their Multiplication? Give the Note. What for their Division? Give How do vou proceed in the Rule of Three in Vulgar Frac- proposition, and rule in its Application and Use? What the Rules to ex- e Cords ARITHMETICAL MARKS AND SIGNS. =The sign of equality and is pronounced, equal to; +The sign of Addition, and is pronounced, added to; -The sign of Subtraction, and is pronounced, subtracted by. EXAMPLES 12+7=19, twelve added to seven will be equal to nineteen. 23–8=15, twenty-three subtracted by eight, equal fifteen. xThe sign of Multiplication, and is pronounced, multiplied into; - The sign of Division, and is pronounced, divided by. EXAMPLES. 8x7=56, eight multiplied into seven equal fifty-six. ; 36-4=9, thirty-six divided by four, equal nine. Division is also implied by the signs 3)6(2 and 2, six divided by three, equal two. :::: The sign of Proportion, and is pronounced, is ta, so is, to. EXAMPLE 6:9::8:12, as 6 is to 9 so is 8 to 12. ✓or Zsignifies the Square Root : thus 81 is read, the square root of 81; or 813 is read 81 in the square root. y or 5 Jenotes the Cube Root, &c. 3 means that 3 is squared, or to be multiplied, by itself. 3 means that 3 is to be cubed. 48 shows that 48 must be raised to the 4th power. 1973x9=198 means that 19 added to 3, and the sum multiplied by 9, equal 198. 12–2x3 2 =3 shows that 12 less the product of 2 multi plied by 3, and divided by 2, equal 3... ARITHMETIC. ARITHMETIC is the art and science of numbers, and has for its operation four fundamental rules, viz. Addition, Subtraction, Multiplication, and Division. To understand these, it is necessary to have a perfect knowledge of our method of Numeration or Notation. NOTATION TEACHES to express numbers by words or characters. When performed by means of characters or figures, ten are employed. Nine of these are of intrinsic value and are called digits, or significant figures, being written and named thus : I one, 4 four, 7 seven, 8 eight, 9 nine. The tenth figure, namely, 0, is called nought or cipher, and denotes a want of value wherever it is found. Besides the simple value of the digits, as noted above, they have each a local one, which depends on the following principle. In a combination of figures, reckoning from right to left, the figure in the first place represents its simple value; that in the second place ten times its simple value; that in the third place an hundred times its simple value; and so on ; each figure acquiring anew a tenfold value for every higher place it occupies. Hence our system of arithmetic is called decimal. The names of places are denominated according to their order. The first is the place of units; the second of tens; the third of hundreds; the fourth of thousands ; the fifth of ten thousands; the sixth of hundred thou. sands; the seventh of millions; and so on. Thus in the number 8888888; 8 in the first place signifies only eight; 8 in the second place eight tens or eighty ; 8 in the third place eight hundred ; 8 in the fourth place eight thousand; 8 in the fifth place eighty thousand ; 8 in the sixth place eight hundred thousand ; 8 in the seventh place eight millions. The whole number is read thus, eight millions, eight hundred and eighty-eight thousand, eight hundred and eighty-eight. Though a cipher has no value of itself, yet it occupies a place; and when set on the right hand of other figures it increases their value in the same teufold proportion : Thus in the number 8080; the ciphers in the first and third places denote, that, though no simple unit or hundreds are reckoned, yet the place of units and that of hundreds are to be kept up to assist in reckoning the tens and thousands. The above number (8080) is read eight thousand and eighty, which, without the two ciphers, would be read eighty-eight. Large numbers are divided into periods and half periods, each half period consisting of three figures. The name of the first period is units; of the second millions ; of the third billions ; of the fourth trillions; and also, the first part of any period is so many units of it; and . the latter part so many thousands of it.* * EXAMPLE. Trillions. Billions. Millions. Units. Periods. 3. Half do. thou. units. thou. units. thou. units. thou. c. x. U. Figures. 484 617 291 387 1. |