EXAMPLES FOR PRACTICE. 63 11. About three million tons of iron are produced yearly in Great Britain, which is twenty times as much as is produced annually in Sweden. How much is produced in Sweden? Ans. 150000 tons. 12. A ship bound from Boston to Australia, a voyage of 18000 miles, sails at the rate of 100 miles a day. How long is she on the passage? 13. The product of two factors is 238700. One of the factors is 770; what is the other? Ans. 310. 14. A cotton crop of 26320 pounds was put up in bales averaging 560 pounds each. How many bales did it make? 15. Sound moves 1120 feet in a second. How long before we hear a cannon, fired at a distance of 12320 feet? EXAMPLES MISCELLANEOUS EXAMPLES To find a sum, add. FOR To find a difference, subtract. To find a quotient, divide. 1. Find the sum, then the difference, then the product, then the quotient, of 125 and 875. 2. A person who had 200 acres in one state, 1173 in another, and 127 in a third, divided his land equally among his wife and four sons. How much did each receive? Find how much land he had in all. Among how many did he divide it? 3. If a clock ticks 3600 times in 1 hour, how often will it Ans. 172800 times. tick in two days of 24 hours each? 4. How many times is 20 x 50 contained in 50 × 20? 5. A barrel of flour contains 196 pounds. If a family of 5 persons use 4 pounds of flour a day, how long will a barrel last them? Ans. 49 days. 6. Three men put in $650 each, and invest the whole in salt, at $2 a sack. How many sacks do they buy? Ans. 975. 64 EXAMPLES IN ADDITION, SUBTRACTION, 7. A merchant worth $43000, after losing $1750 in trade, invested the rest in land, at $10 an acre. did he buy? How many acres 8. What is the difference between 16 x 49 and 49 × 8 × 2? 9. A lady who had eight children, lost two of them. Among the survivors she divided her property; which consisted of $1200 cash, $21550 in stock, and $7250 in bonds. What was the share of each? Ans. $5000. 10. The sum of three numbers is 27846. One of the numbers is 11587; the second is 596; what is the third? Find the sum of the two given numbers. The third will be the difference between their sum and the whole sum. Ans. 15663. 11. A man leaves his three sons $36000. To the first he leaves $14655; to the second, $9875; how much does he leave the third? Ans. $11470. 12. A soapboiler makes 5977 pounds of soap, of which 657 pounds are soft soap, while the rest is in bars. He wishes to pack his bar soap in boxes holding 70 pounds each. How many boxes must he procure? Ans. 76 boxes. 13. How much must I add to 40 times 60, in order to make 3000? How much is 40 x 60? What is the difference between this and 3000? 14. A farmer wishes to buy some land for $720. He lays up $9 a week for one year, or 52 weeks. How much does he still need? Áns. $252. 15. A grocer, having 3 boxes of tea holding 80 pounds each, repacks it in six-pound boxes. How many boxes will it fill? Ans. 40 boxes. 16. Two men go from the same point in opposite directions, one 18 miles a day, the other 23. When they are 369 miles apart, how many days have they travelled? How far apart are they at the end of one day? How many times is this number contained in 369 ? MULTIPLICATION, AND DIVISION. 65 17. A company building a railroad, pay $377235 for labor, and $147690 for other expenses. The road is 15 miles long; what is the cost per mile? Ans. $34995. 18. A farmer has 917 sheep in one field; 189 in another; 276 in a third; and 379 in a fourth. If he divides them into three equal lots, how many will there be in each? Ans. 587. 19. The Vice-President's salary is $8000 a year. If he spends $15 a day, how much will he lay up during his four years' term, allowing 365 days to the year? Ans. $10100. 20. Two men go from the same point in the same direction, one at the rate of 41 miles a day, and the other 24. When they are 493 miles apart, how many days have they travelled? Ans. 29 days. 21. I buy 29 horses for $1885, and sell them at a profit of $290. How much do I get apiece? Ans. $75. 22. A planter raises 25963 pounds of cotton, and buys up 35409 pounds more. If he packs the whole in bales of 458 pounds, how many bales will he have? Ans. 134 bales. 23. Roger Bacon, the inventor of spectacles, lived to the age of 78, and died 350 years before Sir Isaac Newton was born. If Newton was born in 1642, what was the year of Roger Bacon's birth? Ans. 1214. 24. How many hogsheads holding 1295 pounds each will it take to contain 76405 pounds of sugar? Ans. 59 hogsheads. 25. Five partners make $1500 by a speculation. One of them divides his share between his two daughters. What does each daughter get? 26. Find the value of 637+8465367-487. Ans. $150. Ans. 8465517. Ans. 1094947. Ans. 55847775. Ans. 366876. Ans. 68, 8899 rem. FRACTIONS. 103. When a whole is divided into two equal parts, each of these parts is called one Half. When a whole is divided into three equal parts, one of these parts is called one Third; two are two Thirds; &c. When a whole is divided into four equal parts, one of these parts is called one Fourth (or Quarter); two are called two Fourths; three, three Fourths; &c. In the same way we get Fifths, Sixths, Sevenths, &c., by dividing a whole into five, six, seven, &c., equal parts. The name is taken from the number of equal parts into which the whole is divided. 104. The value of the part varies according to the number of parts into which the whole is divided. The more parts it is divided into, the smaller they must be. One half of a thing is greater than one third; one third is greater than one fourth. 103. When a whole is divided into equal parts, if there are two, what is each called? If there are three, what is each called? What are two called? What are three such If there are four equal parts, what is each called? parts called? How do we get Fifths, Sixths, Sevenths, &c.? From what is the name taken?-104. According to what does the value of the part vary? Which is greater, one half or one third? One fourth or one third? 105. These equal parts into which a whole is divided, are called Fractions. Writing of Fractions. 106. Learn how fractions are written. One fourth (quarter) One two-hundredth One thousandth 6 200 1 100ō | Six twelve-hundredths 1200 107. A fraction, therefore, when written, consists of two numbers, one below the other, with a line between. The number below the line is called the Denominator. It shows into how many equal parts the whole is divided, and therefore gives name to these parts. The number above the line is called the Numerator. It shows how many of the equal parts denoted by the Denominator are taken. The Numerator and the Denominator, taken together, are called the Terms of the fraction. 6 is a fraction. 5 and 6 are its Terms. 6 is the Denominator, and shows that the whole is divided into six equal 105. What are such equal parts of a whole called?-106. Write one half; one third; one quarter; &c.-107. Of what does a written fraction consist? What is the number below the line called? What does the Denominator show? What is the number above the line called? What does the Numerator show? What are Numerator and Denominator, taken together, called? Name the terms of the fraction five sixths. Name its numerator; its denominator. |