QHow, then, are fractions represented? A. The quotient, of which 2 is the dividond. 1. If 3 apples be divided equally among 8 boys, what part of one apple will each boy receive? 1 apple among 8 boys would be of an apple apiece, and 3 apples would be 3 times as much; that is, of an apple apiece. Ans. . 2. If 4 oranges be divided equally among 8 boys, what part of an orange is each boy's part? 1 orange among 3 boys, and, oranges are 4 times as much; that is, , Ans. If 2 oranges among 7 boys? A. 4. 9 oranges among 13 boys? 20 oranges among 37 boys? 3. One orange among 2 boys is of an orange apiece, how much is 1 divided by 2, then? Ans. . How much is 1 divided by 3? A. §. The quotient of 5 divided by 6? A. §. Of 3 by 5? Of 7 by 9? Of 8 by 13? Of 11 by 15? 4. What part of one apple is a third part of 2 apples? A third part of one apple is, and a third part of 2 apples must be twice as much; that is, of 1 apple. A.. 5. What part of 1 apple is one fourth (4) part of 3 apples? of 3 apples is 3 times as much as of 1 apple; that is, of 1 apple. A. ‡. 6. What part of 1 apple is of 3 apples? A. §. part of 1 apple is of 4 apples? A. t. what part of 1 apple? Ans. §. What of 4 apples is A PROPER FRACTION. Q. We have seen that the denominator shows how many parts it takes to make a whole or unit; when, then, the numerator is less than the denominator, is the fraction greater, or less, than a whole thing or unit? A. It must be less. Q. What is such a fraction called? A. A Proper Fraction. Q. How may it always be known? A. The numerator is less than the denominator Q. What kind of fractions are AN IMPROPER FRACTION. Q. When the numerator is as large, or larger than the denominator, as, &,, it is plain, that the fraction expresses 1 whole, or more than 1 whole: what is such a fraction called? 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 153, 163, &c.? Q. What kind of fractions are each of the following expressions, viz. 158, 8, 1, 8, 18, 7, 527 TXXXV. TO CHANGE AN IMPROPER FRACTION TO ▲ WHOLE OR MIXED NUMBER. 1. How many whole apples are there in 6 thirds (§) of an apple? In 8 quarters ()? In 2? In 16? In 2? In gg? In 288? 2. How many weeks in 4 of a week? In 2? In 42? In $? In &? 3. How many pints in gills? In 32 gills? In 2 gills? In 130 gills? ? A. 1 and 4. How much is § of a dollar? A. $1. Is = 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. RULE. Q. What, then, is the rule for reducing an improper frac tion 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 barrel of pork a day, would consume in 28 days 28 of a barrel; how many barrels would that be? A. 53 barrels. 3. A inan, 36; how many dollars would that be? saving of a dollar a day, would save in 365 days 4. Reduce 101 to a mixed number. 5. Reduce & to a mixed number. 874 A: $73. A. 20. A. 7212. A. 1311. A. 23179. 10. Reduce 112 to a whole number. A. 144. 1 XXXVI. TO REDUCE A WHOLE OR MIXED NUMBER 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 23? In 3? In 31? In 8? In 12? 3. A father, dividing one whole apple among his children, gave them of an apple apiece; how many children were there? 4. James, by saving of a dollar a day, found, after several days, that he had saved 1 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 30% of a dollar, how many 8ths? OPERATION. 303 ra 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 denominator of the fraction. Q. What do you add to the product? A. The numerator.. Q. What is to be written under this result? A. The denominator. More Exercises for the Slate. 2. What improper fraction is equal to 20? A. 1881. A. 874. A. 38. A. 38. A. 197. 7. What improper fraction is equal to 17? A. 48. 8. What improper fraction is equal to 144? A. 1729. 9. Reduce 30 pounds to 20ths. As of a pound == 1 s., 22s., the question is the same as if it had been stated thus In 30£ 5 s. how many shillings? A. 605 shillings. 10. In 14 weeks, how many 7ths? A. 191101 days. 11. In 26 pecks, how many 8this? A. 2211 quarts. ¶ XXXVII. To reduce A FRACTION TO ITS LOWEST TERMS. Q. When an apple is divided into 4 parts, 2 parts, or 2, are evidently of the apple: now, if we take, and multiply the 1 and 2 both by 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: henee, 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 ob tain; what, then, is equal to ? A. 2, or Q. Now it is plain that the reverse of this must be true; for, if w divide both the 4 and 8 in § by 2. we obtain †, and, dividing the ! and 4 in by 2, we have ; what, then, may be inferred from thes remarks respecting multiplying or dividing both the numerator and de nominator 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 fractio called ? A. The terms of the fraction. called? Q. What is the process of changing into its equal 1. One minute is what part of an hour will OPERATION. 3 of an hour, and 15 minutes are make, reduced to its lowest terms Q. How do you get the in thi example? A. By dividing 15 and 60 each by 5. A. By dividing 3 and 12, each, by 3. How do you know that is reduced to its lowest terms? ecause there is no number greater than 1 that will divid terms of without a remainder |