5000 dollars, and eight Associate Justices, who receive 4500 dollars each? Ans. 41000 dollars. Q. What officers compose the United States Supreme Court? What is the salary of the Chief Justice? What of each of the Associate Justices ? 2. What is the annual expense of the Cabinet of the President of the United States, which consists of a Secre tary of State, a Secretary of the Treasury, a Secretary of War, a Secretary of the Navy, and a Postmaster-General, each of whom receives 6000 dollars per year, and an Attorney-General, who receives 4000 dollars? Ans. 34000 dollars. Q. What officers compose the Cabinet of the President of the United States? Do they all receive the same salary? Who receives the least? 3. The government of the United States is represented at the courts of Great Britain, France, Russia, Prussia, Austria, Spain, Brazil and Mexico, by an agent called a Minister Plenipotentiary, each of whom receives an annual salary of 9000 dollars. Each minister is allowed a Secretary, with a salary of 2000 dollars. What is the total annual expense of these officers? Ans. 88000 dollars. Q. What is the agent called that represents the United States at the Court of Great Britain? How many Courts are thus represented? What are they? What salary is allowed to a minister? Has he a secretary? At what salary? 4. How much does the present debt of Pennsylvania exceed the estimated value of her public improvements, her debt and the estimated value of her property being as follows, in 1843: Q. How was the debt of Pennsylvania contracted? What is the nature of its public property? 5. What is the daily expense of the governments of the following States, the total amount paid per year for each object of expenditure being as represented in the accompanying table? Amount paid for Officers. Judiciary. Legislature. D. D. Prisons and Insane. D. D. Militia. Printing. D. D. D. 365 Maine.... 6,576+ 11,200+ 40,687+ 26,409+ 8,325+ 2000÷365-Ans. 260297 8,000 +365--Ans. +365 Ans. 634365 Ans. Massachu't 16,500+ 50,536-114,071+ 20,506+21,033+11.944÷365-Ans. 5,650 11,840 +365 Ans. Connect 4,734- Virginia.. 19,433 44,550 95,056 64,015+59,237 Q. What are the objects of State expenditures? What is the amount paid to each object in your state? 6. Find the total amount of debt, and the average of debt to each inhabitant of the following countries, the total number of inhabitants, and the debt of each country, being as follows: Q. Do other countries appear to be in debt as well as the United States? What proportion does the proportionate debt of the States bear to that of England? France ? 7. By the census of 1840, the number of inhabitants in the United States was 17,063,353. Find the total amount of the debts of the States, and the amount to each individual, the indebtedness of each State being as follows: Ma OF FRACTIONS. 57. If the unit 1 be divided into any number of equa 'parts, one or more of these parts is called fraction. If the unit 1 be divided into two equal parts, one of these parts is called one half; two of them two halves; three of them three halves; &c. One half, two halves, three halves, four halves, &c., are fractions. As the unit 1 has been divided into two equal parts called halves, there are two halves in 1, four halves in 2, six halves in 3, eight halves in 4, &c.: the number of halves in every case being found by multiplying the number by 2. Q. If the unit 1 be divided into any number of equal parts, what is one or more of these parts called? If the unit be divided into two equal parts, what is one of these parts called? What are two of them called? Three? Four? What is one half? Two halves? Three halves? How many halves in 1? Why? How many in 2? In 3? In 4? In 5? In 6? How do you find the number of halves in a number? How many halves in 100? In 150? In 225 ? 58. If the unit 1 be divided into three equal parts, these parts are called thirds, and one of these parts is one-third; two of them two-thirds; three, three-thirds; four, fourthirds, &c. One-third, two-thirds, &c., are also fractions. The unit 1 being divided into three equal parts, there are three thirds in 1, six thirds in 2, nine thirds in 3, twelve thirds in 4, &c. The number of thirds in any number being found by multiplying the number by 3. Q. If the unit be divided into three equal parts, what are these parts called? What is one of them called? Two? Three? What is onethird? Why a fraction? What is two-thirds? How many thirds in 1? Why? In 2? In 3? In 4? How do you find the number of thirds in any number? How many thirds in 50? In 100? In 150? 59. When the unit 1 is divided into four, five, six, &c. equal parts, these parts are called fourths, fifths, sixths, sevenths, &c., and one fourth, two fourths, one fifth, two fifths, one sixth, two sixths, one seventh, two sevenths, three sevenths, &c., are fractions. There are then four fourths in 1, five fifths in 1, six sixths in 1, &c., since the unit is divided into 4, 5, 6, 7, &c. equal parts. There being four fourths in 1, there must be eight fourths in 2, twelve fourths in 3, &c. The number of fourths in the number being equal to the number multiplied by 4. Thus there are 20 fourths in 5, since 4× 5 gives 20. In like manner there being five fifths in 1, there will be ten fifths in 2; and there being six sixths in 1, there will be 12 sixths in 2, &c. Hence we conclude, that to find the number of fifths, sixths, sevenths, &c., in any number, we multiply by 5 to find the fifths, by 6 to find the sixths, by 7 to find the sevenths, &c. To find the number of fifths in 20, we multiply 20 by 5, and we get 100; there are then 100 fifths in 20. There are 200 tenths in 20, since 20× 10 gives 200. Q. When 1 is divided in 4 equal parts, what are these parts called? What when divided into 5 equal parts? Into 6? How is the unit divided in one-fifth? In two sevenths? What are one fifth, two fifths, one sixth called? How many fifths in one fifth? In three fifths? How many sixths in four sixths? How many fourths in 1? How many fifths? Sixths? How many fourths in 2? In 3? In 4? How do you find the number of fourths in a number? How many fifths in 1? How many sixths? How many sevenths? How many tenths? How many fifths in 2? How many sixths? How many tenths? How many fifths, sixths, sevenths, tenths, &c. in 3? In 4? How do you find the number of fifths in a number? The number of sixths? The number of tenths? How many fifths in 20? How many tenths? How many in 50? How many fifths in ten fifths? 60. A fraction is expressed by two numbers written one above the other, with a line drawn between them; the lower number shows into how many equal parts the unit 1 is divided, and the upper number how many of these parts are expressed in the fraction. Thus, in the fraction one-half, the unit being divided into two equal parts, the lower number is 2; and since one of these parts is taken, the upper is 1; then one-half is written In the fraction three halves, the unit is again divided into two equal parts, but three of these parts are expressed. The fraction is written. In like manner we may express by figures, Four halves, which is written, Nine-twentieths, " The two numbers which compose a fraction, are called its terms. |