Explain the application of the rule to the following examples:

1. Divide 1234 by 100.

2. Divide 2345 by 1000.

3. Divide 34567 by 10000.

4. Divide 4567890 by 100000.

82. GENERAL PRINCIPLES OF DIVISION. First Principle.

Multiplying the dividend by any number multiplies the quotient by that number.

Illustration.-8 is contained in 24 three times; and in 3 times 24 it is contained 9 times; that is, 3 times 3 times.

Second Principle.

Multiplying the divisor by any number divides the quotient by that number.

Illustration.-8 is contained in 72 nine times; but 3 times 8, or 24, is contained in 72 only 3 times; that is of 9 times.

Third Principle.

Multiplying both divisor and dividend by the same number has no effect on the quotient.

Illustration.—8 is contained in 24 three times; and 4, which is one-half of 8, is contained in 12, which is one-half of 24, just three times.

Fourth Principle.

Dividing the dividend by any number divides the quotient by that number.

Illustration. -8 is contained in 72 nine times; but it is contained in 24, which is one-third of 72, only one-third of nine times; that is three times.

Fifth Principle.

Dividing the divisor by any number multiplies the quotient by that number.

8 is contained in 24 three times; but 4, which

is one-half of 8, is contained in 24 twice three, or 6 times.

Sixth Principle.

Dividing both divisor and dividend by the same number has no effect on the quotient.

Illustration.

-8 is contained in 72 nine times; and 4, which is one-half of 8, is contained in 36, which is one-half of 72, just nine times.

By means of these principles, explain the following examples:

1. How many more times is 2 contained in 12, than in 6? Why?

2. How many more times is 3 contained in 18, than in 6? Why?

3. How many times less is 4 contained in 24, than in 72? Why?

4. How many times less is 5 contained in 35, than in 95? Why?

5. How many more times is 7 contained in 28, than 21 in 84? Why?

6. How many more times is 11 contained in 55, than 33 in 99? Why?

7. How many times less is 9 contained in 63, than 18 in 162? Why?

8. Does 144 divided by 12 give a greater, or less, result than 72 divided by 6?

9. Does 338 divided by 26 give a greater, or less, result than 169 divided by 13?

10. Divide 12345 by 23, and prove the result. 11. Divide 23456 by 32, and prove the result. 12. Divide 345678 by 43, and prove the result. 13. Divide 456789 by 54, and prove the result. 14. Divide 54321 by 789, and prove the result. 15. Divide 65432 by 678, and prove the result. 16. Divide 876543 by 567, and prove the result. 17. Divide 987654 by 4567, and prove the result. 18. Divide 896745 by 5476, and prove the result. 19. Divide 785634 by 765, and prove the result. 20. Divide 1090801 by 20301, and prove the result. 21. Perform the operations 243 × 672 ÷ 469. 22. Perform the operations 324 × 126 ÷ 214. 23. Perform the operations 989 X 898 24. Perform the operations 987 X 789879.

789.

25. What is the quotient of 89543 divided by 4321? 26. What is the quotient of 98452 divided by 3412? 27. What is the quotient of 1091820 divided by 12345?

28. 1875 25 + 20 × 23 = what?

29. 864648 X 400 what?

30. 1578 barrels of beef cost $23670; find the cost of one barrel.

31. Divide 38504275 by 3; by 72; by 465. 32. Divide 1246859 by 2; by 84; by 719.

33. Divide 2354075 by 7; by 19; by 439.

34. Divide 9806257 by 4; by 57; by 171. 35. Divide 2950296 by 5; by 27; by 981. 36. Divide 276942 by 457.

37. Divide 789591 by 213.

UNITED STATES CURRENCY.

Ans. 606. Ans. 3707.

83. By United States Currency is understood the money of the United States.

84. This currency is based on the Decimal System. Ten units of one denomination make a unit of the next higher, as in whole numbers.

84 a. The coins used in this system are composed of gold, silver, copper, and nickel.

Value of the several gold coins :

The Double Eagle equals in value Twenty Dollars.
The Eagle equals in value Ten Dollars.

The Half-Eagle equals in value Five Dollars.

The Quarter-Eagle equals in value Two and one-half Dollars.

The Three Dollar and the Dollar gold coins are not much used.

Value of the several silver coins:

The Dollar equals in value One hundred cents.

The Half Dollar equals in value Fifty cents.

The Quarter Dollar equals in value Twenty-five cents. The Dime equals in value Ten cents.

The Half-Dime equals in value Five cents.

The copper coins are the one and the two cent pieces.

The nickel coins are the three and the five cent pieces.

The Dollar Sign is written $.

The decimal point (.) separates dollars and cents.

The Mill, used in calculations, is not coined.

85. To change any number of units to an equivalent value expressed in terms of any lower denomination.

1. Change 25 dimes to cents.

Equivalent. -10 cents make one dime.
2. Change 43 dimes to cents.
3. Change 56 dimes to cents.
4. Change 27 dollars to dimes.

Equivalent. 10 dimes make one dollar.
5. Change 32 dollars to dimes.
6. Change 45 dollars to dimes.
7. Change 57 dollars to cents.
Equivalent. -100 cents make one dollar.
8. Change 71 dollars to cents.

9. Change 73 dollars to dimes; to cents. 10. Change 84 dollars to dimes; to cents. 11. Change 2 cents to mills.

Equivalent. — 10 mills make one cent.

12. Change 8 cents to mills.

13. Change 2 dollars to dimes; to cents; to mills.

85 a. To change any number of units of a lower denomination to an equivalent value expressed in terms of a higher denomination.

14. Change 1200 cents to dimes.

Suggestion. -There can be only one-tenth as many dimes as

there are cents.

15. Change 40 cents to dimes.

16. Change 40 dimes to dollars.

17. Change 500 cents to dimes; to dollars.