to touch the genuine interests of pupils in the story of our national resources and industries rather than to dwell upon the technicalities of minor trades in which they have no immédiate or prospective concern; and to come in contact with human life rather than with those phases of science which are quite as foreign to the interests of boys and girls as are the mere abstract problems of numbers.

4. In the matter of abstract drill work, to recognize the fact that a large number of "problems without content" are necessary to concentrate the attention on the operations and to impart the computing habit. The numbers selected have been those demanded by the conditions of the present day, the fractions and compound numbers being those in common use rather than those never met in business, and the integers being the ordinary ones of daily life. Very large numbers have generally been used only in such applied problems as represent the real conditions that the children meet in their geography, their elementary science, and their newspaper reading.

The necessity for a frequent review of the fundamental operations is recognized by all teachers, and hence the book opens with such a review, presenting the subject in a slightly more scientific manner and introducing such short processes as are really usable in business.

In fine, the book is written for the use of those teachers who wish to preserve the best that was in the old-style arithmetic, with its topical system and its abundant drill, while giving to it a modern arrangement and securing "mental discipline" through problems of to-day rather than through the tiresome, meaningless, unreal inheritances of the past.

DAVID EUGENE SMITH

CHAPTER I

I. A GENERAL REVIEW OF ARITHMETIC

WRITING NUMBERS

1. Reason for this review. This class has now studied most of the important subjects of Arithmetic. Soon we shall take the more advanced business applications. As an aid to this advanced work we should review the foundations of all work in Arithmetic, the common operations.

Where such a review is not thought to be advisable, it will of course be omitted.

2. Origin of our numerals. Our numerals, 1, 2, and so on to 9, originated in India about 2000 years ago. The zero (0) was added more than 1200 years ago, thus making the system the excellent one that we now know. Without the 0 it was but little better than the Roman system. The numerals were learned by the Arabs more than 1100 years ago, and by A.D. 1200 became somewhat known in Europe. About 400 years ago they became well known in schools and in business, and they are now used in most of the civilized world.

3. The great feature of this system. It is the place value that makes the Arabic or Hindoo system better than all others. The Roman VI means five + one, while 51 means five tens + one, the 5 having not only the value five, but the place value tens.

4. Decimal system. Because the places or orders increase tenfold to the left, and decrease by tenths to the right, we call our system a decimal system, from the Latin decem, meaning ten.

1

ORAL EXERCISE

1. How many different figures are used in the Arabic system? How many in the Roman system for numbers below a hundred? /

2. If I write ten five in figures in the two systems, 105 and XV, what values are indicated? Why do the two numbers have different values? What is the use of the 0?

3. In the number 1,904,526,738, give the place value of each figure, as 8 units, 3 tens, and so on. Give the name of each period, as 738 units, 526 thousands, and so on.

4. What do you mean by the words separatrix, order, period, decimal, naught, place value, billion? Do not try to repeat definitions, but answer in your own way.

5. Why is our common system, the Arabic, better than the old Roman system? You might illustrate by trying to multiply one number by another.

6. Read the following numbers taken from book chapters: XXVIII, XLI, LXI, LXXXIX, XCIV, CLXVI.

WRITTEN EXERCISE

1. Write in the Arabic system: MDCLXIX, MCCCXLIV. 2. Write in the Roman system: 49, 79, 94, 96, 99, 146. 3. Write in the Roman system the number of the present year; of last year; of fifty years ago.

4. Write in the Arabic system the number twenty-one million, four hundred seventy-five.

5. Write in common figures the number one billion, one million, one thousand one, and one ten-thousandth.

6. Write in common figures the number of Ex. 5 decreased by 42,675; also by 12.245; also by 295,001.127.