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= Equul.- The sign of Equality; as 4 qrs.=I crt.

signifies that 4 qrs, are equal to 1 cwt.
Minus, or less.-The sign of Subtraction; as so

2=5, that is S lessened by 2 is equal to 6.
+ Plus or more,—The sign of Addition; as, 4+158,

that is + added to 4 more is equal to 8, X Multiplied by.The Sign of Multiplication ; as 4X

6=24, that is 4 multiplied by 6 is equal to 24. Divided by.—'The Sign of Division ; as 8-21,

that is, 9 divided by 2 is equal to 4. :: So is.—The sign of Proportion; as 2:4::8:16,

that is, as 2 is to 4, so is 8 to 16. 7–2+5=10.-Shew's that the difference between 2 and

7, added to 5 is equal to 10. 9_2+5=2.-Signifies that the sum of 2 and 5, taken

tìom 9, is equal to 2.
0–3+1=1.-Over any number of quantities, denote

that they must be taken together which are under
it, thus 10 less the suin of three and 6 is equal to
l; without this character the preceding expres-

sion would be ambiguous.
N.-Prefixed to any number, signifies the Square Root

of that number is required.
V.-Signifies the Cube or Third Power.
N.-Denotes the Biquadrate, or the Fourth Power, &c.
i. e.-id est, that is.
189— Numbers placed in this way denote Division, but
63 are neither more nor less than an improper Vulgar Fraction,

the figures above the line are the Numerator, and those beloir
the line are the Denominator, and the Fraction is called im-
proper, because 189 cannot be tak 11 out of 63, whereas 63
can be taken out of 189 three times over, and 3 is the real

value of the fraction.
A VULGAR FRACTION is to be understood in the following

manner :--- The Numerator may be any indefinite number,
which number signifies that so many parts are to be taken
out of the Denominator. The Denominator is unity divided
into any indetinite number which represents bne, unit, or the

root of numbers.
A Vulgar Fraction may be changed into a Decimal by dividing
the Numerator by the Denominator, and if there is no re-

mainder the Decimal will be equal in value with the fraction.
A DECIMAL is unity divided into equal parts, which parts are

always 10, 100, 1000, &c. A Decimal is only distinguished

from a whole number by pretixing of (,) a comma.
A Decimal may be changed into a Vulgar Fraction of equal

value, hy drawing a line under it and nlacing an unit and
cphers as before remarked

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TUTOR'S ASSISTANT:

BEING A

COMPENDIUM OF ARITHMETIC.

PART I.

ARITHMETIC IN WHOLE NUMBERS.

THE INTRODUCTION.

is bers, and has five. principal or fundamental Rules upon which all its operations depend, viz.

NOTATION of NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION, and Division.

NUMERATION TEACHETH the different Value of Figures by their differex.

Places, and to read and write any Sụm or Number.

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Rulk. There are three Periods ; the first on the Right Hand, "Inits; the second Thousands; and the third Millions ; each consisting of three Figures, or Places. Reckon the first Figure uf each from the left Hand as so many Hundreds, the next

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Tens, and the third as so many single Ones of what is written over thein. As the first period on the Left Hand is read thus, Nine hundred eighty-seven Willions; and so on for any of the rest.

THE APPLICATION.

59

Write down in proper figures the following Numbers : Twenty-three Two hundred and fifty-four. Three thousand, two hundred and four. Twenty-five thousand, eight hundred and fifty-six. One hundred, thirty-two thousand, two hundred forty-five. Four millions, nine hundred forty-one thousand, four hundred.

Twenty-seven millions, one hundred fifty-seven thousand, eight buindred thirty-two.

Seven hundred twenty-two millions, two hundred thirty-one thousand, five hundred and four.

Six hundred two millions, two hundred ten thousand, five bundred.

Write down in Words at Length the following Numbers.
35 2017 519007 5207054 65700047

5201 754058 2071909 900061057
172 20760 5900030 70054308 221900790

NOTATION BY ROMAN LETTERS. 1. One

XXX. Thirty v. Two

XL.

Forty
III.
Three

L. Fifty
IV.
Four

LX Sixty
V.
Five

LXX. Seventy
VI. Sis

LXXX. Eighty VII. Seven

XC. Ninety VIII. Eight

C. Hundred IX. Nine

CC. Two hundred
X.. Ten

CCC. Three hundred
XI.
Eleven

CCCC. Four Ilundred
XII. . Twelve

D. Five Hundred XIII. Thirtcen

DC. Six hundred XIV. Fourteen

DCC. Seven hundred XV. Fifteen

DCCC. Eight hundred XVI Sixteen

TCCCC.Nine hundred XVII. Seventeen

M.

One Thousand XVIII. Eighteen

MDCCCXIII One thousand XIX. Nineteen

eight hundred and thirteen XX. Twenty

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