2. Divide 875692 by 10; by 100; by 1000. Process. 3)588 4)196(3's) Ans. 49(12's) Proof.-3 x 4 x 49=588. consecutively by the others. Analysis. Dividing by 3, we find that there are 196 3's in 588; and since 43's make 12, there are as many 12's in 588 as there are 4's in 196, which is 49. Hence to divide by the factors of a number, divide the given dividend by one of the factors, and the quotients thus arising 8. Divide 5084 by 63, using factors. 9. Divide 13516 by 32, using factors. 10. Divide 8759 by 84, using factors. Process. 2 3)8759 104(84's) +1(12)=12 True rem. 23 of the remainders 2 + 9 + 12 Analysis. Dividing by 3, we find that there are 2919 3's in 8759, and 2 units remaining. Dividing 2919 3's by 4, we find that there are 729 12's in 2919 3's, and 3 3's = 9 units remaining. Dividing 729 12's by 7, we find that there are 104 84's and 1 12 = 12 units remaining. The sum 23, which is the true remainder. 11. Divide 10206 by 72, using factors. 12. Divide 78469 by 108, using factors. Review Problems. ORAL EXERCISES. ART. 79.-1. John labored 7 weeks at $9 a week; he took in payment 5 sheep at $7 each, and the rest in cash how much cash did he receive? Solution. He received the difference between the sum earned and the cost of the sheep. He earned 7 times 9 dollars, or $63. The sheep cost 7 times 5 dollars, or $35. $63 - $35 $28, cash received. 2. If 9 yards of cloth are worth $27, how much are 8 yards worth? 3. If 12 horses cost $3,600, how much do 9 horses cost at the same rate? 4. If 24 pounds of butter cost $7.20, how much will 18 pounds cost? 5. If 8 men can do a piece of work in 32 days, how long will it take 12 men? 6. I gave 10 barrels of potatoes, worth $2.50 a barrel for 5 pairs of shoes: what was the average price of the shoes a pair? 7. If 7 yards of cloth cost $28, what is the cost of 9 yards? 8. Isaac earned $72 in 12 weeks: how much did he earn in 11 weeks? 9. A man bought 12 pounds of beef, and handing the butcher a two-dollar bill, received 20 cents change: what was the price of the beef per pound? 10. If 6 vests can be made from 12 yards of cloth, how many vests can be made from 84 yards? 11. When 9 tons of coal cost $45, how many tons can be bought for $90 ? 12. If eggs are worth 15 cents a dozen, and butter is 24 cents a pound, how many dozen eggs are worth 10 pounds of butter? 13. A man bought 5 coats at $8 apiece, and 4 hats at $2 apiece. He paid for them with apples at $4 a barrel how many barrels did it take? : 14. Harry bought 14 bananas at 3 cents apiece, and after giving away 4, sold the rest at 4 cents each did he gain or lose, and how much? 15. Arthur has 12 cents and Amos 11 times as many, lacking 11 cents: how much has Amos? 16. John paid 60 cents for a slate, a book and a ruler. The slate cost twice as much as the ruler, and the book as much as the slate and ruler. How much did he pay for each? SUGGESTION.-The slate costs twice as much as the ruler, and the book three times as much as the ruler: hence they all cost six times as much as the ruler 60 cents. 17. Three boys have 84 marbles: George has three times as many as John, and Harry has twice as many as George and John have how many has each ? WRITTEN EXERCISES. ART. 80.-1. My horse cost $396, which was $12 more than 12 times the cost of the harness: how much did. the harness cost? 2. Mr. Chapman rode 375 miles in one week and the next week he rode 6 times as far, lacking 987 miles: how far did he ride the second week? 3. The sum of two numbers is 8,769 and the larger is 5,674 what is the less number? 4. The minuend is 10,987 and the subtrahend 9,099: what is the remainder? 5. The subtrahend is 4,670 and the remainder 7,659: what is the minuend? 6. The minuend is 5,678 and the remainder 2,111: what is the subtrahend? 7. The multiplicand is 456 and the multiplier 607: what is the product? 8. The product is 8,704 and the multiplier 32: what is the multiplicand? 9. The dividend is 87,694 and the divisor 65: what is the quotient? 10. The dividend is 6,386 and the quotient 206: what is the divisor? 11. My farm cost $9,460, which lacks $1,800 of being twice as much as the cost of the house: what was the cost of both ? 12. Grace 'is 13 years old and her brother Asa is 15 years old. Three times the sum of their ages lacks 6 years of being the age of their great-grandfather: how old is he? 13. Mr. Harris sold 7,600 bushels of corn; he afterwards bought 3,456 bushels and then had 5,700 bushels: how many bushels had he at first? 14. The number of envelopes made in the United States in one year is about 18,000,000. What is the average number made each day, counting 308 working days in a year? 15. The pyramids of Egypt are supposed to have been built 2,170 years before the birth of Christ: how many years since they were built? 16. A farm of 525 acres produced 45,675 bushels of potatoes what was the average yield per acre? : 17. Friction matches were first used in this country in 1829; 9 years previous, illuminating gas was introduced, and 30 years previous to that it was first used in England what is the last-named date? 18. The Bank of North America was established in 1781, which was 87 years after the founding of the Bank of England. The first bank in Europe was established in Venice 523 years before the Bank of England: how many years from the establishment of the first bank in Europe to the death of General Grant in 1885 ? : 19. The estimated number of Christians in the world is Roman Catholics, 201,000,000; Protestants, 106,000,000; Eastern Churches, 81,000,000. The number of Buddhists is 340,000,000; Mohammedans, 201,000,000; Brahmans, 175,000,000; followers of Confucius, 80,000, 000; followers of Shinto, 14,000,000; Hebrews, 7,000,000. How many less Christians are there in the world than believers in other faiths? 20. Illustrate addition and subtraction by an original problem. 21. Illustrate subtraction and multiplication by an original problem. 22. Illustrate multiplication and division by an original problem. What is addition? REVIEW QUESTIONS. What is meant by the sum or amount ? What is the sign of addition called? What does it mean? Illustrate. How is the sign of equality read? Illustrate its use. Illustrate the use of the dollar mark. What places are occupied by cents? What are the principles of addition ? Give the rule for addition. What is the proof? What is subtraction? What is the minuend? The subtrahend? What is the difference? How is the sign of subtraction read? Illustrate its use. What are the principles of subtraction? Give the rule for subtraction. What is the proof? What is multiplication? What is the multiplicand? The multiplier? The product? What are the factors of a number? What are the factors of the product? How is the sign of multiplication read? Illustrate its use. Explain the use of the parenthesis. What are the principles of multiplication? Give the rule for multiplication. the proof? What is What is division? What is the dividend? The divisor? The quotient? The remainder ? How is the sign of division read? Illustrate its use. Of what is division the reverse ? Give the principles of division. What is short division ? Give the rule for short division. What is the proof? What is long division? Give the rule for long division. How do you divide when the divisor has ciphers on the right? How do you divide by using factors? How is the true remainder found? |