REVIEW OF INTEGERS. INDUCTIVE EXERCISE. 1. At 85¢ per bu., what is the cost of 3 bu. of rye? Of 4 bu.? Of 6 bu.? In obtaining each of the preceding results, which of the two given quantities has been taken as the multiplicand? The multiplier? What does each product denote? Hence, if the cost of one bu. [multiplicand] and the number of bu. [multiplier] be given, how may the cost of all the bu. [product] be found? If the cost of all the bu. [product] and the number of bu. [multiplier] be given, how may the price of one bu. [multiplicand] be obtained? If the cost of all the bu. [product] and the price of one bu. [multiplicand] be given, how may the number of bu. [multiplier] be found? 2. If 1 cord of wood contains 128 cu. ft., how many cu. ft. in 2 cords? In 3 cords? In 4 cords? In obtaining each of the preceding results, which of the two given quantities has been taken as the multiplicand? The multiplier? What does each product denote? Hence, if the quantity of cu. ft. in one cord [multiplicand] and the number of cords [multiplier] be given, how may the quantity of cu. ft. in all the cords [product] be found? If the quantity of cu. ft. in all the cords [product] and the number of cords [multiplier] be given, how may the quantity of cu. ft. in one cord [multiplicand] be found? If the quantity of cu. ft. in all the cords [product] and the quantity of cu. ft. in one cord [multiplicand] be given, how may the number of cords [multiplier] be obtained? In answering each of the following questions, state which terms of multiplication have been given, which term is required, and how the required term is found: 3. How many yards in each suit, if 84 yards are required to make 12 suits? At $8 per barrel, how many barrels can be bought for $56? What is the cost of 5 bushels of wheat at $1.20 per bushel? How many weeks are in 42 days? How many loads are required to haul 56 barrels of flour, allowing 8 barrels to each load. [a]_The multiplicand expresses the weight, measure, value, etc., of ONE of the EQUAL units or quantities under consideration. [b] The multiplier expresses the NUMBER of EQUAL units or quantities considered. [c] The product expresses the total weight, measure, value, etc., of ALL the EQUAL units or quantities under consideration. [d] Hence, when any two of the above terms are given to find the third, employ one of the following formula: MULTIPLICAND X MULTIPLIER = PRODUCT. [e] Addition is employed to find the total weight, measure, value, etc., of two or more UNEQUAL quantities. [f] Subtraction is employed to find the difference of weight, measure, value, etc., of two UNEQUAL quantities. [g] Multiplication is employed to find the sum [product] of two or more successive additions of the SAME addend [multiplicand], the number of successive additions corresponding with the multiplier. [h] Division is employed to find the remainder of two or more successive subtractions of the SAME subtrahend [concrete divisor] from a given minuend [concrete dividend], the number of successive subtractions corresponding with the abstract quotient. PROMISCUOUS EXAMPLES. 1. The difference between two quantities is 1209 pounds, and the greater quantity is 7803 pounds. What is the less quantity? 2. The difference between two quantities is 5009 bushels, and the less quantity is 4007 bushels. What is the greater quantity ? 3. 29850 pounds are equal to 398 times what quantity? 4. The divisor is 295 men, the quotient 86, and the remainder 34 What is the dividend? men. 5. The product is 17505564 gallons, and the multiplicand 439 gallons. What is the multiplier? 6. Five quantities added together equal 3789462 tons. If the sum of four of the quantities is 2172581 tons, what is the fifth quantity? 7. If the sum of 8 addends is 92712 pints, and the sum of 6 other addends is 4275 pints, what will be the sum of the 14 addends? 8. The dividend is $239754, the remainder $172, and the quotient 314. What is the divisor? 9. The continued product of 4 quantities is $29005204. If 3 of the factors are $82, 94, and 71, what is the fourth factor? 10. If the remainder is 9704 boxes, and the minuend 15307 boxes, what is the subtrahend? 11. If the remainder is 40009 inches, and the subtrahend 2009 inches, what is the minuend? 12. If the product is 4445704 acres, and the multiplier 97, what is the multiplicand? 13. George Washington died in the year 1799, aged 67 years. In what year was he born? 14. Ex-President C. A. Arthur was born in 1830, and became President of the United States in 1881. How old was he at the time of his accession to the presidency? 15. The revenue of the United States government for the year ending June 30, 1880, was as follows: Duties, $186522065; internal revenue, $124009374; sales of government land, $1016507; bank taxes, $7014971; Pacific railways, $2493988; customs fees, etc., $1148800; other fees, $2337029; property sold, $282616; coinage profits, $2792187; District of Columbia, $1809469; and miscellaneous, $4099604. What was the total revenue for that fiscal year? 16. On July 1, 1866, the debt of the United States government was $2783425879, and on July 1, 1880, it was $2119596046. How much was the debt reduced between those years? 