Take each of the decimals in Table V. from the following numbers IX. Ex. VIII. - Find the difference between 54.6 and A, B, C, &c. Find the difference between 2.01613 and A, B, C, &c. X. Find the difference between .20153 and A, B, C, &c. XI. Find the difference between .000913 and A, B, C, &c. XII. - Find the difference between .10101 and A, B, C, &c. XIII. - Find the difference between A and B, B and C, C and D, &c. MISCELLANEOUS WRITTEN EXAMPLES. 37. 1800 +4.3 + 180 - 1000 + 1= how many? тобо 38. 2.43.4-180+1000 1000 how many? 39.6.03-1000+10.02 how many? 40..024.3 -10% +3 = how many? 41.8-.02+.5- 1000+6.01 = how many? 42. 8.3.002 +5.004.43 how many? 6 1000 8 43.1% +1000-15.3 - 6 1000 = how many? 44. What is the sum of +100 + 10800 + 1000 ̄ ̄ +10% and 5%? 15 6 45. What is the sum of +.0002 +10000+100000 10 +18 and 3? REVIEW.- What is meant by reducing a fraction to its lowest terms? (87.) Upon what principle does it depend? (88.) MULTIPLICATION OF DECIMALS. ORAL EXERCISES. 1. How many are 3 times 8 tenths? 12 times 8 tenths? 9 times 11 hundredths? 7 times 6 thousandths? FORMULA. .8 × 3 = 2.4. ANALYSIS. -3 times 8 tenths are 24 tenths, equal to 2 units and 4 tenths. 2. How many are 4 times 8 cents? 7 times 11 mills? 9 times 5 tenths? 6 times 12 hundredths? 3. How many are 3 times 1 tenth? 2 hundredths? 5 thousandths? 12 hundredths? 6 ten-thousandths? sandths? 25 thousandths? 4 millionths? 12 hundred-thou 4. What is of 3? of 3? .4 of 3? .7 of 3? .9 of 6? FORMULA. 3×3×.1=&or.3. 3x=3X.2=&or.6. Since 1 tenth of 3 equals of 1, or .3, of 3 equals ANALYSIS. 10 8. What is of 1? of? of? of 2 hundredths: of 1 = 2, or .2 of .1of, or .02. Since 2 tenths of 1-2 tenths, 2 tenths of 1 tenth = =.02. REVIEW. How are integral numbers changed to improper fractions? (89.) How are mixed numbers changed to improper fractions? How are improper fractions reduced to integral or mixed numbers? (90.) Illustrate what is meant by a common denominator of two or more fractions. (92.) What axioms are used in the addition and subtraction of fractions? (93.) Give the analysis of a short example. Give the analysis of an example in the subtraction of rractions. (94.) 9. What is Of .03? Of .08? of 3? Of .3? Of .7? Of .6? Of .09? 10. What is .5 of 8? Of .6? Of .97 Of .03? Of .08? 11. What is 8 of 1? Of 6? Of .2? Of .8? Of .08? PROBLEM. FORMULA. PROCESS. 2.43 3.4 972 729 8.262 ANALYSIS. By the rule for multiplication of fractions, the numerators must be multiplied together for a new numerator, and the denominators for a new denominator. As the denominator of a decimal fraction is always a power of ten, the denominator of the result will be expressed decimally by the sum of the factors of ten in each denominator: hence the following 107. RULE. Multiply as in simple numbers, and point off from the right of the product as many figures for decimals as there are decimal places in both factors. DRILL CARD EXERCISES. MULTIPLICATION. TABLE V. NOTE. - Use only such portions of these exercises as the class may need. 1 Multiply each decimal in Table V. by the following multipliers: XXI. - A X B, BX C, C x D, DX E, EXF, FX G, &c. ORAL AND WRITTEN EXERCISES. 46. How many are 3 times 1 tenth? 8 tenths? 6 hundredths? 25 hundredths? W. 4.3? 25.03? 47. How many are 9 times 2 tenths? 11 hundredths? 7 thousandths ? W. 328 thousandths ? 674 hundredths? 48. How many are 8 times 9 hundredths? 7 tenthousandths? 11 hundred-thousandths? 9 millionths? W. 473 millionths? 203 hundred-thousandths? 49. What is 6 tenths of 3? Of 8 tenths? Of 11 hundredths? Of 12 thousandths? W. Of 27 thousandths? Of 103 hundred-thousandths? 50. What is 8 hundredths of 7? Of .7? Of .09 ? Of .011? W. Of 6.03? Of .4034? 51. W. Multiply 30.003 by 8. By .08. By .12. 52. What is 2 thousandths of 6? Of .007? Of 9 millionths? W. Of 34.67? Of 4.0003? Of 7043 hundred-thousandths? 53. What will 7 barrels of sugar cost, at $20 a barrel ? At $30? W. At $28.25? At $32.37? 54. What is the value of 30 pounds of sugar, at 6 cents per pound? At 8 cents? W. At 8.2 cents? At 81 cents? At 75 cents? 55. At $30 a barrel, what is the value of 2 barrels of sugar? Of 3 tenths of a barrel? Of .6? Of .03? W. Of 2.8 barrels? Of .025? 56. At $2 a box, what is the cost of 2 raisins? Of .3 of a box? W. Of 2.37 ? boxes of Of .81 ? REVIEW.- How are fractions multiplied by integers? (95.) Illustrate by an example. How are integers multiplied by fractions? (96.) Ilustrate by an example. How are fractions multiplied by fractions? (97.) Illustrate by an example. How are fractions divided by integers? (98.) 57. W. A man bought 19.5 barrels of cider, at $2.20 a barrel; he sold it all for $28: did he make, or lose, and how much? 58. W. A man bought .3 of a barrel of cider, at $2 a barrel; he sold what he purchased for $23 : did he make, or lose, by the transaction? 59. W. A boy bought .75 of a bushel of nuts, at $2 a bushel; he sold them again for $2: did he make, or lose, and how much? 60. W. Another boy bought 1.75 bushels of nuts, at $2 a bushel; he sold them again for $2: did he make, or lose, and how much? 61. W. A girl had a ten dollar bill; she bought .38 of a box of raisins, at $23 a box: how much money had she left? 62. 4.3 × § +3.47 − .08 == what? = 63. 43.24 — 2.4 × 63 +40.74 what? 64. (2.01.003)× (1+3)= what? 65. 7 × 1 − (3 × .3) + 121 = what? 66. (6.3.6 × 3)× 8.401 what? 67. (1 × .7 − .8 × .7)× 4.2 × 3 = what? DIVISION OF DECIMALS. ORAL EXERCISES. 1. How many tenths in a unit? In 2 units? units? Ir t 2. In 1 unit how many tenths? How many hundredths? How many thousandths? How many tenthousandths? 3. How many tenths in 1 half of a unit? In 1 fourth? In 1 fifth? REVIEW. - How are integers divided by fractions? (99.) Illustrate by an example. How are fractions divided by fractions? (100.) Illustrate by an example. |