REDUCTION OF UNITED STATES MONEY.

84. Reduction of United States Money is changing the unit from one denomination to that of another, without altering the value of the number. It is divided into two parts:

1st. To reduce from a greater unit to a less, as from dollars to cents.

2d. To reduce from a less unit to a greater, as from mills to dollars.

85. To reduce from a greater unit to a less.

From the table it appears,

1st. That cents may be changed into mills by annexing one cipher.

2d. That dollars may be changed into cents by annexing two ciphers, and into mills by annexing three ciphers.

3d. That eagles may be changed into dollars by annexing one cipher.

The reason of these rules is evident, since 10 mills make a cent, 100 cents a dollar, and 1000 mills a dollar and 10 dollars 1 eagle.

EXAMPLES.

1. Reduce 25 eagles, 14 dollars, 85 cents and 6 mills to the denomination of mills.

2. In 3 dollars 60 cents and 5 mills, how many mills?

3 dollars=300 cents,

60 cents,

360 3600 mills, to which add the 5 mills.

mills?

3. In 37 dollars 37 cents 8 mills, how many mills?
4. In 375 dollars 99 cents 9 mills, how many
5. How many mills in 67 cents?
6. How many mills in $54?

How many mills?
How many mills?

7. How many cents in $125? 8. In $400, how many cents? 9. In $375, how many cents? 10. How many mills in $4? In $6? In $10.14 cents. '11. How many mills in $40.36 cents 8 mills? 12. How many mills in $71.45 cents 3 mills?

86. To reduce from a less unit to a greater. 1. How many dollars, cents and mills in 26417 mills?

ANALYSIS.-We first divide the mills by 10, giving 2641 cents and 7 mills over; we then divide the cents by 100, giving 26 dollars, and 41 cents over: hence the answer is 26 dollars 41 cents and 7 mills: therefore,

OPERATION.

10)2641/7 100)26/41 Ans. $26.417.

I. To reduce mills to cents: cut off the right hand figure. II. To reduce cents to dollars: cut off the two right hand figures: and,

III. To reduce mills to dollars: cut off the three right hand figures.

EXAMPLES.

1. How many dollars cents and mills are there in 67897 mills?

2. Set down 104 dollars 69 cents and 8 mills.
3. Set down 4096 dollars 4 cents and 2 mills.

4. Set down 100 dollars 1 cent and 1 mill.
5. Write down 4 dollars and 6 mills.

6. Write down 109 dollars and 1 mill.

7. Write down 65 cents and 2 mills.

8. Write down 2 mills.

9. Reduce 1607 mills, to dollars cents and mills. 10. Reduce 170464 mills, to dollars cents and mills. 11: Reduce 8674416 mills, to dollars cents and mills. 12. Reduce 94780900 mills, to dollars cents and mills. 13. Reduce 74164210 mills, to dollars cents and mills.

86. How do you change mills into cents? How do you change cents into dollars? How do you change mills to dollars?

87. One number is said to be an aliquot part of another, when it is contained in that other an exact number of times. Thus; 50 cents, 25 cents, &c., are aliquot parts of a dollar: so also 2 months, 3 months, 4 months and 6 months are aliquot parts of a year. The parts of a dollar are sometimes expressed fractionally, as in the following

ADDITION OF UNITED STATES MONEY.

1. Charles gives 91 cents for a top, and 3 cents for 6 quills: how much do they all cost him?

2. John gives $1.37 for a pair of shoes, 25 cents for a penknife, and 12 cents for a pencil: how much does he pay for all?

ANALYSIS.-We observe that half a cent is equal to 5 mills. We then place the mills, cents and dollars in separate columns. We then add as in simple numbers.

3. James gives 50 cents for a dozen oranges, 12 cents for a dozen apples: and 30 cents for a pound of raisins: how much for all?

OPERATION.

$1.375 .25

.125 $1.750

OPERATION.

$0.50

.125

.30 $0.925

88. Hence, for the addition of United States money, we have the following

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

87. What is an aliquot part? How many cents in a dollar? In half a dollar? In a third of a dollar? In a fourth of a dollar?

II. Add up the several columns as in simple numbers, and place the separating point in the sum directly under that in the columns.

PROOF.-The same as in simple numbers.

EXAMPLES.

1. Add $67.214. $10.049, $6.041, $0.271, together.

1. A grocer purchased a box of candles for 6 dollars 89 cents a box of cheese for 25 dollars 4 cents and 3 mills a keg of raisins for 1 dollar 12 cents, (or 12 cents and 5 mills;) and a cask of wine for 40 dollars 37 cents 8 mills: what did the whole cost him?

2. A farmer purchased a cow for which he paid 30 dollars and 4 mills; a horse for which he paid 104 dollars 60 cents and 1 mill; a wagon for which he paid 85 dollars and 9 mills: how much did the whole cost?

3. Mr. Jones sold farmer Sykes 6 chests of tea for $75.641; 9 yards of broadcloth for $27.41; a plow for $9.75; and a harness for $19.674: what was the amount of the bill?

4. A grocer sold Mrs. Williams 18 hams for $26.497; a bag of coffee for $17.419; a chest of tea for $27.047; and a firkin of butter for $28.147: what was the amount of her bill?

5. A father bought a suit of clothes for each of his four boys; the suit of the eldest cost $15.167; of the second, $13.407; of the third, 12.75; and of the youngest, $11.047: how much did he pay in all ?

88. How do you set down the numbers for addition? How do you add up the columns? How do you place the separating point? How do you prove addition?

6. A father has six children; to the first two he gives each $375.416; to each of the second two, $287.55; to each of the remaining two, $259.004: how much did he give to them all?

7. A man is indebted to A, $630.49; to B, $25; to C, 87 cents; to D, 4 mills: how much does he owe?

8. Bought 1 gallon of molasses at 28 cents per gallon; a half pound of tea for 78 cents; a piece of flannel for 12 dollars 6 cents and 3 mills; a plow for 8 dollars 1 cent and 1 mill; and a pair of shoes for 1 dollar and 20 cents: what did the whole cost?

s; a

9. Bought 6 pounds of coffee for 1 dollar 12 cents; a wash-tub for 75 cents 6 mills; a tray for 26 cents 9 mills broom for 27 cents; a box of soap for 2 dollars 65 cents 7 mills; a cheese for 2 dollars 87 cents: what is the whole amount?

10. What is the entire cost of the following articles, viz. : 2 gallons of molasses, 57 cents; half a pound of tea, 371 cents; 2 yards of broadcloth, $3.373 cents; 8 yards of flannel, $9.875; two skeins of silk, 12 cents, and 4 sticks of twist, 8 cents?

SUBTRACTION OF UNITED STATES MONEY.

1. John gives 9 cents for a pencil, and 5' cents for a top, how much more does he give for the pencil than for the top? 2. A man buys a cow for $26.37, and a calf for $4.50: how much more does he pay for the cow than for the calf?

NOTE.-We set down the numbers as in addition, and then subtract them as in simple numbers.

OPERATION.

$26.37

4.50

$21.87

89. Hence, for subtraction of United States money, we have the following

RULE.-I. Write the less number under the greater so that units of the same value shall stand in the same column.

89. How do you set down the numbers for subtraction? How do you subtract them? Where do you place the separating point in the remainder? How do you prove subtraction?