II. If the divisor is 6 and the quotient is 8, what is the dividend, if there is no remainder? 12. If the divisor is 7, the quotient 6, and the remainder 5, what is the dividend? 13. State a short way of dividing a number ending in a cipher by 10. 14. Divide at sight: 150 by 10; 270 by 10; 1200 by 10. 15. State a short way of dividing a whole number ending in two ciphers by 100. 16. Divide at sight: 600 by 100; 1200 by 100; 5000 by 100. 17. State a short way of dividing a whole number ending in three ciphers by 1000. 18. Divide at sight: 5000 by 1000; 17,000 by 1000; 50,000 by 1000. 19. How many tens are there in 7000? how many hundreds? how many thousands? 20. How many tens are there in 9,000,000? how many hundreds? how many thousands? how many ten-thousands? how many hundred-thousands? Illustrative Examples 1. Divide 134,568 by 452. 297 452)134568 904 4416 4068 3488 3164 324 How is the figure 2 in the quotient obtained, and for what does it stand? How was the 904 obtained? How was the 4416 obtained? What was divided to obtain the figure 9 in the quotient, and for what does it stand? How was the 4068 obtained? How was the 3488 obtained? What was divided to obtain the 7 in the quotient? How was the 3164 obtained? What is the quotient, and what the remainder? Check: 452 × 297 + 324 = 134,568. NOTE. The quotient may be placed to the right of the dividend thus: 452)134568(297 2. Divide 716,239 by 346. 2070 346)716239 692 2423 2422 19 How may the first quotient figure, 2, be estimated and for what does it stand? 346 x 2000=what? What does the 692 represent? How may the second quotient figure, 0, be estimated? What was divided to obtain the 7 in the quotient, and for what does it stand? 346 x 70 =what? What is the quotient, and what the remainder? Check: 346 x 2070 +19716,239. NOTE. The method of dividing by expressing the successive partial dividends is called long division. The method of dividing without expressing the partial dividends is called short division. Special Forms Divide 6783 by 10; by 100; by 1000. 10)6783 678 3 100)6783 1000)6783 Name the quotient and remainder in each example. Cutting off the last figure of a number divides the number by 10, and the figure cut off expresses the remainder. Cutting off the last two figures of a number divides it by 100, and the figures cut off express the remainder; and so on. 5. Divide, at sight, each of the following numbers by 10, stating the quotient and the remainder: 546; 679; 591; 1021; 1466; 1923. 6. Divide, at sight, each of the following numbers by 100, stating the quotient and the remainder: 711; 910; 1565; 7706; 8109; 9001. 7. Divide, at sight, each of the following numbers by 1000, stating the quotient and the remainder: 1111; 2760; 4723; 6400; 7913; 8001. Miscellaneous Problems Exercise 12 1. Add 2 million 65 thousand 4 hundred, 14 million 860 thousand 16, 17 million 4 thousand 220, and 175 million 24 thousand 3 hundred 6. 2. The following are recent estimates of the wealth of the nations named; find their total wealth. United States 130 billion dollars; Great Britain and Ireland 82 billion dollars; France 65 billion dollars; Germany 60 billion 500 million dollars; Russia 40 billion dollars; Austria-Hungary 25 billion dollars; Italy 20 billion dollars; Belgium 9 billion dollars; Spain 5 billion 400 million dollars; Netherlands 5 billion dollars; Portugal 2 billion 5 hundred million dollars; Switzerland 2 billion 4 hundred million dollars. 3. If two trains are running from a certain point, one due north at the rate of 25 miles an hour, and the other due south at the rate of 40 miles an hour, how far apart are they in 3 hours? 4. Below are given the expenditures in a recent year in the United States for the articles named; find the total. 5. After borrowing $175 a farmer had sufficient to pay for 25 acres of land at $ 50 per acre. How much had he at first? 6. A dealer owns two tracts of land, the first containing 476 acres and the second 95 acres more than the first. How many acres do both tracts contain? 7. A laborer bought a house for $1850; he paid $ 800 cash and agreed to pay the balance in monthly payments of $15 each. How many of these monthly payments must he make? 8. A carload of coal weighed 67,500 lb.; how many tons (2000 lb.) will this make, and how many pounds over? 9. What was the average gain per head on 25 horses bought for $4375 and sold for $5000? 10. A farmer mixed an equal number of bushels of corn and of oats for horse feed and found that the mixture |