ARITHMETIC

SIMPLIFIED.

BY T. PIGOTT,

MASTER OF THE BRITISH SCHOOL, DONCASTER.

"IF IT WERE DONE, WHEN 'TIS DONE, THEN 'TWERE WELL,
"IT WERE DONE QUICKLY."-Shakspeare.

DONCASTER :

SOLD

BY T. BROOKE AND CO. HIGH-STREET;

C. WHITE, BAXTER

GATE; MASON AND SCOTT, LEEDS; AND WALKER, OTLEY,

ENTERED AT STATIONERS' HALL.

DONCASTER:

It is not necessary that the Author should state all his reasons for publishing the following pages. Having found, in the practice of teaching, that all existing Mental Arithmetics were exceedingly deficient in ar rangement, both in the Rules and Questions, he proceeded to make an entirely new, and what appeared to him, a natural arrangement for the use of his own school; and finding it to answer beyond his most sanguine expectations, it was suggested to him, by some of his friends, as being worthy of being offered to the public. Not willing to run any risk, he determined to offer it to be published by subscription, and the readiness by which it was met, by a numerous list of subscribers, is to him exceedingly gratifying, and he hopes that it will, in some measure, meet their expectations. He particularly presses upon all Parents or Teachers, who raay use his book, to proceed upon the system laid down. To commence with exercising the senses, and developing the faculties. To teach principles, not isolated questions; and would particularly caution them against putting it into the hands of Children, as a task book. It is not formed for decreasing the Teacher's labour, but for increasing it,

INTRODUCTION.

THE advantages of Mental Arithmetic are so great that it ought to form one of the principal parts in the education of all classes. In preparing for the commercial transactions of life, its claims are the very first: but, independently of this, when properly taught, it is one of the best means of disciplining the mind, the demonstrations of number being so much easier than those of magnitude, and consequently more suitable for children.

In teaching, the first principles and examples must be made plain to the senses, by the use of the slate, or the black board. The first must be seen by intuition, and so on for all the rest: intuition the most thorough. The pupil must not advance one step into the regions of darkness, every succeeding operation should be based upon something previously known. For this purpose, the examples and rules are so arranged as the first shall require but one operation of mind, the second two, and so on. The examples under each rule are divided into two parts, to be learned in two distinct courses. The tables are all placed at the end of the book, and should be learned as they are wanted in the study of the rules, but learned most thoroughly, for upon a knowledge of tables and data depend the power of the Mental Arithmetician, and enable him to answer questions which, to the uninstructed, appear truly astonishing: an attainment not to be accomplished by a few lessons, learned in an irregular manner, but by a thorough training of the mental faculties, and clear views of the principles of

DEFINITIONS.

1.-Arithmetic is the science of numbers, and teaches the art of making calculations. The figures made use of are the following:-1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

2.-MENTAL ARITHMETIC is the art of calculating by the mind, without the aid of symbols.

3.-NUMERATION teaches how to read, and notation how to write any number of figures..

4.-ADDITION teaches how to add two or more sums into one; as 8, 7, 12, 6 added together, the sum is 33.

5.-SUBTRACTION teaches how to take a less number from a greater, and shows the remainder or difference; as 7 taken from 22, the remainder is 15.

6.-MULTIPLICATION shews what one number will amount to when repeated a certain number of times; as 10 repeated 6 times will be 60.

7.-DIVISION teaches how to separate a given number into a certain number of parts; as 18, divided into 3, parts, each part will be 6.

8.-The following signs are used to express these rules:+ Addition; - Subtraction; × Multiplication;÷Division; = equality; as 8+4=12. 8-3=5. 6×6= 36, 3666.

9.—An Integer or Unit is one whole number; as 1 yard, 1 shilling, or 1 penny.

10.-A part of 1 is called a fraction, and is thus written; (three eighths), or (three fourths). The bottom figure shews how many parts it is broken into, and is called the denominator; the top figure shews how many are taken, and is called the numerator.