To find the interest on any sum, for any time, at 6 per cent., . 128 To find the interest on any sum, for any time, at any per cent., When partial payments are made on notes, bonds, etc., Given the time, rate per cent., and interest, to find the principal, 140 Principal, time, and interest given, to find the per cent., Principal, rate per cent., and interest, to find the time, To find the discount and present worth, To find the present worth of a sum at compound discount, 156 Table to assist in finding the present worth at compound interest 157 To find the amount of an annuity, Table by which to find the present worth of an annuity, To find the present worth of an annuity in reversion, Tables-more for curiosity than utility, Evolution defined, Extraction of the square root of a whole number, When the number is a vulgar fraction, When many figures are required, Examples involving the principles of the square root, When the number has decimals, When the number is a vulgar fraction, Examples involving the principles of the cube root, ARITHMETIC. CHAPTER I. DEFINITIONS. 1. ANY whole number is called an integer. 2. Any number which can be divided by 2, without a remainder, is called an even number. 3. All numbers which can not be divided by 2, without a remainder, are called odd numbers. 4. Any number which can be produced by multiplying two or more numbers together, each of which is greater than a unit, is called a composite number. Thus, 35 is a composite number, since it can be produced by multiplying 5 and 7 together. 5. The numbers which are multiplied together to produce a composite number, are called factors. Thus, 3 and 8 are factors of 24; so, also, are 4 and 6. 6. A composite number which is composed of two equal factors, is called a square number. Thus, 4, 9, 16, and 49, are square numbers. 7. A composite number which is composed of three equal factors, is called a cube number. Thus, 8, 27, and 64, are cube numbers. 8. One of the equal factors which compose a square number, is called the square root of the number. Thus, 7 is called the square root of 49. 9. One of the equal factors which compose a cube number, is called the cube root of the number. Thus, 3 is the cube root of 27. 10. All numbers which are not composite, are called prime numbers. Thus, 1, 2, 3, 5, 7, 11, and 13, are prime numbers. 11. Unity divided by a number is the reciprocal of that number. Thus,,, and, are the reciprocals of 2, 3, and 4. 12. A number taken without regard to the particular kind of unit, is called an abstract number. 13. A number considered in reference to a particular unit, is called a concrete number, or a denominate number. Thus, 8 yards is a denominate number, whose unit is one yard; 37 days is a denominate number, whose unit is one day. SYMBOLS. 2. THE Symbol, is called the sign of equality; and denotes that the quantities between which it is placed are equal or equivalent to each other. Thus, $1=100 cents; which is read, one dollar equals one hundred cents. 2. The symbol +, is called plus; and denotes that the quantities between which it is placed are to be added together. Thus, 6+2=8; which is read, six and two added equals eight. 3. The symbol, is called minus, and denotes that the quantity which is placed at the right of it is to be subtracted from the quantity on the left. Thus, 6-2=4; which is read, six diminished by two equals four. 4. The symbol x, is called the sign of multiplication, and denotes that the quantities between which it is placed are to be multiplied together. Thus, 6 x 2= 12; which is read, six multiplied by two equals twelve. Multiplication is sometimes expressed by a dot, (.); Thus, 3.4, is the same as 3 × 4. 5. The symbol, is called the sign of division, and denotes that the quantity on the left of it is to be divided by the quantity on the right. Thus, 6÷2=3; which is read, six divided by two equals three. Division is also denoted by placing the divisor under the dividend, with a horizontal line between them, like a vulgar fraction. Thus, is the same as 6÷2. 6. A number placed above another number, a little to the right, is called an exponent. Thus, in the expressions, 62, 73, 2 and 3 are exponents of 6 and 7, respectively. 7. An exponent placed over a quantity, denotes that the quantity is to be used as a factor as many times as there are units in the exponent. Thus, 24-2×2×2×2 =16. 8. When the exponent is 2, the result is called the second power of the quantity over which it is placed. Thus, 72=7×7=49=the second power of 7. 9. When the exponent is 3, the result is called the third power of the quantity over which it is placed. Thus, 43-4x4x4-64 the third power of 4. The higher powers are denoted in the same way. 10. The symbol √, denotes that the square root of the quantity over which it is placed is to be taken. Thus, √4=2; which is read, the square root of four equals two. |