Operation. First multiply .50 cents, the tax on 1 poll, $37.50 amount on polls. Then $237.50-$37.50-$200, the sum to be assessed $8000)$200.000(.025, the per cent. or tax on $1. 160 00 40 000 40 000 And $500 ×.025-$12.50, the tax on the man's property. .50×3= 1.50, tax for polls. Ans. $14.00, his whole tax. 3. What amount of tax does a man living in the same parish pay, whose property is valued at $450, and pays for 2 polls? 4. A tax of $750 is assessed on a district to build a new school-house; the property of the district is valued at $15000. What is the tax on a dollar; and what is a man's tax whose property is $1150? 5. What is B's tax for erecting the same school-house, whose property is $1530? 6. A tax of $14752.50 is levied on a certain County, whose property is valued at $562875, and which has a list of 5825 polls, which are assessed at 60 cents apiece. What per cent. is the tax; and what is the amount of C's tax, who pays for 4 polls, and has property valued at $5000 ? 7. What is D's tax, who living in the same County, pays for 2 polls, and is worth $3500 ? 8. What is G's tax, who pays for 5 polls, and is worth $15300? 279. In making a tax bill for a whole town, district, &c., assessors, having found the tax on $1, usually make a table, showing the amount of tax on any number of dollars from 1 to $10; then on 10, 20, 30, &c. to $100; then on 100, 200, &c. to $1000. 9. A tax of $3506.25 was levied on a corporation, composed of 12 individuals, whose property was valued at $175000, and who were assessed for 25 polls at 25 cents apiece. What was the tax on a dollar? Ans. 2 cents on 1 dollar. Note. Having found the tax on $1, we will make a table to aid us in making out the tax bill of the corporation. Since the tax on $1 is $.02, it is obvious that multiplying $.02 by 2 will be the tax on $2; multiplying it by 3, will be the tax on $3, &c. 10. In the above assessment, what was A's tax, whose property was valued at $1256, and who pays for 3 polls? Operation. $1000 pays $20.00 200 66 50 3 polls 66 4.00 1.00 .12 .75 Amount, $25.87. $1256 is composed of 1000+ 200+50+6. Now, if we add the taxes paid on each of these sums together, the amount will be the tax paid on $1256. A's tax, therefore, was $26.62. 11. What was B's tax, who paid for 4 polls, and had property to the amount of $1461 ? 12. C paid for 1 poll, and the valuation of his property was $5863. What was the amount of his tax? QUEST.-279. When a tax bill is to be made for a whole town, dis trict, &c., what course do assessors usually take? 13. D paid for 1 poll, and the valuation of his property was $7961. What was his tax? 14. E paid for 2 polls, and his property was valued at $14236. What was his tax? 15. F paid for 2 polls, and his real estate was valued at $21000; his personal property at $4500. his tax? What was 16. G's property was valued at $20250, and he paid for 1 poll. What was his tax? 17. H paid for 2 polls, and the valuation of his estate was $15360. What was his tax? 18. J's property was valued at $33000, and he paid for 4 polls. What was his tax? 19. K paid for 1 poll, and his property was valued at $15013. What was his tax? 20. L paid for 3 polls, and his property was valued at $4500. What was his tax? 21. M paid for 1 poll, and the valuation of his property was $30600. What was his tax? SECTION X. PROPERTIES OF NUMBERS.* DEFINITIONS. ART. 280. The progress as well as the pleasure of the pupil in the study of Arithmetic, depends very much upon the accuracy of his knowledge of the terms, which are employed in mathematical reasoning. Hence, particular care has been taken to define all the most important terms, as they have been introduced, and it is of the utmost importance for the pupil to understand their true import. QUEST.-280. Upon what does the progress and pleasure of the student in Arithmetic very much depend? * Barlow on the Theory of Numbers. DEF. 1. Numbers are divided into two classes, Abstract and Concrete. When they are applied to particular objects, as peaches, pounds, yards, &c., they are called concrete. When they are not applied to any particular object, they are called abstract. (Art. 45. Obs. 1.) Thus, when it is said that two and three are five, the two, three, and five denote abstract numbers. 2. A whole number is called an integer. (Art. 105.) 3. Whole numbers or integers are divided into prime and composite numbers. 4. A prime number is one which cannot be produced by multiplying any two or more numbers together. Thus, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, &c. are prime numbers. OBS. 1. A prime number, therefore, is exactly divisible only by itself and a unit. 2. One number is said to be prime to another, when a unit is the only number by which both can be divided. The number of prime numbers is unlimited. The first twelve are given above. The pupil can easily point out others. 5. A composite number is one which may be produced by multiplying two or more numbers together. (Art. 55. Obs. 1.) Thus, 4, 6, 8, 9, 10, 12, 14, 15, 16, &c. are composite numbers. 6. An even number is one which can be divided by 2 without a remainder; as 4, 6, 8, 10, &c. 7. An odd number is one which cannot be divided by 2 without a remainder; as 1, 3, 5, 7, 9, 15, &c. OBS. All even numbers are composite numbers; an odd number is sometimes a composite, and sometimes a prime number. QUEST.-Into how many classes are numbers divided? What is an abstract number? A concrete number? What are whole numbers called? Into how many classes are whole numbers divided? What is a prime number? Obs. Are prime numbers divisible by other numbers? When is one number said to be prime to another? How many prime numbers are there? What is a composite number? What is an even number? An odd number? Obs. Are even numbers prime or composite? What is true of odd numbers in this respect? 8. One number is a measure of another, when the former is contained in the latter a certain number of times without a remainder. (Art. 93. Obs. 1.) 9. One number is a multiple of another, when the former contains the latter a certain number of times without a remainder. (Art. 98.) 10. The aliquot parts of a number are the parts by which it can be measured, or into which it may be divided. Thus, 3 and 7 are the aliquot parts of 21. 11. The reciprocal of a number is the quotient arising from dividing a unit by that number. Thus, the reciprocal of 2 is; the reciprocal of 3 is ; &c. PROPERTIES OF THE SUMS, DIFFERENCES, PRODUCTS, &c. OF NUMBERS. 281. By properties of numbers is meant those qualities or elements which are inherent and inseparable from them. 1. The sum of any two or more even numbers, is an even number. 2. The difference of any two even numbers is an even number. 3. The sum or difference of two odd numbers, is even ; but the sum of three odd numbers, is odd. 4. The sum of any even number of odd numbers is even; but the sum of any odd number of odd numbers is odd. 5. The sum, or difference, of an even and an odd number, is an odd number. 6. The product of an even and an odd number, or of two even numbers, is even. 7. If an even number be divisible by an odd number, the quotient is an even number. 8. The product of any number of factors is even, if any one of them be even. 9. An odd number cannot be divided by an even number without a remainder. QUEST.-When is one number a measure of another? What is a multiple? What are aliquot parts? What is the reciprocal of a number? 281. What is meant by properties of numbers? |