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Explanation of Characters used in this Book.
Equal to, as 12d. = ls. signifies that 12 pence are equal to I shilling
+ More, the sign of Addition; as, 5+7=12, signifies that
5 and 7 added together, are equal to 12.
- Minus, or less, the sign of Subtraction; as, 6–2=4, sig
nifies that 2 subtracted from 6, leaves 4.
X Multiply, or with, the sign of Multiplication; as,
4x3=12, signifies that 4 inultiplied by 3, is equal to 12.
The sign of Division; as, 8--2=4, signifies that 3 divided by 2, is equal to 4; or thus, =4, each of which signify the same thing.
:: Four points set in the middle of four numbers, denote
them to be proportional to one anutier, by the rule of three ; as 2:4::8:16; that is, as 2 to 4, so is 8 to 16.
✓ Prefixed to any number, supposes that the square root of
that number is required.
✓ Prefixed to any number, supposes the cube root of that
number is required.
ARITHMETIC is the art of computing by numbers, and has five principal rules for its operation, viz. Numeration, Addition, Subtraction, Multiplication, and Division.
Numeration is the art of numbering. It teaches to express the value of any proposed number by the following characters, or figures :
1, 2, 3, 4, 5, 6, 7, 8, 9, 1--or cipher. Besides the simple value of figures, each has à local value, which depends upon the place it stands in, viz. any figure in the place of units, represents only its simple value, or so many ones; but in the second place, or place of tens, it becomes so many tens, or ten times its simple value ; and in the third place, or place of hundreds, it becomes a hundred times its simple value, and so on, as in the following
Note. --Although a cipher standing alone signifies nothing ; yet when it is placed on the right hand of figures, it increases their value in a tenfold proportion, by throwing them into higher places. Thus, 2 with a cipher annexed to it, becomes 20, twenty, and with two ciphers, thus, 200, two hundred.
2. When numbers consisting of many figures, are given to be read, ji. will be found convenient to divide them into as many periods as we can, o; six figures each, reckoning from the right hand towards the left, calling the first the period of units, the second that of millions, the third billions, the fourth trillions, &c. as in the following number :
8 0 7 3 6 2 5 4 6 2 7 8 9 0 1 2 5 0 6 4. Period of 3. Period of
11. Period of
506792 The foregoing number is read thus-Eight thousand and seventy-three trillions ; six hundred and twenty-five thousand, four hundred and sixtytwo billions ; seven hundred and eighty-nine thousand and twelve millions ; five hundred and six thousand seven hundred and ninety-two.
N. B. Billions is substituted for millions of millicns,
4 3 2 1 -Four thousand 321.
5 4 3 2 1 -Fifty-four thousand 321.
8 7 6 5 4 3 2 1 -87 million 651 thousand 321.
To know the value of any number of figures : Rule.-1. Numerate from the right to the left hand, each figure in its proper place, by saying, units, tens, hundreds, &c. as in the Numeration Table.
2. To the simple value of each figure, join the name of its place, beginning at the left hand, and reading to the right.
1234, One tiousand two hundred and thirty-four. 54026, Fifty-four thousand and twenty-six. 123461, One hundred and twenty-three thousand four
hundred and sixty-one. 4666240, Four millions, six hundred and sixty-six thou
sand two hundred and forty. NOTE. For convenience ir eading large numbers, they may be divided into periods of three figures each, as follows:
987, Nine hundred and eighty-seven. 937 000, Nine hundred and eighty-seven thousand. 987 000 000, Nine hundred and eighty-seven million. 987 654 321, Nine hundred and eighty-seven million, six
burdred and fifty-four thousand, three hundred and twenty-one.
To write numbers. Rule.-Begin on the right hand, write units in the units place, tens in the tens place, hundreds in the hundreds place, and so on, tuwards the left hand, writing each figure according to its proper value in nuineration ; taking care to supply those places of the natural order with ciphers which are omitted in the question
EXAMPLES. Write down in proper figures the following numbers : Thirty-six. Two hundred and seventy-nine. Thirty-seven thousand, five hundred and fourteen. Nine millions, seventy-two thousand and two hundred. Eight hundred millions, forty-four thousand and fitty-five.
SIMPLE ADDITION. IS putting together several smaller numbers, of the same denomination, into one larger, equal to the whole or sum total; as 4 dollars and 6 dollars in one sum is 10 dollars.
Rule.- laving placed units under units, tens under tens, &c. draw a line underneath, and begin with the units ; after adding up every figure in that columii, consider how many tenis are contained in their suul ; set down the remainder under the units, and carry so many as you have tens, to the next column of tens; proceed in the same manner through every column or row, and set down the whole amount of the lost row.