RULE. Multiply each descending denomination by as many of the next lower denomination as make one in that which you are about to reduce ;-thus proceed till the question is brought into the denomination required.

PROOF. Divide the last product by the last multiplier, and that quotient by the next, &c. If the last quotient be equal to the first multiplicand, the work is right.

Note. When there are several denominations in the question, as for instance, pounds, shillings, &c. bring in the odd shillings when multiplying by 20, the odd pence when multiplying by 12, &c. Proceed in like manner with all questions of this nature.

N. B. When there is a remainder after dividing, it is always

of the same denomination with the dividend.

D

1 Reduce 378 O

2

3

oo oo o to barley-corns.* 71850240. 27 5 18 3 1 8 1 to barley-corns.† 5262037 38 3 9 0 0 0 0 to inches.

2433222

· 28160

* 1760 yards make one mile; therefore when the question is miles only, multiply the miles By 1760; the product will be yards.

In reducing rods to yards, in long measure, multiply the rods by 5; then add half the multiplicand to the product, which sum will be the multiplicand, multiplied by 5 1-2.

In reducing rods to yards, in square measure, multiply the rods by 30; then add one quarter of the multiplicand to the product.

Note. I call 365 days a year, although it falls short a little, yet it is exact enough for common purposes.

3. Reduce 1796 years to

2. In 16 years, 5 months, seconds?

how many minutes?

yrs. mo.

16 5

13

yrs.

1796

365

FEDERAL MONEY.

CASE I. To reduce dollars to cents.

RULE. Place two ciphers at the right hand of the dollars,

and the work is done.

CASE II. To reduce dollars to mills.

RULE. Annex three ciphers to the dollars.

CASE III. To reduce dollars and cents to cents.

RULE. Remove the comma from between the dollars and cents, and the work is done.

CASE IV. To reduce dollars and cents to mills.

RULE. Remove the comma as in Case 3d, and annex one cipher to the right hand.

CASE VI. To reduce dollars, cents and mills to mills.

RULE. Remove the commas from between the dollars and cents, and cents and mills, and the whole sum is mills.

Note 1st.

When you would bring cents into dollars, point off the two right hand figures for cents; the left hand figures are dollars.

EXAMPLES.

1. In 38575 cents, how many dollars? 2. In 38705 cents, how many dollars?

Note 2d.

$385, 75 Answer. $387, 05 ""

To bring mills into dollars, cents, &c. point off the first right hand figure for mills, the two next for cents; the left hand figures are dollars..

EXAMPLES.

1. În 85697 mills, how many dollars, cents, &c. ?

$85, 69, 7 Ans.

2. In 387548 mills, how many dollars, cents, &c.?

$387, 54, 3 Ans..

3. In 586085 mills, how many dollars, cents, &c.?

$586, 08, 5 Ans.

REDUCTION BY DIVISION.

REDUCTION BY DIVISION* teaches to bring a low denomination to its equivalent value in higher denominations; and is the reverse of Reduction by Multiplication, and is proved by it. RULE. Divide the lowest denomination given, by so many of that lowest as make one in the next higher denomination; thus proceed with every ascending denomination, till you have brought the question into the denomination required.

2. In 16963 farthings, how many pounds, shillings, &c.?

3. In 99628 farthings, how many pounds, shillings, &c.?

This is called Reduction Ascending.

£103 15 7 Ans.