33. Fractions are expressed by a numerator and a denominator. 34. The Denominator shows how many equal parts the unit is divided into, and gives the name to the fraction. (a.) It may be written at the right of the numera tor in words; as, 4 tenths, 9 sevenths, 8 seventeenths, or under the numerator, thus: 3 numerator.. denominator. 35. The Numerator shows how many there are of those equal parts. (a.) It may be written either at the left of the denominator, as 3 tenths, 4 sevenths, or over the denomi nator, thus: denominator. numerator. 36. The Numerator and Denominator taken together are called the terms of a fraction. 1. When an apple is divided into 3 equal parts, what are the parts called? When divided into 4 equal parts? When into 7? 2. When an orange is divided into 8 equal parts, what are the parts called? When divided into 4 parts? 11 parts? 9 parts? 6 parts? 3.. When a peach is divided into 2 equal parts, what is each one of the parts called? When divided into 5 equal parts? Into 3 equal parts? Into 7 equal parts? Into 11 equal parts? 4. When a melon is divided into 5 equal parts, what is one of the parts called? What are 2 parts called? 3 parts? 5 parts? 5. When a pie is cut into 8 equal parts, what are two parts called? 6 parts? 3 parts? 1 part? 7 parts? 4 parts? 6. What is meant by 1, t, t, t, &c.? ANS.-By one-half is meant ONE of the Two equal parts into which a thing or number is divided; one-third is ONE of the THREE equal parts; one-fifth is ONE of the FIVE equal parts; &c. 7. What is meant by 3, 1, 5, &c.? ANS.-By two-thirds is meant Two of the three equal parts into which a unit or number of units is divided; the term three-fifths means THREE of the FIVE equal parts into which a unit or number of units is divided, &c. NOTE. When no definite number of units is expressed, one unit is always understood. 8. When a melon is divided into six equal parts, what is one of the parts called? ANS.-One-SIXTH of 1 melon. 9. When an orange is divided into six parts, what is 1 part called? What are 3 parts called? 4 parts? 10. When a pie is divided into 12 equal parts, what is 1 part called? What are 5 parts called? 7 parts? 8 parts? LESSON XLII. REDUCTION. 37. Principle.-If both numerator and denominator are multiplied by the same number, the value of the fraction will not be changed, because The number of the parts increases in the same ratio as the size diminishes. 24 ILLUSTRATION. = Form a series * of fractions from each of the following primary fractions, by multiplying both numerator and denominator by each consecutive number from 1 to 20. *To be read from slates or paper as a class cxercise. TABLE Of all the primary fractions, the denominators of which are less than 13. 38. Principle.-If both numerator and denominator are divided by the same number, the value of the fraction will not be changed, because The number of the parts diminishes in the same ratio as the size increases. NOTE FOR THE TEACHER.-Write on the blackboard exercises of fractions formed from the foregoing table of primary fractions. RECITATION.-Let the teacher point, and the class name the primary fraction individually or in concert; thus, 1, 1, 1, &c. The exercise may be varied as follows: 1. Commence at the left hand and pass toward the right. 2. Commence at the right hand and pass toward the left. 3. Commence at any place in the line and pass in either direction. 4. Point to any number, the class naming the result instantly. LESSON XLIV. 39. A Proper Fraction is less than a unit; as, , &c. 40. An Improper Fraction is one equal to or greater than a unit, as, 44, &c. 41. A Mixed Number is a whole number added to a fraction: as 3+, 2+. The sign is usually omitted: as 78. 1. How many halves in 5 apples? FORM.-Since in 1 apple there are 2 halves, in 5 apples there are 5 times 2 halves, which are 10 halves, hence, in 5 apples there are 10 halves of an apple. 2. How many fourths in 3 pears? 6 melons? 9 oranges? 8 pies? 12 lemons? 19 cakes? 3. How many sevenths in 3? In 4? In 6? In 5? 4. How many fifths in 6? In 13? In 12? |