2. A farmer has sheep in five fields; in the first, he has 917; in the second, 249; in the third, 413; in the fourth, 1000; and in the fifth, he has 197. How many sheep has he in the five fields? Ans. 2776 sheep. 3. A person owes to one man 302 dollars, to another man he owes 707 dollars, and has owing to him 2000 dr lars. How much will remain after paying his debts? Ans. 991 dollars. 4. A farmer receives for his wheat 103 dollars, for Lis corn 60 dollars, for his butter 511 dollars, for his cheese 1212 dollars, for his pork 601 dollars. He pays towards a new farm 1000 dollars, for a new wagon 50 dollars, for hired help on his farm 290 dollars, for repairing house 173 dollars. How much money has he remaining? Ans. 974 dollars. 5. A person wills 1200 dollars to his wife, 300 dollars for charitable purposes, and what remains is to be equally divided among 6 children. Allowing his property to amount to 8562 dollars, how much would each child have? Ans. 1177 dollars. E. A man gave 13558 collars for a farm; he then sold 73 acres, at 75 dollars per acre; the remainder stood him in at 59 dollars per acre. How many acres did he purchase? Ans. 210 acres. 7. Four boys divide 336 apples as follows: the first takes one sixth of the whole; the second takes one fourth of what was left; the third takes one half of what was then left; the fourth has the remainder. What number of apples did each boy have? The first had 56. 8. An estate of 8100 dollars was divided among 9 children in the following way: the first had 100 dollars and one tenth of the remainder; after this the second had 200 dollars and one tenth of the residue; again, the third had 300 dollars and one tenth of the remainder, and so on; each succeeding child had 100 dollars more than the one immediately preceding, and then one tenth of what still remained. What was the share of each? Ans. {They shared equal; each had 900 dollars. 9. A and B each owe C: A owes 1472 dollars, which is less than what B owes him, and yet the difference between A's and B's debts is 719 dollars. How much does Bowe C? Ans. 2191 dollars. 10. Admitting the earth to move 68000 miles per hour, how far will it move in one day; and how far in a year of 365 days? 1632000 miles in one day. Ans. 595680000 miles in one year. 11. If the President of the United States expends daily 60 dollars, how much will he be able to save at the end of the 365, out of his salary of 25000 dollars? Ans. 3100 dollars. 12. An army, consisting of 4525 men, have 103075 loaves of bread. At the end of 21 days, 500 men are killed in a battle Now, if each man in each day eat one loaf of bread, how many days after the battle will the bread sustain the army ? Ans. 2 days. 13. Two locomotives start from the same place, and move in the same direction; the first goes 25 miles each hour, the second only 15 miles. After the first has passed a distance of 100 miles it commences a backward motion, maintaining the same velocity, until it meets the second locomotive. How many hours after starting will they meet? And at what distance will they meet from the starting point? They will meet in 5 hours, Ans. at a distance of 75 miles. 14. One hundred miles of railroad track are to be laid with heavy rail, requiring 116 tons to the mile. After receiving iron at 52 dollars per ton to lay 58 miles, the price per ton was increased so as to make the whole cost of the entire road 612944 dollars. What was the latter price per ton of the iron? Ans. 54 dollars. FRACTIONS. 32. A fraction is a part of a unit. Several methods are used to express fractions or parts of units, which give rise to several distinct kinds of fractions. Those usually employed in arithmetic are VULGAR or COMMON FRACTIONS, and DECIMAL FRACTIONS. What is a fraction? What two methods are usually employed to express fractions? VULGAR FRACTIONS. 33. Vulgar fractions consist of two distinct parts or terms, the one written above the other, with a straight horizontal line between them, as in division, (ART. 23.) The number above the line is called the numerator. number below the line is called the denominator. The The denominator shows how many parts the unit is divided mto; and the numerator shows how many parts are used. Thus is a vulgar fraction, whose numerator is 5 and denominator 8 it is read five eighths. A vulgar fraction may be considered a concise method of expressing division, (ART. 23,) where the numerator corresponds to the dividend, and the denominator to the divisor. Thus is the same as 5 divided by 8, and it may therefore be read one eighth of fue, or, as above, five eighths of one. In the same way indicates that 1 is divided into 9 equal parts: it is read one ninth of one. After the same manner, is read one seventh of three, or three sevenths of one. is read one eleventh of six, or six elevenths of one. When the numerator is equal to the denominator, the value of the fraction is a unit. When the numerator is less than the denominator, the value is less than a unit, and the expression is called a proper fraction. When the numerator is greater than the denominator, the value is greater than a unit, and the expression is called an improper fraction. Thus, each of the expressions,, §, 18, 13, &c., is equal to a unit. Each of the expressions, 1, 4, 4, 5, †, to, &c., is a [roper fraction. Each of the expressions, f, 7, 8, 1, 4, 17, &c., is an improper fraction. When a whole number and fraction are connected, the expression is called a mixed number. Thus, 41, 37, 5, 229, &c., are mixed numbers. The whole number is called the integral part of the expression, and the fraction is called the fractional part. When several fractions are connected by the word of, the expression is called a compound fraction. The expressions, of of 5, 4 of 7 of % of 1, of of 3 of 1⁄2, &c., are compound fractions. Any number may be made to assume the form of an improper fraction, by writing under it a unit for the denominator. Thus, 2, 3, 4, 5, 7, &c., are the same as i, 1, 1, 4, 7, &c. Fractions sometimes occur, in which the numerator, or denominator, or both, are themselves fractional; such expressions are called complex fractions. 342101 Thus, 4 2 104, &c., are complex fractions. 4, 71, 37, 9, A fraction is said to be inverted when the numerator and denominator exchange places. Thus: the fractions, 3,4, 7, fo, 4, 4, when inverted, become, 4, 4, 4, 4, 7. What is a vulgar fraction? Which is the numerator of a vulgar fraction? Which the denominator? What does the denominator show? What does the numerator show? In the vulgar fraction five eighths, which is the numerator, and which the denominator? How is it read? What may a vulgar fraction be considered a concise |
