COMPOUND ADDITION.

By Compound Addition we are taught to add numbers of different denominations, such as pounds, ounces, &c., for the purpose of finding the sum, or amount.

RULE.

1. Write down the numbers so that each denomination may stand directly under each other of its kind, leaving a small space between them.

2. Add the right-hand denomination, the same as in Simple Addition.

3. Then divide that amount by as many as it requires, of that denomination, to make one in the next.

4. Set down the remainder under that denomination, and carry the quotient to the next deñomination, and add it in: if there be no remainder, set down a cipher.

5. Continue in this way through to the last denomination, which add, the same as in Simple Addition, and set down the whole amount.

Proof, the same as in Simple Addition.

REVIEW.

What is Compound Addition?

Rule.-1. How do you

write down numbers? 2. How do you add? 3. How do 4. What is done with the remainder? 5. Proof.

you divide?

What then?

20 4 28 T. cwt. qr. lbs. 2 3 2 11

14

2

sum 8

3 16

EXAMPLES.

16

16

Oz.

dr.

6

11

0 18 10

8

12

14

9 2 18 13 2

Explanation. This example belongs to Avoirdupois weight. The first denomination at the right is drams, which add, the same as in Simple Addition, and the amount is 34; divide by 16, because 16 drams make 1 ounce, and we have 2 ounces in the quotient, and 2 drams over; set down the 2 drams, and carry the 2 ounces to the denomination of that name, which add in, and it will make 29 ounces; divide the 29 ounces by 16 for the pounds, and it will give 1 pound and 13 ounces over; set down the 13 ounces, and

60

carry the 1 pound to the next denomination; then add that denomination, and it will give 46 pounds; divide the pounds by 28 to get the quarters, and you have 1 quarter and 18 pounds; set down the 18 pounds, and carry the 1 quarter to the denomination of that name, which add in, and you have 6 quarters; which divide by 4, because 4 quarters make 1 cwt., and you have 1 cwt. and 2 quarters; set down the 2 quarters, and carry the 1 cwt. to the next denomination, and add it in; and there will be 9 cwt. and none to carry, because it is less than a ton; then add and set down all the next denomination. This is the sum.

(22.) Purchased 4 hogsheads of sugar, which weighed as follows: 1st, 4 cwt., 2 qrs., 18 lbs.; 2d, 5 cwt., 3 qrs., 21 lbs.; 3d, 6 cwt., 2 qrs., 12 lbs. ; 4th, 6 cwt., 3 qrs., 19 lbs.: what is the weight of them all ?

Ans. 24 cwt., 0 qr., 14 lbs. (23.) A merchant sold 4 pieces of sheeting; the 1st piece contained 33 yds., 2 qrs., 1 na.; 2d, 35 yds., 3 na.; 3d, 40 yds., 3 qrs., 3 na.; 4th, 45 yds., 2 qrs., 1 na.: required the number of yards. Ans. 155 yds. 1 qr., 0 na.

(24.) A farmer disposed of 4 bags of grain, which measured as follows: 1st, 4 bush., 3 pks., 4 qts., 2d, 3 bush., 1 pk., 7 qts.; 3d, 3 bush., 2 pks., 5 qts., 1 pt.; 4th, 4 bush., 1 pk., 5 qts.: how much grain did he sell?

Ans. 16 bush., 1 pk., 5 qts., 1 pt. (25.) A grocer purchased 4 hogsheads of vinegar, which measured as follows: 1st, 58 galls., 1 qt., 1 pt.; 2d, 59 galls., 2 qts., 0 pt.; 3d, 58 galls., 1 qt., 1 pt.; 4th, 57 galls., 2 qts.: how much in all? Ans. 233 galls, 3 qts., 0 pt.

(26.) A farmer has divided his farm into 5 large fields; the 1st contains 32 A., 1 R., 21 po.; 2d, 27 A., 2 R. 18 po.; 3d, 34 A., 1 R., 30 po.; 4th, 35 A., 1 R., 11 po.; 5th, 26 A., 3 R., 28 po.: required the number of acres in the farm.

