dividing a denominate number into as many equal parts as
there are units in the divisor.

1. Divide 25 15s. 4d. by 8.

ANALYSIS. We first say 8 into 25, 3 times OPERATION.

and 1 or 20s. over. Then, after adding the 8)d25 15s. la

15s. we say, 8 into 35, 4 times and 3s. over. ^ -j F~?

Then, reducing the 3*. to pence and adding in
the 4rf., we say, 8 into 40, 5 times.

123. What is division of denominate numbers? Give the rule for
division. How do you prove division ? How do you divide when the
divisor is a composite number ? What will be the unit of each quo-
tient figure ?



DENOMINATE NUMBERS. 131

OPERATION.

t366w.
2. Divide 366tt. 3pfc. Iqt. by 7.

ANALYSIS. In this example we
find that 7 is contained in 36 bushels
5 times and 1 bushel over. Reducing
this to pecks, and adding 3 pecks,
gives 7 pecks, which contains 7, 1
time and no remainder. Multiplying
by 8 quarts and adding, gives 7
quarts to be divided by 7.

7)7(lqt




Ans. bbu. \pk. Iqt.

Hence, for the division of denominate numbers we have the
following

RULE. I. Begin with the highest, denomination and
divide as in simple numbers :

II. Reduce the remainder, if any, to the next lower de-
nomination, and add in the units of that denomination for
a new dividend.

III. Proceed in the same manner through all the denomi-
nations.

PROOF. By multiplication, as in simple numbers.

NOTES. 1. If the divisor is a composite number, we may divide
by the factors in succession, as in simple numbers.

2. Each quotient figure has the same unit as the dividend from
which it was derived.

3. If the divisor is greater than 12 and not a composite number,
the operation is the same as long division.



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