weighed 1760 lb. How many bushels of feed had he, a bushel of corn weighing 56 lb. and a bushel of oats 32 lb.? II. In a certain city the average age of citizens over 70 years old is 75 years and the sum of their ages is 900 years. How many such citizens are there? 12. A carload of 35 trolley rails, each 56 ft. long and weighing 45 lb. to the foot, weighs how much? 13. Find the sum of all the numbers that can be written each with the figures 3, 4, 5, and 6. 14. In an election in which A, B, and C were the candidates, A received 160 votes, B 120 votes, and C sufficient to elect him by a majority of 12; how many votes were cast? 15. How far apart are two towns if one is 365 miles east of a certain point and the other is 120 miles east of the same point? 16. The farm land in the United States, exclusive of buildings, was valued at $13,058,008,000 in 1900 and $28,386,770,000 in 1910. What was the average increase in value for each of the 10 years? 17. Find the weight of a load consisting of 10 bbl. of flour (196 lb.), 3 bbl. of salt (280 lb.), and 5 bbl. of beef (200 lb.). 18. Recently it was estimated that 40,744,200 gal. of water was furnished each 24 hr. to 373,800 persons in Milwaukee. How much was furnished each person? 19. A farmer's corn crib held 1026 bu. of corn; his corn crop filled the crib and he had 126 bu. over. What was his corn crop? 20. Recently it was estimated that each person in Philadelphia used 210 gal. of water every 24 hr., but that each person should not use more than 150 gal. in that time, the additional amount used being wasted. Estimating the population of Philadelphia at 1,600,000, how much water did they waste every 24 hr.? 21. A man borrowed $5000. He paid back $2750 at one time, $300 at another, and the remainder in three equal payments. How much was each of these three payments? 22. Minnesota contains 58,915 sq. mi., and Delaware 2050 sq. mi. Minnesota would make how many states. the size of Delaware and how many square miles over? 23. How many eggs are there in 24 crates each containing 36 doz.? 24. The following are the new possessions of the United States and the areas thereof. Find the total of the areas. 25. A clock that strikes the hours strikes how many times in a week? 26. A farmer was paid for a horse 9 ten-dollar bills, 6 five-dollar bills, 8 two-dollar bills, and 14 dollar bills. How much was he paid for the horse? 27. A merchant was given a 20-dollar bill in payment of a debt of $2. What bills did he give in change if he used the least number possible? 28. The minuend is 274 and the subtrahend is 196. What is the difference? 29. How many pounds of coal remain on a car after 25,250 lb. have been unloaded, if at first it contained 58,600 lb.? 30. The multiplicand is 1728 and the multiplier is 144. What is the product? 31. The divisor is 46, the quotient 19, and the remainder 25. What is the dividend? 32. The freight rate on electrical goods shipped firstclass from Chicago to Portland, Ore., is $3 per 100 pounds. Find the freight on a shipment of 2600 pounds of these goods. 33. A farm that cost $50 per acre was sold for $65 per acre. If the gain was $1125, how many acres did the farm contain ? 34. How long will 4 men, each husking an average of 40 shocks of corn a day, require to husk 4800 shocks? 35. The multiplicand is 275 and the product is 218,350. What is the multiplier ? Arithmetical Expressions 44. An arithmetical expression, or simply an expression, is any number or combination of numbers expressed in arithmetical symbols. Thus, 7, 3+2, 6+2−5, 3× 6, and 8÷4 × 2 are expressions. 45. Parts of an expression connected by a plus or a minus sign are called terms of the expression. Thus, in the expression 6 +12 − 2 × 4 + 6 ÷ 2 there are 4 terms; namely, 6, 12, 2 × 4, and 6 ÷ 2. 46. The operations of multiplication and division indicated in any term of an expression should be performed before the terms are combined; and if two or more such operations are indicated in the same term, they should be performed in the order of their occurrence from left to right. - Thus, in the expression 6 × 8 ÷ 4 + 12 ÷ 6 × 2 − 24 ÷ 4 ÷ 2, and the whole expression, equals 12 +4 – 3, or 13. 47. The value of an expression is the result obtained by performing the operations indicated. 48. When an expression is enclosed in parentheses ( ), in braces, in brackets [ ], or placed under the vincuthe value of the expression is to be found and used instead of the expression as a whole. lum Find the value of: Exercise 13 I. 5+4+7-2-5x2 3. 12÷6+6÷2-4÷4 2. 6x5+3x2-4×3 4. 648+6x4÷2 5. 8÷4x2+8x4÷2-8÷4÷2 6. 4×125 +250-6 × (250-125)+500-250+25 7. 375 x 40+ 50+1200+ 60 x 40-(1000-600) 8. 176040 + 3 x 1200 ÷ 60+4 × 1500+30 FACTORING 49. The factors of a number are such numbers as multiplied together will produce the number. 50. A number that has no other factor than itself and 1 is a prime number. A number composed of other factors than itself and 1 is a composite number. 51. When all the factors of a number are prime numbers, they are called the prime factors of the number. 52. An even number is a number that is divisible by 2; an odd number, one that is not divisible by 2. |