The Idea of a Fraction developed. 1. If a melon be cut into two equal pieces, what part of the melon will one piece be? 2. How many halves in a melon? How many halves in any thing? 3. If a melon be cut into four equal pieces, what part of the melon will one piece be? Two pieces? Three pieces? 4. How many fourths in an apple? How many fourths in any thing? 5. Which is the greater, one half or one fourth of an apple? How many fourths equal one half? 6. If a cake be cut into three equal pieces, what part of the cake will one piece be? 7. How many thirds in a cake? How many thirds in any thing? 8. If a cake be cut into six equal pieces, what part of the 'cake will one piece be? Two pieces? Three pieces? Four pieces? Five pieces? 9. How many sixths in any thing? 10. Which is the greater, one third or one sixth of a cake? How many sixths equal one third? 11. A single thing is a unit. in a unit? How many thirds? How many sixths? How many halves How many fourths? 12. What is meant by one third? Ans. One third is one of the three equal parts of a unit. 13. What is meant by two thirds? One fourth? Three fourths? One sixth? Three sixths? 14. Which is the greater, two thirds or a unit? Five thirds or a unit? Three fourths or a unit? Four fourths or a unit? Art. 55. Such parts of a unit as two thirds, three fourths, five sixths, etc., are called Fractions. A fraction may be expressed by two numbers, one written under the other, with a horizontal line between them; as,, 3, 8. The number below the line denotes the number of equal parts into which the unit is divided. It is called the Denominator. The number above the line denotes the number of equal parts taken. It is called the Nu merator. Read the following fractions, and tell, in each case, into how many equal parts the unit is divided, and how many parts are taken: Art. 56. A Fraction is one or more of the equal parts of a unit. Art. 57. A fraction is expressed by two numbers, called the Numerator and the Denominator. The Denominator of a fraction denotes the number of equal parts into which the unit is divided. The Numerator of a fraction denotes the number of equal parts taken. The numerator and denominator are called the Terms of a fraction. LESSON II. Integers and Mixed Numbers reduced to 1. How many thirds in an apple? How many thirds in 2 apples? 2. How many fourths in 3 pears? SOLUTION.-In 1 pear there are 4 fourths, and in 3 pears there are thrice 4 fourths, which are 12 fourths. There are 12 fourths in 3 pears? 3. How many sixths in 3 oranges? In five oranges? 6 oranges? 8 oranges? 4. How many fifths in 3? 5? 8? 10? 5. How many eighths in 4? 6? 8? 10? 5 halves. There are 5 halves in 2 and 1 half oranges. 7. How many fourths in 2 and 3 fourths? 8. How many thirds in 5 and 2 thirds? 8 and 1 third? 7 and 2 thirds? I. A.-7. 9. How many sixths in 5 and 2 sixths? 8 and 3 sixths? 12 and 5 sixths? 10. How many tenths in 6 and 3 tenths? 7 and 5 tenths? 8 and 7 tenths? 11. Read 63; 331; 457; 2511; 50; 66%. 12. How many fifths in 63? 8g? 12? WRITTEN EXERCISES. 13. Reduce 157 to ninths. 1573 to ninths. 14. Reduce 96 to eighths. 96 to eighths. 15. Reduce 351 to twelfths. 468 to ninths. 16. Reduce 73,6 to elevenths. 639 to sevenths. 17. Reduce 5317 to a fraction. SUGGESTION. Reduce the mixed number to twentieths. Art. 58. A Mixed Number is an integer and a fraction united; as, 51, 163, 334. |
