PREFACE

THIS Intermediate Arithmetic is intended for fifth and sixth years. It is divided into two parts.

Part One includes the work of the fifth year. elementary treatment of Fractions, Decimals, Percentage, It gives an Denominate Numbers, and Practical Measurements. 'Part Two includes the work of the sixth year. It gives a complete treatment of Fractions, Decimals, Denominate Numbers, and an elementary course in Percentage, Practical Measurements, and business forms.

The aim of this book is twofold: first, to give the pupil mathematical skill; second, to give him mathematical power. To these ends attention is invited to the following:

1. The prominence given to drill intended to give skill. 2. The "Study of Problems" intended to give mathematical power.

3. The plan which provides an easy treatment of each subject before the complete treatment.

4. The easy steps in gradation.

5. The emphasis given to business arithmetic.

6. The abundance of exercises for oral drill.

The importance of oral drill has led the author to lay special emphasis on this kind of work. Pupils should be drilled thoroughly on the oral development and exercises in each subject, before taking up the written work.

The two treatments of topics, the number and the variety of problems, the systematic reviews, and the easy steps in the gradation of the work will, we believe, meet with the approval of teachers.

SAMUEL HAMILTON.

INTERMEDIATE ARITHMETIC

PART I- FIFTH YEAR

REVIEW OF NOTATION AND NUMERATION

1. In 364 for what does the 4 stand? the 6? the 3? 3643 hundreds, 6 tens, 4 ones.

2. Tell for what each figure stands in 2475. Read the number.

Each figure has a value that depends upon its place in the number. The first place beginning at the right of a number is called ones' place; the second, tens' place; the third, hundreds' place; the fourth, thousands' place, etc.

3. Show that the left-hand 2 in the number 222 has a value, because of its place, that is 10 times the value of the middle 2, and 100 times the value of the right-hand 2.

When a number contains more than three figures, it is separated into groups or periods of three figures each, beginning at the right. The names of the places in each period are the same. The name of the first period is units; of the second period, thousands; of the third, millions; and of the fourth, billions.

4. In the number 864,203,614,869, what name is given to the period 864? to the period 203? to 614? to 869?

Notation is a method of writing numbers by means of figures or letters.

Numeration is a method of reading numbers represented by figures or letters.