The system here presented to the public, it is believed, answers all these more general ends of scientific education, and has, besides, the very great merit of abridging the mechanical part of the solutions so much as to dispense with full five sixths of the figures that are ordinarily employed. This is not only a saving of time and labour, but what is of vast importance in arithmetical solutions, it greatly diminishes the liabilities to mistakes, and at the same time facilitates their detection. This work is submitted to the public with the confidence that it is a very great practical improvement, and that it not only greatly increases the pleasures of the study, but renders the science easily attainable to those who find it extremely difficult to master by the mechanical rules and unreasoning methods so generally in use. The first part of the work being intended for beginners, the mechanical part of the solutions are performed in the usual manner, but as the pupil advances, the exercises are so arranged as to gradually prepare him to understand and appreciate the improved method. TEACHERS AND PURCHASERS, Wishing to obtain this work, Naylor's Geography, Baldwin's Gazetteer, or Pelton's Outline Maps, can have them carefully forwarded to order to any part of the United States. Address BENJAMIN NAYLOR, No 12 Marshall Street, Philadelphia. This work, and the Author's Geography for sale also by W. A. Leary, 158 North Second Street, Uriah Hunt and Son, No. 44 North Fourth Street, ARITHMETICAL CHARACTERS OR SIGNS. The sign + (plus) placed between numbers signifies at they are to be added together, thus, 4+8 make 12. The sign (minus) signifies subtraction, thus, 12—4 leaves 8, that is, 12 less 4 leaves 8. = The sign signifies equal, as 12 inches 1 foot; that is, 12 inches are equal to one foot. The sign signifies multiplication, as 6×8=48; that is, 6 multiplied by 8 is equal to 48. The sign signifies division, as 48÷8-6; that is, 48 divided by 8 is equal to 6. Division is also represented thus, 54-6; that is, 54 divided by 9 is equal to 6. Numbers placed in this manner, 14-6+9 show that different operations are to be performed, thus 14-6+9 signifies that 6 is to be taken from 14, and 9 added to the remainder. The line at the top is called a vinculum, and connects all the numbers over which it is drawn. These are called parentheses, and these [ ] brackets; they are frequently used instead of a vinculum, thus, (14-6)+9=17, or (14—6)×9=72. A figure or number with a small figure placed over it, thus, 82 signifies that the figure or number is to be raised to such power as the small figure indicates, for instance, 82 signifies the second power of 8, or that 8 is to be multiplied by itself, thus, 82-8×8-64; and 83 =8x8x8=512― the third power of 8; 81 the fourth power of 8, &c. = The sign ✔ prefixed to a number shows that the square root is to be extracted. This sign prefixed to a number shows that the third or cube root is to be extracted. The square root is also denoted thus 9 and the cube root thus (27). EXAMPLES. How do you read the expression, 12+8+6+4=30? Ans. 12 plus 8, plus 6, plus 4 is equal to 30. How do you read the expression, 14+9+5—12=16? Ans. 14 plus 9, plus 5, minus 12, is equal to 16. How do you read the expression (16+8—11)×4=52 ? Ans. 16 plus 8, minus 11, multiplied by 4, is equal to 52. How do you read the expression, (9×4+14)÷5=10? Ans. 9 multiplied by 4, plus 14, divided by 5 is equal to 10. How do read the expression, (48÷4)×7)—16—68 ? Ans. 48 divided by 4, the quotient multiplied by 7, and 16 subtracted from the product leaves 68. How do you read the expression, 36×12+14=62? Ans. 36 divided by 9, the quotient multiplied by 12, and 14 added to the product, make 62. How do you read the expression, 4×6×5+8×3—2×8=128? Ans. 4 times 6 times 5, plus 8 times 3, minus 8 times 2, is equal to 128. How do you read the expression, 12+12×5—18+7=57? How do you read the expression, 13+23-12x3+8=80? to 80. How do you read the expression, 72x3+9 25? Ans. The second power of 7 multiplied by 3 plus 9, divided by 6 is equal to 25. How do you read the expression (26-6)×4 -5 Ans. 26 minus 6, multiplied by 4, divided by 7 times 3 minus 5, is equal to 5. |