MISCELLANEOUS EXAMPLES.

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MISCELLANEOUS EXAMPLES IN FEDERAL MONEY.

1. If a person spends $410.28 in a year, how much is that a week, allowing 52 weeks to a year? Ans. $7.89.

2. A man buys 4 barrels of flour, at $5.95 a barrel; 18 chickens, at 29 cents each; and 56 pounds of butter, at 271 cents a pound. What does the whole cost? Ans. $44.42.

Find the cost of each item; then add the three amounts.

3. Bought 3 pair of gloves, at $.75 a pair; 12 yards of lace, at $1.38 a yard; 10 yards of sheeting, at 45 cents a yard. What is the cost of the whole? Ans. $23.31.

4. A lady buys 2 turkeys at $1.25 each, and 5 bushels of potatoes at 94 cents a bushel. How much change will she receive for a $20 bill? Ans. $12.80.

5. A man pays for some land $400 cash and $192.80 in produce. If there were 57 acres, how much does the land cost him per acre? Ans. $10.40.

6. If a boy buys 12 knives for $7.50, and sells them at 75 cents apiece, how much does he make on each ? Ans. $.125.

Find the cost of 1 knife, and subtract it from the selling price.

7. Divide $2117.71 equally among 35 families, and find the share of each. Ans. $60.506.

8. Four persons contribute $8000 for a speculation. The first puts in $99.05; the second, $2460.30; the third, $986. What does the fourth put in? Ans. $4454.65.

9. If 184 pounds of coffee are sold for $52.44, what is the rate per pound? Ans. $.285.

10. A father who has $2450 in stock, a house valued at $4750, and bonds to the amount of $15040, divides the whole equally among his two sons and three daughters. What is the share of each? Ans. $4448.

11. If 40 acres of meadow land are worth $1260, what is of the tract worth?

Ans. $840.

REDUCTION.

173. How many cents in five dollars?

In 1 dollar there are 100 cents, and in 5 dollars 5 times 100 cents, or 500 cents. Answer, 500 cents.

We have here changed the denomination from dollars to cents, without changing the value. This process is called Reduction. We have reduced dollars to cents.

174. Reduction is the process of changing the denomination of a number without changing its value.

175. There are two kinds of Reduction :

1. Reduction Descending, in which we change a higher denomination to a lower, as dollars to cents. Here we must multiply.

2. Reduction Ascending, in which we change a lower denomination to a higher, as cents to dollars. Here we must divide.

Reduction Descending.

176. Reduce $27 to mills.

$27 100

2700 c. 10

27000 m.

100 cents make $1; in $27, therefore, there are 100 times 27 cents, or (annexing two naughts) 2700 cents.

There are 10 mills in 1 cent; in 2700 cents, therefore, there are 10 times 2700 mills, or (annexing one naught) 27000 mills. Answer, 27000 mills.

173. Solve the example given. What have we done in this example ?174. What is Reduction ?-175. How many kinds of reduction are there? What do we do in Reduction Descending? What operation must we perform ? What do we do in Reduction Ascending? What operation must we perform 2 -176. Reduce $27 to mills, explaining the steps.

27460+5=27465 m. Ans.

Reduce 2746 cents to mills: 2746 × 1027460 m.

Add in 5 mills:

Compare this result with $27.465, the amount to be reduced. It is the same, with the dollar mark and point omitted.

178. GENERAL RULE FOR REDUCTION DESCENDING. Multiply the highest given denomination by the number that it takes of the next lower to make one of this higher, and add in the number belonging to such lower denomination, if any be given.

Go on thus with each denomination in turn, till the one required is reached.

179. Federal Money.-In federal money, the above rule is applied as follows. See the examples in §176, 177.

1. To reduce dollars to mills, annex three naughts; to reduce dollars to cents, two; to reduce cents to mills, one.

2. To reduce dollars and cents to cents, or dollars, cents, and mills, to mills, simply remove the dollar mark and the point.

180. Reduce the following:

177. Reduce $27.465 to mills, explaining the steps. How does the result compare with the original amount?-178. Recite the general rule for reduction descending.—179. Give the rules for the reduction of federal money.

7. Reduce 5 eagles to mills.

8. How many cents in 28 eagles?

9. How many mills in 15 double eagles?

10. How many half-dimes in 73 eagles?

11. Reduce $450.59 to mills.

12. How many dimes are $671 worth?

Ans. 50000 m.

Ans. 28000 c.

How

Ans. 50 d.

13. A lady gets a half-eagle changed to dimes. many dimes should she receive?

14. If a boy gets a $10 bill changed to half-dimes, how many should he receive?

Ans. 200 half-dimes.

Reduction Ascending.

181. Reduce 27465 mills to dollars.

10 mills make 1 cent; therefore in 27465 mills there are as many cents as 10 is contained times in 27465. Dividing by 10 (cutting off one figure), we get 2746 cents, and 5 mills over.

10) 27465 m.

100) 2746 c., 5 m.

Ans. $27.465.

100 cents make 1 dollar; therefore in 2746 cents there are as many dollars as 100 is contained times in

2746. Dividing by 100 (cutting off two figures), we get $27, and 46 cents over. Answer, $27, 46 cents, 5 mills; or,

$27.465.

Compare this result with 27465 mills, the amount to be reduced. We have simply pointed off three figures from the right, and inserted the dollar mark.

182. In § 177 we reduced $27.465, and obtained 27465 mills. In 8181 we reduced 27465 mills, and obtained $27.465. Thus it will be seen that Reduction Descending and Reduction Ascending prove each other.

181. Reduce 27465 mills to dollars, explaining the steps. How does the result compare with the amount given to be reduced?-182. By comparing the examples in § 177 and 181, what do we find?

REDUCTION ASCENDING.

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183. GENERAL RULE FOR REDUCTION ASCENDING. -Divide the given denomination by the number that it takes of it to make one of the next higher. Divide the quotient in the same way, and go on thus till the required denomination is reached. The last quotient and the different remainders form the answer.

184. Federal Money.-In federal money, the above rule is applied as follows :—

To reduce mills to dollars, point off three figures from the right; to reduce cents to dollars, two; to reduce mills to cents, one.

4. How many dollars in 70000 mills?

5. How many dollars in 85310 cents?

6. How many eagles are 50 gold dollars worth?
7. Reduce 2500 dimes to eagles.

8. How many dimes are equal to 600 mills?
9. Reduce 46000 cents to double-eagles.

10. Reduce 4676 mills to cents.

11. How many half-eagles in 1500 cents? 12. How many dollars in 200 half-dimes?

13. How many double eagles in 1200 half-dimes?

14. Reduce 1623487 cents to dollars.

15. How many mills in 5 three-dollar pieces?

16. How many cents in 4 quarter-eagles?

183. Recite the general rule for reduction ascending.-184. Give the rule for the reduction of federal money.