Pictures of Numbers

31. Numbers are sometimes represented by pictures called graphs.

1. In Figure 1 each line opposite the name of a state stands for the amount of arid land in that state, each one eighth inch of the line representing 1 million acres. In Arizona there are two million acres of arid land. Read the amount of arid land in each state.

2. In Figure 2 each unit of a heavy line represents 1 million 500-pound bales of cotton exported from the United States during the year named opposite the line.

(Notice that the line opposite 1911 consists of 8 units, each divided into halves. In that year there were exported 8 million 500-pound bales.)

Read the number of bales exported each year.

The Roman System

32. The Romans represented numbers by seven letters, and combinations of them. These letters are I, representing one; V, five; X, ten; L, fifty; C, one hundred ; D, five hundred; and M, one thousand.

33. The combinations used to represent the nine simple numbers, the tens, the hundreds, and the thousands, are formed according to the following principles :

1. Every time a letter is repeated, its value is repeated.

2. When a letter or a combination of letters of less value is written after a letter or a combination of letters of greater value, the sum of the values is expressed.

3. When a letter of less value is written before one of greater value, the difference of their values is expressed. 4. A dash placed over a letter or a combination of letters makes the letter or combination represent thousands.

34. In writing numbers between those in the table, Sec. 33, hundreds are written after thousands, tens after hundreds, and units after tens.

Thus, 1567 is written MDLXVII; 2053, MMLIII; 4508, IVDVIII; 3600, MMMDC.

NOTE. The use of the Roman system of notation is confined chiefly to the numbering of chapters and sections of books, pages of prefaces and introductions, medical prescriptions, public documents, divisions on clock dials, etc.

Exercise 5

Write by the Roman system the following:

1. The nine simple numbers.

2. The nine tens.

3. The nine hundreds.

4. The numbers between 20 and 30.

FUNDAMENTAL PROCESSES

TO THE TEACHER. Pupils have already learned how to add, subtract, multiply, and divide, but they should practice these operations until they can perform them rapidly and with accuracy.

Addition

35. Addition is the process of uniting two or more numbers into one number called their sum.

NOTE. Similar amounts, and only such, may be united (added); the result (sum) is similar to the amounts added.

(Accuracy and Speed Test.

Exercise 6

Practice until you can add the exercises on this page in less than 2 minutes. Check the result by seeing if the sum found when the columns are added upward agrees with the sum found when the columns are added downward.)