# A Treatise on Arithmetic, Combining Analysis and Synthesis: Adapted to the Best Mode of Instruction in Common Schools and Academies

Brown, Taggard & Chase, 1857 - 355 „š «Š’›Õ«

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 ARITHMETIC l 1 Numeration 3 Addition 7 Subtraction 14 Multiplication 20 Division 26 Compound Numbers 36 Reduction 45
 Profit and Loss 178 Partnership 185 Compound Partnership 187 Taxes 189 Alligation 193 Single Position 201 Double Position 203 Involution and Powers 206

 Signs Definitions and General Principles 48 To Find Prime Numbers 51 To Resolve a Number into its Prime Factors 54 To Find the Greatest Common Measure of Numbers 55 To Find the Least Common Multiple of Numbers 59 Convenient Facts 62 Vulgar Fractions 64 To Multiply a Fraction by a Whole Number 65 To Divide a Fraction by a Whole Number 67 To Multiply a Fraction by a Fraction 68 To Divide a Fraction by a Fraction 72 To Reduce a Fraction to its Lowest Terms 74 To Reduce an Improper Fraction to a Whole or Mixed Number 75 To Reduce a Mixed Number to an Improper Fraction 76 To Reduce a Complex Fraction to a Simple One 77 Miscellaneous Examples 91 Page 93 Decimal Fractions 98 15 104 Examples 155 Ratio 160 Proportion 164 Compound Proportion 171 Conjoined Proportion 174
 Evolution 210 Square Root 212 Application of Square Root 219 Cube Root 228 Application of Cube Root 236 Extraction of Roots of All Degrees 237 Arithmetical Progression 239 Geometrical Progression 247 Annuities 25 256 Permutations Arrangements and Combinations 260 Arrangements 261 Combinations 263 Miscellaneous Examples 266 46 Miscellany 274 Contractions in Multiplication 275 Contractions in Division 279 Identity of Division Fractions and Ratios 281 Barter 283 Practice 284 47 Circulating Decimals 286 Continued Fractions 291 The Calendar and Chronological Problems 298 Application of Arithmetic to Geometry 307 Gauging 338

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«Š’›Õ… 26 - The number to be divided is called the dividend. The number by which we divide is called the divisor.Ģ
«Š’›Õ… 76 - To reduce a mixed number to an improper fraction, ó RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.Ģ
«Š’›Õ… 43 - DRY MEASURE 2 pints (pt.) = 1 quart (qt.) 8 quarts =1 peck (pk.) 4 pecks = 1 bushel (bu...Ģ
«Š’›Õ… 80 - Therefore, multiplying both terms of a fraction by the same number does not alter its value.Ģ
«Š’›Õ… 210 - The square root of a number is one of its two equal factors.Ģ
«Š’›Õ… 223 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.Ģ
«Š’›Õ… 141 - RULE. Divide the given interest by the interest of the principal, for the given time, at 1 per cent., and the quotient will be the rate.Ģ
«Š’›Õ… 51 - The least common multiple of two or more numbers is the least number that is exactly divisible by each of them.Ģ
«Š’›Õ… 33 - To divide by 10, 100, &c., we simply cut off as many figures from the right of the dividend as there are ciphers in the divisor.Ģ
«Š’›Õ… 75 - To reduce an improper fraction to a whole or mixed number, ó RULE : Divide the numerator by the denominator ; the quotient will be the whole or mixed number.Ģ