Ans. 156 A., 2 R., 28 po.

(27.) There are 4 persons, A., B., C., and D., whose ages are as follows: A., 76 yrs., 9 mo., 3 w. 4 da.; B., 84 years, 5 da.; C., 92 yrs., 6 m., 3 w., 4 da.; D., 102 yrs., 7 mo., 2 w., 4 da., 6 h. : required their united ages.

5 mo.,

Ans. 356 yrs., 5 mo., 2 w., 3 da., 6 h. (28.) Purchased 4 boat-loads of wood; the 1st boat had 27 C., 94 ft.; 2d, 32 C., 111 ft.; 3d, 28 C., 84 ft.; 4th, 25 C., 47 feet: required the quantity of wood purchased. Ans. 114 C., 80 ft.

(29.) A merchant sold 4 pieces of cloth; the 1st piece contained 25 yds., 2 qrs., 1 na.; 2d, 26 yds., 3 qrs., 2 na.; 3d, 27 yds., 1 na.; 4th, 24 yds., 2 qrs.: required the number of yards in the 4 pieces, and the value thereof at 5 dollars per yard. Ans. 104 yds.; value D520. (30.) 2 T., 3 cwt., 1 qr., 18 lbs., 12 oz. +5 T., 6 cwt., 2 qrs., 18 lbs., 11 oz., 5 dr.+7 T., 6 cwt., 3 qrs., 20 lbs.+5 T., 2 cwt., 1 qr., 12 oz.

Ans. 19 T., 19 cwt., 1 qr., 2 lbs., 3 oz., 5 dr. (31.) On a journey of 4 days, I rode the 1st day 42 m., 4 fur., 19 po.; 2d day, 41 m., 5 fur., 30 po.; 3d, 43 m., 7 fur., 25 po.; 4th, 45 m., 4 fur., 19 po.: required the distance travelled in 4 days. Ans. 173 m., 6 fur., 13 po.

(32.) In 5 piles of cord-wood, the 1st measures 4 C., 60 ft.; 2d, 7 C., 82 ft.; 3d, 9 C., 110 ft.; 4th, 10 C., 45 ft.; 5th, 11 C., 65 ft. required the quantity of wood in the 5 piles. Ans. 43C., 106 ft.

COMPOUND SUBTRACTION.

THIS rule is used when numbers of different denominations are given to be subtracted, or a smaller number taken from a greater, of a like denomination, and show their difference, or remainder.

RULE.

1. Write down the larger number, and directly under it the less number, so that the same denominations shall stand under each other.

2. Begin at the right-hand, and subtract the lower from the upper number, if that be the largest, and set down the remainder.

3. But if the lower number is more than the one above it, then subtract from as many as it takes of that denomination to make one in the next; take the difference, and add it to the upper number, and set it down.

4. Carry one, and add it to the next lower denomination, and continue through the sum in this manner, and in the last denomination subtract the same as in integers.

Proof, the same as in integers, observing to carry as above directed.

REVIEW.

What is Compound Subtraction? 1. How do you write down the given numbers? 2. How do you subtract? 3. If the lower number is more than the one above it? 4. How Proof.

will you carry when you borrow?

EXAMPLES.

10 20 4 28 16 16

É»

cwt. qrs. lbs. Oz. dr.

7 2 14

11

12

-4 4 1 6

15

5

3 1

7

12

8

Explanation.-Write

the value of the respective denominations over each; then, 4 from 12 and 8 remain; 15 from 16 and 1 remains, which added to 11 makes 12; then 1 to 9 7 2 14 11 12 proof. carry to 6 is 7,7 from 14, 7; 1 from 2, 1; 4 from 7,3; 4 from 9, 5: then to prove it, add the two lower numbers, or the subtrahend and remainder, and their sum will be equal to the upper number, or minuend.