A. An Improper Fraction. Q. How may it be known? A. The numerator is greater than the denomi nator. Q. What kind of fractions are, 42, §, &c.? A MIXED NUMBER. Q. What is a mixed number A. A fraction joined with a whole number. Q. What kind of fractions are 15, 163, &c. ? Q. What kind of fractions are each of the following expressions, Az. 158, 8, 21, 8, 10, 73, 501 XXXV. TO CHANGE AN IMPROPER FRACTION TO A WHOLE OR MIXED NUMBer. 1. How many whole apples are there in 6 thirds (§) of an apple? In 8 quarters ()? In 2? In ? In 2? In 28? In 288? 2. How many weeks in 4 of a week? In 2? In 2? In 56? In 84? 3. How many pints in gills? In 32 gills? In 48 gills? fn 120 gills? 4. How much is of a doll..r? A. $1. Is ? A. 1 and 1. Is? Is 16? Is 7? Is 2? Is 25? Q. What is the finding how many whole things are contained in an Improper fraction called? A. Reducing an improper fraction to a whole or mixed number. 1. James, by saving of a dollar a day, would save in 33 Lays; how many dollars would that be? OPERATION. 16) 33 Ans. 2 dollars. In this example, as make 1 do lar, it is plain, that as many times as 16 is contained in 33, so many dollars it is; 16 is contained 2 times and 1 over; that is, 2 dollars. RULE. Q. What, then, is the rule for reducing an improper fraeon to a whole or mixed number? A. Divide the numerator by the denominator More Exercises for the Slate. 2. A regiment of soldiers, consuming of a barre, of pork a day, would consume in 28 days 28 of a barrel; how many bariels would that be? A. 5 oarrels. 6384 to a mixed number. to a mixed number. .9. 13. 9. Reduce to a mixed number. A. 23479. 272 10. Reduce 172 to a whole number. A. 144. TXXXVI. TO REDUCE A WHOLE OR MIXED NUM BER TO AN IMPROPER FRACTION. 1. How many halves will 2 whole apples make? Will 3* Will 4? Will 6? Will 20? Will 100? 2. How many thirds in 2 whole oranges? In 2}? In 2}? In 3? In 3? In 8? In 12? 3. A father, dividing one whole apple among his children, gave them of an apple apicce; how many children were there? 4. James, by saving of a dollar a day, found, after several days, that he had saved 13 of a dollar; how many 8ths did he save? and how many days was he in saving them? 5. How many 7ths in 2 whole oranges? In 24? In 24? In 34? This rule, it will be perceived, is exactly the reverse of the last, and proves the operations of it. 1. In 303 of a dollar, how many 8ths? RULE. Q. What, then, is the rule for reducing a mixed or whole number to an improper fraction? A. Multiply the whole number by the denomi nator of the fraction. Q. What do you add to the product? Q. What is to be writto. under this result? A. The denominator More Exercises for the Slate. 2. What improper traction is equal to 20? A. 181. A. 87. 12 A. 38. 9.38. A. 17. 7. What improper fraction is equal to 17? A. 182. 8. What improper fraction is equal to 1445? A. 1739. 9. Reduce 30 pounds to 20ths. As of a pound—1 s., 2s., the question is the same as if it had been stated thus In 30£ 5 s. how many shillings? A. 605. 605 shillings. 10. In 14 weeks, how many 7ths? A. 191101 days. 11. In 26 pecks, how many 8ths? A. 2211 quarts ¶XXXVII. TO REDUCE A FRACTION TO ITS LOWEST TERMS. are evi Q. When an apple is divided into 4 parts, 2 parts, or dently of the apple: now, if we take , and multiply the 1 and 2 both øy 2, we shall have again; why does not this multiplying alter the value? A. Because, when the apple is divided into 4 parts, or quarters, it takes 2 times as many parts, or quarters, to make one whole apple, as it will take parts, when the apple is divided into only 2 parts, or halves: hence, multiplying only increases the number of parts of a whole, without altering the value of the fraction. Q. Now, if we take, and multiply both the 2 and 4 by 2, we of ain; what, then, is equal to ? A. 2, or Q. Now it is plain that the reverse of this must be true; for, if we divide both the 4 and 8 in by 2, we obtain, and, dividing the 2 and 4 in by 2, we have; what, then, may be inferred from these remarks respecting multiplying or dividing both the numerator and denominator of the same fraction? A. That they may both be multiplied, or di vided, by the same number, without altering the value of the fraction. Q. What are the numerator and denominator of the same fraction called? A. The terms of the fraction. Q. What is the process of changing into its equal called? Mental Exercises. 1. Reduce to its lowest terms. 7 Reduce to its lowest terms. to its lowest terms. Operation by Slate illustrated. 1. One minute is what part of an hour will OPERATION. 3) 12 4' of an hour, and 15 minutes are make, reduced to its lowest terms Q. How do you get the in this example? A. By dividing 15 and 60 each by A. By dividing 3 and 12, each, by 3. Q. How do you know that is reduced to its lowest terms A. Because there is no number greater than 1 that will divid both the terms of without a remainder From these illustrations we derive the following RULE. Q How do you proceed to reduce a fraction to its lowest terms? A. Divide both the terms of the fraction by any number that will divide them without a remainder, and the quotients again in the same manner. Q. When is the fraction said to be reduced to its lowest terms? A. When there is no number greater than 1 that will divide the terms without a remainder 90 630 4. Reduce of a tun to its lowest terms. A. 4. 1 XXXVIII. TO MULTIPLY A FRACTION BY A WHOLE NUmber. ? 1. If 1 apple cost How much is 2 times 2. If a horse eat of a bushel of oats in one day, how many bushels will he eat in 2 days? In 3 days? How much is two tines? 3 times ? of a cent, what will 2 apples cost: 3. William has of a melon, and Thomas 2 times as much; what is Thomas's part? How much is 2 times ? 2 times? 2 times? 3 times ? 6 times? Q. From these examples, what effect does multiplying the numera tor by any number appear to have on the value of the fraction, if the denominator remain the same? A. It multiplies the value by that number. Q. 2 times is; but, if we divide the denominator 4 (in) 2, we obtain ; what effect, then, does dividing the denominator by any number have on the value of a fraction, if the numerator remain the same? 4. It multiplies the value by that number. |