The Western Calculator, Or, A New and Compendious System of Practical Arithmetic

De pleasant and rapid. The teacher will then be justly rewarded for his labor and trouble in this part, by the approbation of parents, and the gratitude of his scholars, who will have acquired the necessary qualifications (accuracy and expertness) for the great variety of studies and avocations in future life, which require the aid of arithmetic and mathematics.

PART II.

ARITHMETIC IN MIXED OR COMPOUND NUMBERS.

SECTION I.

FEDERAL MONEY

Is so called from its being the general currency established by the Federal, or United States' government, and is justly considered superior to every other kind of currency now in use for its simplicity and plainness.

From this table it will readily be seen, that addition, subtraction, multiplication, and division of federal money may be performed as if they were whole numbers. It will also be seen that to reduce any number of mills to cents, it is only necessary to point, or cut off the last figure, as 100 mills =10,0 cents; and cents in the same way to dimes, as 100 cents=10,0 dimes, and dimes to dollars, as 100 dimes=10,0 dollars, and dollars to eagles, as 100 dollars=10,0 eagles; and also that eagles may be brought to dolls. and dolls. to dimes, &c. by adding a cipher to each one, as 10 E.=100 dolls.1000d.=10000c.-100000m.

In all calculations in federal money, according to com mon custom, it is usual to omit the names of eagles, dimes,

and mills, and only to reckon by dollars and cents; the eagles being considered as so many 10 dollars, the dimes as so many 10 cents, and the mills as fractional parts of the cent. See the following

TABLE.

34, 1 2

4 5 6, 25

8 2 6 4, 7 5

Dolls.

1,25 cents

34,12 and a fourth cents

456,25 and a half cents

8264,75 and three-fourth cents

Note. 1. In addition, subtraction, multiplication, and division of federal money, if the sums are dollars only, the amount, remainder, product, or quotient, will be dollars; but when the sums consist of dollars and cents, or cents only, the two first right hand figures are cents, and all the rest are dollars.

2. When fractions of cents are used according to the above tabl every four of them make one cent: in adding, or subtracting thal we carry one for every four; and in multiplying, the upper figure, called the numerator, is to be multiplied by the multiplier, and divided by the lower figure, called the denominator.

1. Add 25 eagles, 62 dollars, 8 dimes, 75 cents, and 5 mills.

Ans. 313d 55c 5m. 2. A person deposited at bank 1055 dollars in notes, 260 dollars in gold, 3650 dollars in silver, and 2,50 cents: how much is the amount? Ans. 4967d 50c. 3. Bought a barrel of sugar for 39 dollars 871⁄2 cents, a bag of coffee for 22 dollars 182 cents, and a pound of tea for 2 dollars 12 cents; how much do they all cost?

Ans. 64d 18 c. 4. Bought goods to the amount of 645 dollars 95 cents,. paid at the time of purchase 350 dollars; how much remains to be paid? Ans. 295d 952.

5. A man lent his friend 1000 dollars, and received at sundry payments, first 160 dollars 25 cents, second 285 dollars 664 cents, third 300 dollars 284 cents; what remains yet to be paid? Ans. 253d 793c.

6. What is the product of 102 dollars 19 cents, multiplied by 120? Ans. 12262d 80c. 7. What will 16 barrels of flour amount to, at 4 dollars

50 cents per barrel?

Ans. 72d. 8. How much will 132 pieces of calico come to, at 17 Jollars 37 cents a piece? Ans. 2293d 50c. 9. What is the quotient of 3022 dollars 50 cents, divided by 5? Ans. 1204d 50c.

10. A butcher bought 18 beef cattle for 252 dollars 90 cents; how much did he pay for each? Ans. 14d 05c. 11. Bought 45 yards of linen for 22 dollars 50 cents, what was the price of one yard? Ans. 50cts.

12. If 25 men expend 15555 dollars 50 cents in the erection of a bridge, how much has each one to pay, if the shares are equal? Ans. 622d 22c

Having treated of federal money separately, inasmuch as it requires to be well understood, secing it is the general currency in the United States; we now proceed to the other parts of mixed numbers, or as they are frequently termed, divers denominations.

SECTION 2.

OF COMPOUND ADDITION.

COMPOUND Addition is the collecting together, and thereby ascertaining the amount of several quantities, of divers denominations.

RULE.

Place the numbers in such a manner, that all of the same denomination may stand directly under each other, then beginning with the lowest denomination, add as in whole numbers, carry at that number which will make one of the next greater; set down the reinainder (if any) and so proceed till all are added.

PROOF as in simple addition.

ENGLISH MONEY.

The denominations are, pounds, shillings, pence and far

things, and are

Thus valued: