PAGE. Reduction of denominate fractions, . . . To reduce fractions from one denominate value to another, . 43 To find what fractional part one quantity is of another, . . 45 Numeration table of whole numbers and decimals, Subtraction of decimals,-multiplication of decimals, Abridged multiplication of decimals, . - - - Division of decimals, - - - - - Abridged division of decimals, To change a vulgar fraction to a decimal, . Whether a vulgar fraction can be accurately decimated, .. When it can be expressed, to determine the number of decimals, When the decimals do not terminate they recur in periods, . Perfect repetends, . . . . . . . . Method of decimating when many figures are required, - Continued fractions defined, - To convert a vulgar fraction into a continued fraction, . To convert a continued fraction into a vulgar fraction,.. Use of continued fractions, • • - -. . Properties of continued fractions, . . . .. Compound Proportion, . . . . . . To find the interest on $1, for any time, at 6 per cent., To find the interest on any sum, for any time, at 6 per cent., 131 To find the interest on any sum, for any time, at any per cent., 132 When partial payments are made on notes, bonds, etc., Given the time, rate per cent., and interest, to find the principal, 138 Principal, time, and interest given to find the per cent., . 139 Compound interest defined, . . . . Table to facilitate the casting of compound interest, . Compound discount defined, . . . To find the present worth of a sum, at compound discount, . Table to assist in finding the present worth, at compound interest, Annuities defined, -to find the amount of an annuity, Table by which to find the amount of an annuity, - - To find the present worth of an annuity, Table by which to find the present worth of an annuity, , When the number has decimals, .' When the number is a vulgar fraction, - - - Examples involving the principles of the square root,' Extraction of the cube root of a whole number, . . When the number is a vulgar fraction, . . When many decimals are required, . Examples involving the principles of the cube root, Extraction of roots of all powers, . . . Duodecimals defined, . . . . . Multiplication of duodecimals, . . New method of multiplying duodecimals, - Alligation defined,-Alligation Medial, . When one of the ingredients is limited, When two or more of the ingredients are limited, . When the whole compound is limited, . . Permutation defined, . . . . . When the individual things are all different, - . When several of the individual things are alike, . Combination defined, - - - . . Combinations with repetitions, . Combinations without repetitions, . Variations with repetitions, . . . . Variations without repetitions, . 202 . . . 212 . ARITHMETIC. -. CHAPTER I. 2. Any number which can be divided by 2, without a remainder, is called an even number. 3. All numbers which cannot 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 compos. ite 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 num. ber, 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. 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, t, is called plus; and denotes that the quantities between which it is placed are to be added togeth. er. 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, 6X2=12, which is read, six multiplied by two equals twelve. 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, 62=3, which is read, six divided by two equals three. |