15. Reduce, 7, and to equivalent fractions having a common denominator. Art. 65. When a fraction is changed to an equivalent fraction with greater terms, it is reduced to Higher Terms. Several fractions having the same denominator, are said to have a Common Denominator. Art. 66. PRINCIPLE.-The multiplication of both terms of a fraction by the same number does not change its value. to Art. 67. RULES. 1. To reduce a fraction higher terms, Divide the given denominator by the denominator of the fraction, and multiply both terms by the quotient. 2. To reduce fractions to a common denominator, Divide the least common multiple of the denominators by the denominator of each fraction, and multiply both terms by the quotient. LESSON VI. Addition of Fractions. 1. A boy gave 1 fourth of a pine-apple to his brother, 1 fourth to his sister, and 1 fourth to a playmate what part of it did he give away? How many fourths are ++? 2. A grocer sold 1 eighth of a cheese to one customer, 2 eighths to another, and 3 eighths to another: what part of it did he sell? How much is + ÷ + } ? 3. How many sixths in ,, and §? 1, 1, and ?,, and g? 4. A boy gave 1 half of his money for a knife, and 1 third of it for a ball: what part of his money did he spend? SUGGESTION. Change and to sixths. and ? 8. How many fifteenths in and ? and ? and ? 9. How many twentieths in and ? and ? and ? and ? and ? 10. How many twenty-fourths in 4, 3, 4, and ? In,,, and ğ? WRITTEN EXERCISES. 6 11. What is the sum of 5, 13, 13, 13? 139 23 12. What is the sum of 13, 3, 5, and 249 249 249 24 ? ? Change the fractions to twentyfourths; add the numerators of the new fractions; and reduce the resulting improper fraction to a mixed number. 15. What is the sum of ,, and? g 16. Add,, and . 17. Add , 72, and 11. t, ΤΣ 18. Add , 3, and 13. 19. Add 1, 3, and 17. 24. What is the sum of 163, 183, and 371⁄2? First add the fractions and then the in PROCESS. 163 12 tegers. 283 = 12 72, Ans. 1. Write the under the fractions and add the 1 with the integers. 25. Add 451, 67, and 62§. 26. Add 37, 18, 331, and 25. 27. Add 301, 663, 84, and 1333. 28. Add 75, 108, 160%, and 207. Art. 68. RULES.-To add fractions, Reduce the fractions to a common denominator, add the numerators of the new fractions, and under the sum write the common denominator. 2. To add mixed numbers, Add the fractions and the integers separately, and combine the results. LESSON VII. Subtraction of Fractions. 1. Albert had 2 thirds of an orange and he gave 1 third to his sister: how many thirds had he left? How much is less? less? 3 2. Charles bought 3 fourths of a pound of raisins, and then gave 1 fourth of a pound to his playmate what part of a pound had he left? How much is less? less ? 4 3. A farmer bought of a bushel of flax-seed, and sold of a bushel to a neighbor: what part 13. From take. PROCESS != }} -} = , Ans. : 7 from 7. from 1. }} from 1. First subtract the fractions and then the integers. Since is greater than, add to 2, making 11⁄2, and then take the from, writing under the fractions, and adding 1 to the 8 units before subtracting the integers. |
