22. Further Short Cuts in Addition.-Additions can of ten be simplified by adding and subtracting the same num One number may sometimes be broken up into the sum of two other numbers. Thus, 3527 35+25+260 + 2 = ? = Three or more numbers may often be rearranged advantageously. Thus, Carry out the following without using pencil and paper: 10. Let the teacher suggest other exercises for practice. 11. A grocery bill contained the following amounts: 37, 25, and 23 ¢. Give the total amount. 12. John's sales of magazines for 4 weeks were 17, 15, 13, and 12. How many magazines did he sell during the 4 weeks? 13. Henry earned 35 one day and 47 the next day. How much did he earn during the two days? 14. Mary put into her savings-bank 47 ¢, 25 ¢, and 33 é for each of 3 weeks. How much did she put into her savings-bank during these 3 weeks? 15. 3a[2a5b] = ? 16. 7r(3r2+4r) = ? 17. 5g 5g3-7g2} = ? 18. 7x[3x2-4x3] = ? 19. (2m+3n) (3m2 - 5mn + 6n2) = ? 1000 23. Short Cuts in Subtraction.-To subtract from a power of 10, as 100 or 1000, think of it as 9010 or 990 + 10. Begin at the left and subtract each digit from 9, except unit's digit, which is subtracted from 10. In subtracting numbers of two digits, if 563 = 9910 = 563 437 the unit's digit of the subtrahend is the larger, add enough to it to make zero and then add an equal amount to the minuend. Why will this give the correct difference? 43 27 (43 + 3) — (273) 46 30 = ? = = 5. A lady paid 25 a can for salmon that she bought two years ago for 18 é a can. How much more did she pay for it this year? 6. What change will be received from a $10 bill if the purchase was $4.35? $6.35? $7.85? 7. What change will be received from a $5 bill if the purchase was $2.65? $ 3.26 ? $2.97 ? 24. Short Cuts in Multiplication and Division.-While several short cuts arise in division, it is in multiplication that they abound. Often seemingly difficult multiplications can easily be reduced to mental processes or at least be greatly simplified. 25. Multiplication and Division by a Power of 10.State the rule for multiplying by 10; by 100; by 1000; by any power of 10. State the rule for dividing by 10; by 100; by 1000; by any power of 10. 26. Buying and Selling by the Hundred or the Thousand. -Point off the proper number of places and find the product of this number and the given price. 27. Buying and Selling by the Ton.-First divide the amount in pounds sold by 1000 and then by 2; or divide the price by 2, which gives the price per 1000. 5. 360.25 103 340.16 ÷ 102 2025.5 ÷ 102 3045.5 ÷ 102 6. How many tons are there in 3400 lb. ? 4800 lb. ? 2460 lb. ? 5640 lb. ? 3280 lb.? 2640 lb. ? 1960 lb. ? 7. 8. Find the cost of 4820 lb. soft coal at $5.25 per ton. 9. Find the cost of 5960 ft. lumber at $60 per M. 28. Changing Order of Multipliers. The product of 25 X 719 X 4 can be found with the numbers arranged in six different ways or orders. What are these? Some of these make the work a simple mental operation; as, 25 X 4 X 719. Carry this out. Such rearranging of the order in multiplications and divisions greatly simplifies the work. EXERCISES Carry out without pencil and paper as far as possible: 8. 2 X 250 X 7 12. 4. 2 X 59 X 5. 12 ÷ 7 X 35 13. Suggest five multiplications that can be simplified by this process. 29. Multiplying by 11, 22, etc.—To multiply by 11, multiply by 10 and add to this the given number. In practice, write unit's digit of the num ber multiplied for unit's 752 7520 342 6840 11 752 22 684 7524 = 7524 digit in the product; add same for the other digits. Explain. To multiply by 22, 33, etc., multiply by 11 and then each digit by 2, 3, etc., before writing the product. 30. Multiplying by Sums or Differences. Many simplifications are based upon the principles, 9. Suggest at least five multiplications that can be simplified by the use of the principle in Art. 30. 16. A meter is 1.09 yd. How many yards long are 98 m. ? 17. When a draft payable in gold in France costs 19.50¢ per franc in the United States, what will be the cost of a draft of 500 francs? of 4000 francs? of 8500 francs? 18. What should I pay a man working for me 9 hr. at 35¢ per hour? 19. How many square feet are there in the floor of a room 15 ft. by 18 ft.? 12 ft. by 16 ft.? 19 ft. by 24 ft. ? |