Addition of Vulgar Fractions,

Subtraction of Vulgar Fractions,

Multiplication and Division of Vulgar Fractions,

Reduction of Decimals,

Promiscuous Questions,

Rule of Three,

Simple Interest,

Compound Interest-Discount,

Commission and Brokerage,

Percentage,

Insurance,

Banking,

Loss and Gain-Fellowship,

Taxing,

Equation of Payments,

Custom House Business,

Each word, one, two, three, four, five, six, &c., points out how many things are spoken of. These words are called NUMBERS. Hence, NUMBERS are the expressions for several things of the same kind.

Questions. What is a single thing called? One and one? Two and one? Three and one? Four and one? Five and one? Six and one? Seven and one? &c. What are Numbers ?

§ 2. The unit of a number is one of the equal things which the number expresses. Thus, if the number be six apples, one apple is the unit; if it be five pounds of tea, one pound of tea is the unit; if it be ten feet of length, one foot is the unit; if it be four hours of time, one hour is the unit.

Q. What is the unit of a number? What is the unit of the number six apples? Of the number five pounds of tea? Of the number ten feet? Of the number four hours?

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§ 3. ARITHMETIC treats of numbers. Numbers are expressed by certain characters, called figures. ten of these characters. They are

O which is called a cipher, or Naught,

There are

Q. Of what does arithmetic treat? How are numbers expressed? How many figures are there? Name them.

§ 4. The character 0 is used to denote the absence of a thing. As, if we wish to express by figures that there are no apples in a basket, we write, the number of apples in the basket is 0. The nine other figures are called. significant figures, or Digets.

1 expresses a single thing, or a unit of a number.

2

3

456789

two things of the same kind, or two units. three things

four things

five things
six things

seven things
eight things

nine things

or three units.

or four units.

or five units.

or six units.

or seven units. or eight units.

or nine units.

Q. What does 0 express? What are the nine other figures called? How many things does 1 express? How many things does 2 express? How many units in 3? In 4? In 5? In 6? In 7? In 8? In 9?

§ 5. If we wish to express the number ten, we have no separate character for it. We must combine the characters already known. This we do by writing 0 on the right hand of the 1; thus, 10, which is read ten.

This 10 is equal to ten of the units expressed by 1. It is, however, but a single ten, and in this sense may be regarded as a unit, the value of which is ten times greater