171. ORAL AND WRITTEN EXERCISES. 1. What are 16 times 5 ? 12 1st Process. 1689, or 20 = 63, Ans. 4 2d Process. 16 x = 12 2, or 63, Ans. 3 16 times are Solution. ; changing to smallest terms by dividing both terms by 4 (Art. 150), we have 20, or 63, Ans. In the second process we divide both terms by 4 before multiplying. 4 in 16 = 4; 4 in 12 =3. We then have 4 × § = 20, or 63, Ans. This dividing by, or striking out, equal factors in both numerator and denominator is called cancellation. It may very often be used in multiplication and division of fractions to shorten the process. Find the product of the following fractions and in 172. To find the Product of an Integer and a Mixed Number. Inductive Exercises. 1. What will 23 yards of silk cost at $5 a yard? Solution. As 1 yard costs $5, 2 yards will cost 24 times $5. of $5 is $, and of $5 are 3 x 8, or $45, or $34. 2 × $5 are $10. $10 + $33 are $ 133, Ans. 2. Find the cost of 23 yards at $4 a yard. 3. What will 5 bushels of wheat cost at $13 a bushel? Solution. As 1 bushel costs $13, 5 bushels cost 5 X $ 13. 588, or $ 17. 5 X $1-$5. $5+$17= $67, Ans. 4. If one man digs 4 bushels of potatoes in a day, how many bushels will 7 men dig? 5. Find the product of 143 and 18. 5, or 10. multiplier. of 18 = In the second process we use the mixed number as the 4 X 18 = = 72, and 10 X 18= 180. Uniting these three partial products, we have as before 262, Ans. In multiplication we generally use the smaller of the two numbers as the multiplier, care being taken in explanations to consider the real multiplier abstract and the real multiplicand of the same denomination as the product. (Art. 80.) 173. To find the product of an integer and a mixed number, First find the product of the integer and the fraction, and then the product of the two integers, and add the results. 37. How far will a pedestrian walk in 24 hours if he walks 4 miles an hour? 38. If one egg weighs 23 ounces, what will a dozen weigh? The price of one pound, &c., being given, find the cost of 39. 2 pounds at $.12. 46. 65 pounds at $.25. 47. 125 gallons at $.37. 48. 200 yards at $.413. 49. 57 tons at $75. 50. 183 bushels at $ .65. 51. 511 dozen at $ 2.50. 52. 6 reams at $ 3.75. 40. 3 weeks' board at $5. 174. To find the Product of Fractions and Mixed Numbers. Inductive Exercises. 1. What part of an apple is 1st Process. Solution. As the product is 5. Find the product of 10 × 3 = 45 = 3, Ans. the same, whatever the order of , 2d Process. = Ans. 10 2 3 factors (Art. 80), 1% X is the same as of 1% and of Changing of 1% 60 5 X, or 5. to lowest terms, by striking out the common factors 3 and 5 from each term, we have , Ans. In the second process we have struck out or canceled these common factors before multiplying. 175. To find the product of fractions and mixed numbers, Change the mixed numbers to improper fractions, and then multiply all the numerators together for the numerator of the product, and all the denominators for the denominator of the product. Find the product of the following fractions and mixed numbers: 46. What will of a yard of silk cost at $4 a yard? Find the cost of 47. 5 bushels of potatoes at $.663 a bushel. 48. 6 pounds of coffee at $.33 a pound. 49. 78 pounds of tea at $.871 a pound. 50. 1 cords of wood at $ 63 a cord. 51. 6 dozen hats at $ 161 a dozen. |