How many inches in of 1 foot? In of 1 foot? In of 1 foot? of 1 foot? 4. Copy upon your slates and read the following 4 5 6 7 8. 9 fractions: ; 10; 10; 10; 10; 10; 10; 10; 10. Read thus: One tenth; two tenths; three tenths, etc. What is meant by of 1 dime? of 1 dime? of 1 dime? of 1 dollar? How many cents in of 1 dollar? of 1 dime? How many cents in of 1 dollar? of 1 dime? of 1 dollar? 5. 5 13 7 5. Copy and read the following fractions: 3 ; ; ; ; ; 15: 75 20. 8 Read thus: One eleventh; five elevenths; one twelfth, etc. What is meant by How many months in 6. What is meant by of 1 year? of 1 apple? of 1 year? of 1 year? of an apple? Ans. 8 of the 21 equal parts into which the apple is divided. 29 3 7. What is meant by of an orange? of a dollar? of a mile? 5 of a year? 5 of a year? 8. How many days in year? 365 365 365 of a year? In 7% of a 365 9. How many cents in 8 of a dollar? of a dollar? 44. A FRACTION is one or more than one of the equal parts of a unit. (1.) The figure or figures below the line indicate the number of equal parts into which the unit is divided. It determines the name, therefore, to be applied to each part, and is called the denominator. (2.) The figure or figures above the line indicate the number of these equal parts taken, and is thence called the numerator. (3.) The numerator and denominator, taken together, are called the terms of the fraction. FRACTIONS. EXERCISES 1. If you give away 3 of an apple, into how many equal parts must it be divided? What name do you give to each of these parts? Which figure in the fraction indicates the name to be given to the parts? Which figure indicates the number of parts you give away? Which figure is the numerator? Which the denominator? What are the terms of the fraction? 4 7 8 2. State the numerator, the denominator, and the terms of each of the following fractions: ;;;; # Ti 3. 17 45. Properly, a fraction represents a less number of equal parts than is contained in the unit divided; hence, (1.) A proper fraction is one whose numerator is less than the denominator. Also, a greater number of equal parts than is contained in the unit may be represented in the form of a fraction; hence, (2.) An improper fraction is one whose numerator is equal to or greater than the denominator. (3.) The value of a fraction is the quotient of the numerator divided by the denominator EXERCISES. 1 Copy upon your slates and read the following expressions: =1;=1; 1=1; §=1; 8=1; 7=1; 8=1; 3=1; 18=1; 37=1, etc. Read thus: Two halves equal one; three thirds equal one, etc. 2. What is meant by of an apple? Ans. 2 of the 2 equal parts into which the apple is divided. How many halves in an apple? How many thirds? How many fourths? How many fifths? Sixths? Hundredths? 1 5 2. 3. If you divide each of 3 apples into 2 equal parts, how do you represent three of those parts by figures? Five of the parts? Six of the parts? Ans. ;G How do you represent one of the parts? Two of the parts? Four of the parts? Ans. ;; 4. Copy upon your slates and read the following expressions: 1}; 1=2; {=2}; §=3; 1=31, etc. Read thus: three halves equal one and one half, four halves equal two; five halves equal two and one half, etc. 5. How many apples are represented by the fractions £ ? 10? 11? 12? 19? 25? etc. Ans. 4 apples, etc. 6. If you divide each of two apples into 3 equal parts, how many thirds have you in all? 7. How are four thirds represented by figures? Five thirds? Six thirds? 8. How many apples are represented by the fractions 7? ? ? 40? 11? 12? 28? 31? etc. 9. If you divide each one of a number of oranges into four equal parts, and on counting the parts find 12, how many oranges have you divided? 10. How many oranges are represented by the frac tions ??? J? § ? q? 12? 27? 11. What is the value of the fraction ? ? 7 ? g? V 12? etc. Ans. 1; 11, etc. 46. A mixed number is a whole number united to a proper fraction. 47. To find a half; third; fourth, etc., of any number, divide the number by 2; 3; 4; 5, etc. EXERCISES. 1. How much is of 3? 4? 5? 6? 7? 8? 17? 21? 35? 47? Ans. 11; 2; 21, etc. 2. What is of 4? 5? 7? 9? 15? 25? 57? 59? 61? 43? 125? 87? 5164? etc. 3. What is 76? 96? 100? Ans. 1; 13. of 8? 12? 16? 5? 6? 19? 35? 57? 125? Ans. 2; 3; 4, etc. 4. What is of 57? 39? 19? 33? 45? 75? 48? 63? 79? 125? Ans. 11, 7, etc. of 137? 4 of 523? ¦ of 1000? ¦ of 378? of 132? 5. What is Yo of 125? 6. What is of 1728? Ans. 225, etc. of 169?of 196?' of of 324?' of 361? Ans. 144, etc. REDUCTION OF FRACTIONS. 48. The reduction of a fraction consists in changing its form, or the value of its terms, without altering the value of the fraction. EXERCISES. 1. Which is the longer, & of an inch or 1⁄2 of an inch? 2. Which is the longer, of a line or of the same line? 5 3. Which contains the greater number of cents, 10 of a dime or of a dime? 4. In of an apple how many halves of an apple? 5. In of an orange how many thirds of an orange? 6. Which is the larger fraction, or ? or ? or ? or ? 7 Which fraction has the larger terms, or ? or ? or ? 49. A fraction is said to be in its lowest terms when there is no number except 1 that will divide both of them without a remainder. 50. To reduce a fraction to its lowest terms. (1) PROBLEM.-Reduce the fraction to its lowest terms. (2) REDUCTION.-2 is the largest number that will divide the terms without a remainder. 2 in 2, 1; 2 in 4, 2 times. (3) RESULT.-Hence, 2). RULE. Divide both terms of the fraction by the largest number that will divide them without a remainder. 5 10. 12. 2. Reduce each of the following fractions to its lowest terms: ; 1; 8; foi fai fi f; 8; 18: 1:18: 37; 18: 38. 17 19. 20 Ans. 3. Reduce ; 2; 18; 15; 18; 21; 37, each to its low est terms. Ans. 4. Reduce ; ; 11; 18; 19: 18; 33, each to its lowest terms. 14; 10 15 12 Ans.. 5. Reduce; 26; 30; 40; 48; 13; 8, each to its lowest terms. 16 20 Ans. . 6. Reduce ; 2; 3; 13; 1; fo; 3, each to its lowest terms. 21 15 251 14 7. Reduce ; 22; 18; 13; 39; 2; 8, each to its lowest terms. 8. Reduce 18; 15; 28; 35; 30; 25; 18, each to |