ORAL EXERCISE 1. Why will there be three decimal places in the product of 0.75 multiplied by 0.3? of 2.325 multiplied by 7? 2. How do you know the number of decimal places in the product of 0.62 and 2.79? of 2.756 and 3.123? Without multiplying, tell the order of the decimal part of each of the following: WRITTEN EXERCISE 1. 43.2 x 98.6. 4. .823 x 2946. 7. 3.49 × 80.23. 10. 2.99 × 124.63. Multiply the following: 13. 234.5 by 8.001. 15. $683.45 by 0.2. 17. $283.75 by 42.8. 19. 25 × 9.2. 20. 23. 5.9 × 9.5. 24. 27. 48.1 x 32.5. 30. 26.8 x 80.8. 33. 60.9 × 90.6. 5. 1.203 x 2.67. 3. 68.7 x 40.5. 6. 53.6 × 2.889. 9. 98.9 × 69.89. 12. 52.9 x 68.023. 14. 0.500 by 0.600. 37 x 4.6. 21. 48 × 0.8. 22. 96 × 9.6. 6.7 × 1.8. 26. 5.4 × 3.5. 29. 43.7 × 74.1. 32. 30.5 x 57.2. 35. 8.25 × 6.37. 38. 17.2 × 26.35. 41. 2.175×6.73. 44. 0.273 × 0.625. 45. 0.352×6.725. 46. 3.33 x 6.963. 47. 0.163 x 0.413. WRITTEN EXERCISE 1. At $1.75 each, what will 17 books cost? 2. What is the perimeter of a square 34.7 ft. on a side? 3. At $75.50 an acre, what will 25.5 acres of land cost? 4. At $0.75 a yard, what will 32.2 yd. of China silk cost? 5. At $125 a front foot, how much will a city lot cost having a frontage of 72.3 ft.? 6. At $65.50 an acre, how much must a man pay for 200 acres of land? for 25.4 acres? for 3.75 acres? 7. At $17.52 a front foot, what will a piece of land 28.33 ft. front cost? 8. A tank when full holds 42.8 gal. How much does it contain when .37 full? 9. A certain rectangle is .78 as wide as it is long. It is 4.9 in. long. What is the perimeter? 10. A certain rectangle is 3.42 times as long as it is wide. It is 4.8 ft. wide. What is the perimeter? 11. A city lot is 45.8 ft. wide and 76.3 ft. deep. What is the area of the lot? What is it worth at $1.50 a square foot? 12. The circumference of a circle is 3.1416 times the diameter. If the diameter is 42.27 ft., what is the cir cumference? 13. How many square rods of land are there in a piece of land 80 rd. wide and 114.1 rd. long? How many acres? What is it worth at $75 an acre? 14. There are three towns, A, B, C, forming the three corners of a triangle. From A to B is 27.32 mi., from B to C it is 1.4 times as far, and the perimeter of the triangle is 72.8 mi. How far is it from C to A? DIVISION OF DECIMALS ORAL EXERCISE 1. Divide 10 by 2; 100 by 20. Compare the results. 2. Divide $2.50 by 5; $25 by 50. Compare the results. 3. If multiplying both dividend and divisor by the same number does not change the quotient, how does the quotient of 360 ÷ 4 compare with that of 36 ÷ 0.4? 187. Division of decimals. Since both dividend and divisor may be multiplied by the same number without changing the quotient, therefore, In the division of decimal fractions, multiply both dividend and divisor by the power of 10 that shall make the divisor an integer, and divide as in United States money. 188. Divide 6.25 by 2.5. The result is the same if we divide 62.5 by 25, thus making the divisor an integer. Dividing as in United States money, 62.5 ÷ 25 = 2, with 12.5 still to be divided. 12.5 ÷ 250.5. There fore the quotient is 2.5. 2.5 25)62.5 50 125 12 5 In developing this before a class, the decimal point in 12.5 should be preserved at first, and finally dropped as unnecessary. 189. Illustrative problems. 1. Divide 16.35 by 500. Here it is better to divide both dividend and divisor by 100, canceling the zeros and moving the decimal point two places to the left. 500).1635 .0327 2. Divide 3.82 by 2.5, carrying the quotient to one deci mal place. = Multiplying both numbers by 10, we have 38.2 ÷ 25 1.5, with 7 remainder. If we do not write the fraction in the quotient, the quotient is written 1.5+, meaning 1.5 and a fraction less than. 3. Divide .049 by .17, carrying the quotient to two decimal places. 0.28, Multiplying both numbers by 100, we have 4.9 ÷ 17 with 14 remainder. If we do not write the fraction ‡ in the quotient, the quotient is written 0.29-, meaning 0.28 and a fraction more than 1. In the following divisions, carry the quotient to three 19. 976.34.125. 20. 483.62 ÷ 42.7. 21. 826.3 ÷ 12.5. |