3 if you pay 3 cents for one fifth (†) of an orange, what will a whole orange cost? 4. If you pay 2 dollars for one eighth (1) of a ticket, wha will a whole ticket cost? Q. How many halves to an apple, or any thing? Q. How many thirds? Fifths? Eighths? Sixteenths! Q. When an apple, or any thing, is divided into two equal parts, would you call one of these parts a half or a third Into 3 equal parts, what is one part called? Q. Into 4 parts, what is 1 part called? When an apple, or any thing, is divided into two equal parts, how would you express one part, on the slate, in igures. A. I set the 1 down, and draw a line under it; Then write the 2 under the line. Let me see you write down in this manner, on the slate, Que half. One third. One fourth. One fifth. One sixth. Two sixths. Three sixths. Three eighths. Eight twelfths Q. What are such expressions as these called 1 A. Fractions. Q. When, then, any whole thing, as an apple, a unit, &c. is broke divided into equal parts, what are these paris called ? A. Fractions. Q. Why called fractions? A. Because fraction signifies broken. Q. You have seen, that, when any whole thing is divided into parts, these parts are called thirds; into 4 parts, called fourths: what then, does the fraction take its name or denomination from? A. From the number of parts into which any thing is divided. Q. When an apple is divided into € parts, and you are desirous of lving away 5 parts, how would you express these parts? A. §. Q. What is the 6 (in ) called? A. The denominator. Q. Why so called? A. Because it gives the name or denomination to the parts. Q. What is the 5 (in §) called ! Q. Why so called? A. Because it numerates or numbers the parts Q. Which is the numerator, then? A. The number above the line. Q. Which is the denominator? A. The number below the line. A. The number of parts a unit, or any thing, in divided into. Q. What does the numerator show? A. How many parts are taken, or used. Q. In the expressions, 16, 12, 30, which are the numeratom, and which are the denominators? Q. If you own 28 of a vessel, how many parts is the vessel spposed to be divided into? and how many parts do you own? A. 40 parts, and I own 28 parts. Q. Is of an apple more than of it? Q. What fraction, then, is greater than? Than Than Than Than? What fraction is less than? Than Than ? Than? Q. From these remarks, what appears to be a correct definition of fractions? A. They are broken parts of a whole number. Q. How are they represented? A. By one number placed above another, with a line drawn between them. Q. In Simple Division, you recollect, that the remainder was represented in like manner; what, then, may justly be considered the origin of fractions? A. Division. Q. What may the numerator be considered? A. The dividend. Q. What may the denominator be considered A. The divisor. Q. What, then, is the value of a fraction? A. The quotient of the numerator divided by the denominator. Q. What is the quotient of 1 dollar divided among 2 men ↑ What the quotient of 7 divided by 81 A. 1. QHow, then, are fractions represented ? A. The quotient, of which { 2 is the dividend. 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 8 boys, and 4 oranges are 4 times as much; that is, , Ans. If 2 oranges among 7 boys? A. . 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. J. 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? 4 of 3 apples is 3 times as much as 1 of 1 apple; that is, of 1 apple. A. 4. 6. What part of 1 apple is of 3 apples? A.. What part of 1 apple is of 4 apples? A..of 4 apples is what part of 1 apple? Ans. A PROPER FRACTION. Q. We have seen that the denominater shows how many parts it takes to make a whole or unit; when, then, the aumerator 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 t, t, f, &c. ? AN IMPROPER FRACTION. Q. When the numerator is as large, or larger than the denominator, as, & f,, it is plain, that the traction expresses 1 whole, or more than I 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 4, 4, f, &c. 1 A MIXED NUMBER. Q. What is a mixed number? A. A fraction joined with a whole number. Q. What kind of fractions are 15, 161, &c.? Q. What kind of fractions are each of the following expressions, viz. 158, 8, 2, 8, 18, 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 24? In #? In 488? 2. How many weeks in 4 of a week? In 28? In 42? In ? In ? 3. How many pints in gills? In 2 gills? In gills? In 130 gills? 4. How much is of a dollar? A. $1. Is ? A. 1 and 1. Is? Is ? Is 7? Is 24? 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 days; how many dollars would that be? OPERATION. 16) 33 Ans. 2 dollars. In this example, as 18 make 1 dol. 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, 216 dollars. 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 23 of a barrel; how many barrels would that be? A. 5 barrels. 3. A man, saving of a dollar a day, would save in 365 days 385; how many dollars would that be? 4. Reduce 1281 to a mixed number. A. $73. A. 20. A. 7219. A. 43. 8. Reduce 167 to a mixed number. 9. Reduce 384 to a mixed number. A. 12 A. 13. A. 23149. 10. Reduce 112 to a whole number. A. 144. ¶ XXXVI. 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 apiece; 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? |