17. A speculator purchased 50 beeves at the average price of $42 per head, paid $100 additional for pasturage, and afterwards sold them for $48 per head. How much did he gain 18. Two pedestrians start from the same place and walk in opposite directions. If one travels north at the rate of 36 miles per day, and the other south at the rate of 28 miles per day, how far apart will they be at the close of the ninth day? 19. If 32 men can do a job of work in 14 days, how long will it take 56 men to do the same job? 20. A merchant bought calicoes amounting to $325; cotton, $275; silks, $843; and other articles, $1324. He paid $2346 in cash, and gave his note for the balance. What was the face of the note? 21. Bought MCXLVIII feet of half-inch boards, DCCCLXXIV feet of inch boards, MMLIX feet of flooring, and DCCCCXXXVIII feet of scantling. What was the total amount purchased? 22. My assets are as follows: Personal accounts, $3457; notes on hand, $986; real estate, $7580; cash, $3575; and merchandise, $5700. I owe Smith & Co., $450; W. B. Jones, $345; James Ridgeway, $3480; and on outstanding notes, $3750. When these debts are paid, how much shall I be worth? 23. A farmer had 35 acres in oats which, when harvested, averaged 43 bushels per acre. He retained 500 bushels for his own use, and sold the remainder at 56 cents per bushel. How much did he receive? 24. A, B, and C united their means to buy a farm, containing 324 acres, for $11340. A wanted 98 acres; B, 143 acres; and C, the remainder. How much ought each to pay if the land was of uniform value? 25. A contractor agreed to grade a section of railroad for $50000. He paid for hauling $10000; for wages, $19275; and for other expenses, $16372. How much did he gain by his contract? 26. Two pedestrians start from the same place and travel in the same direction, one at the rate of 26 miles per day, and the other at the rate of 35 miles per day. How far apart will they be at the close of the fourteenth day? 27. At an election, the total number of votes cast for three candidates was 5342. The first candidate received 2872 votes, and the second candidate 752 votes less than the first. How many votes did the third candidate receive? 28. A bought two houses for $18950, paying $3500 more for one house than for the other. What was the cost of each? 29. If $378 be paid for 42 barrels of flour, how many barrels can be bought for $315, at the same price per barrel? 30. I paid $340 for two watches, one of which cost $26 less than the other. What did I pay for each? 31. A man bought 75 acres of land for $2550, and sold 23 acres of it at $40 per acre, and the remainder at $38 per acre. What was his gain? 32. A man, by will, left his property, valued at $42350, to his wife and three children. To his wife he left $15375; to his oldest child, $5718 less than to his wife; and to his second child, $418 less than to his oldest. What did the youngest receive? 33. A contractor expected to complete a contract in 38 days by employing 75 men; but, after working 28 days, 25 of his men became sick and unable to work. In how many days can the remainder of the men complete the job? 34. If there are 128 cubic feet in one cord of wood, how many cords are in a pile containing 9728 cubic feet of wood? 35. If there are 32 quarts in a bushel, how much can be obtained for 5 bushels of chestnuts by retailing them at 8 cents per quart? 36. A merchant's sales during the week were as follows: Monday, $275; Tuesday, $225.35; Wednesday, $248.40; Thursday, $175.55; Friday, $193, and Saturday, $324.10. What were his average sales per day? REM.-Averages are obtained by dividing the sum of all the terms by the number of terms. 37. If a mechanic spend $2 per week for liquors and tobacco, and there are 52 weeks in a year, in how many years will he have spent money enough to buy a house and lot worth $832? 38. In 1880 the population of Baltimore was 332313, and that of Boston, 369832. How much greater was the population of Boston? 39. The War of the Revolution commenced in 1775, and the war with Mexico in 1846. How many years between these two dates? 40. I owe A $475, B $673, C $384, and D $570. If I pay A $234, B $325, C $125, and D $250, what will be my total remaining indebtedness? 41. Two steamboats start together from the same place to go up the Mississippi River. 47 hours after starting, the faster boat was 141 miles ahead of the slower. If the faster boat's rate of speed averaged 12 miles per hour, how far was the slower boat from the starting point? 42. A manufacturer sold to a dealer 23 sets of parlor furniture for $1633, and the dealer sold to a customer one of these sets at $6 profit. The customer handed the dealer 4 twenty-dollar gold pieces. How much change should be returned to the customer? 43. I bought 8 yards of calico at 7 cents per yard, 5 yards of cloth at $1.15 per yard, and 24 yards of muslin at 12 cents per yard. If I give the clerk a ten-dollar bill, how much change should be returned? 44. A farmer sold to a merchant 9 pounds of butter at 25 cents per pound; 14 dozen eggs at 12 cents per dozen; and 9 chickens at the rate of $3 per dozen. He bought from the merchant 3 gallons of molasses at 60 cents per gallon; 6 pounds of coffee at 17 cents per pound; and with the remainder of the money due him bought sugar at 12 cents per pound. How many pounds of sugar did he buy? 45. A and B united together to purchase 75 pounds of coffee for $13.50. If A took 45 pounds of the coffee and B the remainder, how much of the purchase-money ought each to have contributed? 46. A man bought a house and lot for $5975.30, paying $2172.45 more for the house than for the lot. What was the cost of each? |