7. Twelve thousand three hundred forty-five.

8. Six hundred seventy-eight thousand nine hundred twelve.

9. One million three hundred fifty-seven thousand nine hundred twenty-four.

10. Sixty-eight million one hundred forty-three thousand seven hundred ninety-two.

11. One thousand one; one thousand ten; one thousand one hundred.

12. One thousand one hundred one; one thousand one hundred ten; one thousand one hundred eleven.

13. Two thousand three; four thousand fifty.

14. Forty-five thousand twenty-six.

15. Eighty thousand two hundred one.

16. Ninety thousand one.

17. Four hundred ten thousand two hundred five.

18. One hundred thousand ten.

19. Three million seventy thousand five hundred nine.

20. Forty-five million eighty-three thousand twenty-six. 21. Nine hundred nine million ninety thousand.

22. Seven hundred million ten thousand two.

23. Forty billion two hundred thousand five.

24. Seven hundred twenty-six billion fifty million one thousand two hundred forty-three.

25. Eighty billion seven hundred three million five hundred four.

RAY'S MOD. PRACT. AR. -2

12. Numeration is the reading of numbers when expressed according to a system of notation.

To read numbers in the Arabic system :

Rule.

1. Begin at the right, and point off the number

into periods of three figures each.

2. Begin at the left, and read each period as a number composed of hundreds, tens, and units, giving the name of the period.

NOTES.-1. The left-hand period will sometimes contain but one or two figures.

2. It is customary to omit the name of the units' period.

Read:

2. 41582; 763491; 2519834; 375486921; 4923176358. 3. 37584216974; 432685729145; 6253971438267.

4. 1300; 2540; 6070; 8009; 13200; 1005.

5. 682300; 8600050; 3040; 50004; 704208.

6. 7085; 62001; 400009; 2102102; 9001003.

7. 130670921; 6900702003; 23004090701; 9420163070.

8. 570000010326049; 103478511992485.

9. 900020108000507; 800820020802008.

THE ROMAN SYSTEM OF NOTATION

13. To express numbers, the Roman notation uses seven letters as follows:

NOTE.

The Roman system of notation is so called because it was the method of expressing numbers used by the ancient Romans. It is now used to mark the chapters of books, the dial plates of clocks,

etc.

Principles. I. Repeating a letter repeats its value.

Thus, II represents two; III, three; XX, twenty; XXX, thirty; CC, two hundred; CCC, three hundred; MM, two thousand. NOTE. The letters V, L, and D are never repeated.

II. When a letter is placed after another of greater value, their values are to be united.

Thus, XI represents eleven; VII represents seven; LXXX repre sents eighty.

III. When a letter is placed before another of greater value, its value is to be subtracted from that of the greater.

Thus, IV represents four; IX, nine; XC, ninety; CD, four hundred; CM, nine hundred.

IV. When a letter is placed between two letters, each of greater value, its value is to be subtracted from the sum of the other two.

Thus, XIV represents fourteen; XIX, nineteen; XXIV, twentyfour; CXL, one hundred forty.

V. A bar placed over a letter multiplies its value by 1000. Thus, V represents five thousand; X, ten thousand; L, fifty thousand; M, one million; CD, four hundred thousand.

ADDITION

15. 1. If you have 2 cents and find 3 cents, how many will you then have? Ans. 5 cents.

Why? Because 2 cents and 3 cents are 5 cents.

2. I spent 12 cents for a slate, and 5 cents for a copybook. How many cents did I spend ?

Ans. 17 cents. Why?

3. John paid 6 cents for an orange, 7 cents for pencils, and 9 cents for a ball. How many cents did all cost? Ans. 22 cents. Why?

4. Joseph paid 5 cents for a daily paper, 10 cents for a weekly paper, 25 cents for a monthly magazine, 30 cents for a book of poems, and 40 cents for a novel. How much did he spend? Ans. 110 cents.

16. The operation in these examples is termed addition. Addition is the process of uniting two or more numbers into one number.

The number obtained by addition is the sum or amount.

17. The sign of addition (+), called plus, means more; when placed between two numbers, it shows that they are to be added. Thus, 4 + 2 means that 4 and 2 are to be added.

The sign of equality (=) denotes that the quantities between which it stands are equal. Thus, the expression 4 + 2 6 means that the sum of 4 and 2 is 6. 4 plus 2 equals 6.

=

It is read,