Divide as indicated, seeing how many problems you can solve in five minutes; in ten minutes: 45. If 35 floor tiles together weigh 113.75 lb., what is the average weight of each ? 46. If $1548 is divided equally among a dozen persons, how much is the share of each? 47. If $2193.75 is divided equally among 15 persons, how much is the share of each? 48. If a piece of land containing 12.75 acres is cut into 17 equal building lots, what is the area of each ? 49. If the dividend is 420, the quotient 32, and the remainder 4, what is the divisor? 50. If the dividend is 73 times the remainder, and the quotient is 24, and the divisor is 12, what is the remainder? 2 18. Division of denominate numbers by abstract numbers. Divide 33 ft. 9 in. by 15. We divide 33 ft. by 15 and have 2 ft., with a remainder of 3 ft., which, reduced to inches (36 in.) and added to 9 in., equals 45 in., which is still to be divided. Again, 45 in. ÷ 15 = 3 in. 19. Division of denominate numbers by bers. 2 ft. 3 in. 15)33 ft. 9 in. 3 ft.=36 in. 45 in. 45" denominate num Divide 23 ft. 4 in. by 3 ft. 4 in. Here either 23} ft. ÷ 33 ft. = 30 ft. ÷ 10 ft. = 7; or 1. 23 ft. 4 in. ÷ 3 ft. 4 in. = In the first case we reduce to feet; in the second, to inches. 8. 4868 cu. ft. 1200 cu. in. ÷ 23. 9. 22 hr. 40 sec. 5 hr. 30 min. 10 sec. 10. How much is an eighth of 116 lb. 8 oz.? 11. 4557 sq. ft. 54 sq. in. ÷ 147 sq. ft. 90 sq. in. 12. How much is half of 2 hr. 53 min. 18 sec.? 13. How much is a quarter of 11 yd. 2 ft. 8 in.? 14. If a cubic foot of gold weighs 1187 lb. 8 oz., and if gold is 19 times as heavy as water, what does a cubic foot. of water weigh? 15. If it takes a man 8 hr. 31 min. 24 sec. to walk a certain distance, how long will it take an automobile to travel the same distance, if it goes 12 times as fast? 1. Tell why ORAL EXERCISE 2; also why ÷ 2 =. 2. Tell why 1÷}= 3; also why 2÷3=6, and 5÷}=15. 3. Because 515, tell why 5 = of 15, or 5. = 4. Because 5, tell why of, or 14. 5. Because÷}=14, and because of % = 14, what operation may be performed in place of dividing one fraction by another? 20. Dividing fractions. In dividing by, we may 1. Reduce to a common denominator and divide the new numerators. 14 ÷ 11 = 14, just as $15 ÷ $14 = 14, or 15 ft. 14 ft. 19. Or we may = = 2. Invert the divisor and multiply. That is, ÷=4 X. We use this operation rather than the other, because it is easier and gives the same result. Always indicate the multiplication first and cancel if possible. 21. Dividing mixed numbers. In dividing 15 by 72, we might 1. Reduce to a common denominator, and divide the new numerators. 62 ÷ 31 = 62 ÷ 31 = 2. Or 2. Multiply both dividend and divisor by a common denominator, and then divide. That is, 15 ÷ 7 = 62 ÷ 31, by multiplying by 4. But practically we 3. Reduce to fractional forms and multiply by the inverted divisor. That is, 15 ÷ 73 = 31 ÷ 31 = 2. 31. 776.5 12952. 32. 1201÷147. 33. 52÷17. 34. How many strips of cloth, each 53 yd. long, can be cut from a strip 37g yd. long? 35. How many city lots, each 31 ft. front, can be cut from a piece having 2224 ft. front? 36. How many yards of cloth at 31 a yard can be bought for a dollar and a half? GENERAL PRINCIPLES OF THE OPERATIONS ORAL EXERCISE 1. If I put 4 ct. with 3 ct., do I have the same result as if I put 3 ct. with 4 ct.? What does this tell about the order of adding numbers? 2. If I wish to add 4, 3, and 5, shall I get the same result by first adding 4+3 and then 5, as by first adding 3 + 5 and then 4? What does this tell about grouping numbers? 3. How does 3 x 4 compare with 4 × 3? What does this tell about the order of multiplying numbers? 22. Law of order in addition. The sum is the same whatever the order of the addends. 23. Law of grouping in addition. The sum is the same however the addends are grouped. That is, (23) + 5 = 2 + (3 + 5). 24. Law of order in multiplication. The product is the same whatever the order of the factors. 1. Make a rectangle in. by in., and separate it into -in. squares, and show that 5 × 3 = 3 x 5. 2. Show that (2 × 3) × 4 = 2 × (3 × 4), and state the law of grouping in multiplication. = 3. We have found that 2+ 3 3 + 2, and 2 × 3 = 3 × 2. Does 2 ÷ 3 = 3÷2? Write out a statement about it. |