2. What is the product of and? What is the product of thirds and sevenths? What is the product of halves and fifths? What is the product of tenths and tenths? 3. What is the product of and? of 0.7 and 0.3? of 0.3 and 0.3? of and? of 0.3 and 0.9? 183. Multiplying by decimals. Required to multiply 0.67 by 4. Since 4 times hundredths is hundredths, the 268 is hundredths, and the decimal point goes before the 6. That is, 4 times = 268 = 2.68. 0.67 4 2.68 To multiply 52 by 0.03. The product of 52 and hundredths is hundredths. Therefore the answer is hundredths and the decimal point goes before the 5. That is, 18 of 52 = 158 = 1.56. §§ 184 and 185 may be introduced here if desired. 52 0.03 1.56 13. At 6.95 in. to a step, how high do some stairs of 184. Multiply .42 by .35. .42 .35 That is, 210 126 .1470 If we were to multiply 42 by 35, the result would be 1470. And since hundredths multiplied by hundredths equals ten-thousandths, the result is .1470. 185. Decimal places in the product. Therefore, in multiplying decimals, 1. Multiply as with integers. 2. Point off as many decimal places in the product as there are decimal places in all the factors. It is unnecessary to remember this rule, since it is easy to see that the product of tenths and tenths is hundredths, of tenths and hundredths is thousandths, and so on. It is often helpful, however. 186. Multiply 6.2 by 3.5. If we were to multiply 62 by 35, the result would be 2170. And since tenths multiplied by tenths equals hundredths, the result is 21.70 (that is, 2170 or 21%), or 21.7. 6.2 3.5 310 186 21.70 or 21.7 17. A meter being 39.37 in. long, how many inches in 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: 3. 2.8 x 7.9. 4. 2.007 × 6.09. 5. 1.203 × 2.67. WRITTEN EXERCISE 1. 43.2 x 98.6. 4. .823 x 2946. 7. 3.49 x 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. 3. 68.7 x 40.5. 6. 53.6 × 2.889. 9. 98.9 × 69.89. 12. 52.9 x 68.023. 37 x 4.6. 21. 48 × 0.8. 22. 96 × 9.6. 26. 5.4 × 3.5. 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 circumference? 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 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. 12.525 = 0.5. Therefore the quotient is 2.5. 2.5 25)62.5 50 12 5 12 5 In developing this before a class, the decimal point in 12.5 should be preserved at first, and finally dropped as unnecessary. |