But since the value of the fraction is not to be changed, the denominator and the numerator must be multiplied by the same number. To change to 35ths, the denominator and the numerator must be multiplied by 7, giving To change to 35ths, the denominator and the numerator must be multiplied by 5, giving 35. Hence, and, changed to similar fractions, equal and 3. Problems. Change to similar fractions 3. 5 5 7 9 2 3 4 5 3, 8, 7 ; 3, 1, 8. 17. 4, 3, 11; 3, 10, 1, §. 2. 3, 1, 1. 1, 4, 1; 1, 9, 1. 8. 4. 7 2 6 2. 10 4 5 8 9 10 8, 4, 4, 4; 3, 3, 9.9.1%, 11, 11; 1, §, 9, 26. 10. To what similar fractions are 3, 5, 72 equal? 11. Change to equivalent fractions having a common denominator of a foot and of a foot; $2 and $7. 9 12. Change to similar fractions of an acre, of an acre, 1 of an acre, of an acre. 10 252. Example 2.-Change 3, §, and to similar fractions having the least common denominator. 253. Rule to Change Dissimilar Fractions to Similar Fractions. I. Find the least common multiple of the denominators of the given fractions, for the least common denominator. . II. Divide the least common denominator by the denominator of each fraction, and multiply both terms of the fraction by the quotient. The resulting fractions will be the least similar fractions required. Change to similar fractions having the least common denominator 11 17 24. Change to least similar fractions §, 1, 2, 3. 25. Find the least similar fractions equal to 13 器 16 1, 18, 3526. Change, 33, 33, 144, 121 to least similar fractions. 27. What least similar fractions are equal to 19, 1, 18, and 1? To 18, 15, 16, 74? 11, 13%, 13, 2? 11 73 28. To what least similar fractions may the dissimilar fractions $4, $1, $36, and $35 be changed? 29. Change to equivalent fractions having the least common denominator 5, 37, 4, and 18s. 9 30. Reduce, 14, 14, 1, and to similar fractions having the least common denominator. Review Problems. 1. What are the lowest terms to which 39 740 672 234 1110 30249 35391 can be reduced? 2. Change to improper fractions 995, 100, 16, 444,1T 15 9 707 8889 4. Change 25 to the form of a fraction having 25 as its denominator. Change it to ones, to 8ths, to 100ths, to 1000ths. 5. Express 7, 3, 31, 17 as 30ths, as 60ths, as 75ths, as 225ths. 6. Reduce to similar fractions 7, 8, 11,,; 24, 8, 101. 7. Change to least similar fractions 4, 5, 38, and 70%. 8. Ten thirteenths equal how many one hundred fortythirds? How many two hundred forty-sevenths? 36 9. What improper fractions equal 505,5? 700% ? 2000? 7000,? 80801? 9009? 10090199? 10. How many 200ths of a ton are in 743 and 25,3 tons? 40 11. Express each of the integers 1, 3, 5, 11, 25, 100 as a fraction having as its denominator 1, 3, 5, 11, 25, and 100. 12. In 1004 hogsheads, how many 63rds of a hogshead? How many 252nds? How many 9ths? How many 21sts? 13. Arrange four 5's so that their value shall be 56. 14. Change as many as possible of the following fractions to 60ths: 3, 72, 24, 18, and 1; to 72nds; all to 360ths. 5 19 15. Which is the largest of four lots containing respectively, 98, 2, and 18 of an acre? 60 160 16. One day a fruit-dealer sold 75 baskets of apples, each containing of a bushel. How many bushels did he sell? 17. How many quarter-pounds are in a piece of walnutcandy weighing 93 pounds? 123 pounds? 163 pounds? 18. Change $5, $1, $31, $11, $9,99 to hundredths. 8 19. What are the least similar fractions to which 59, 1779 11236, 8, and 11g can be changed? 20. What are the least similar fractions to which 1, 510, 10%, 5, and 1005, can be changed? 1 Review Questions. 1. What is meant by Reduction of Fractions? What are the terms of a fraction? How is a fraction reduced to lower terms? When is it in its lowest terms? How is a fraction changed to its lowest terms? Illustrate by an example. State the principle. Repeat the rule to change a fraction to its lowest terms. 2. When is a fraction changed to higher terms? What is meant by a given denominator? How is a fraction changed to higher terms? Illustrate by an example. State the principle. Repeat the rule to change a fraction to higher terms or to a given denominator. 3. What is an Integer? A Fraction? How is an integer changed to a fraction? Give an example. Repeat the rule. Repeat the rule to change a mixed number to an improper fraction. 4. Define Improper Fraction. What is a mixed number? Tell how to change an improper fraction to an integer or a mixed number. Give an example, and explain it. Repeat the rule to change an improper fraction to a mixed number or an integer. 5. Define Similar Fractions. What are dissimilar fractions? What is meant by a common denominator? By the least common denominator? How are dissimilar fractions changed to similar fractions? Illustrate by an example. State the principles. Repeat the rule to change dissimilar fractions to least similar fractions. is the sum of 2 fourths and 3 fourths? Of 2 fifths and 3 fifths? 3. If Frank has 2 fourths of an apple, and Edgar has 3 fourths, how many fourths have both? 4. How many ninths are 4 ninths and 7 ninths? § + §? 5. What is the sum of and? Of 1 + 2 + { ? 6. What is the numerator of the sum of 3 + 1 + ¦ ? What is the denominator? 7. How do you add similar fractions, or fractions having a common denominator? 8. What is the unit of 2 cents? and 3 feet be united in one sum? Of 3 feet? Can 2 cents 9. What is the unit of 2 thirds? Of 3 fourths? Can 2 thirds and 3 fourths be united in one sum? Why? 10. To what similar fractions can and be changed? Change them to similar fractions, and find their sum. 11. To what kind of fractions must and be changed before they can be added? What least similar fractions do they equal? What is their sum? 12. Harry paid $3 for a knife, and $3 for a box of paints. How much did he pay for both? 254. Analysis. - Since Harry paid $3 for a knife, and $3 for a box of paints, he paid for both the sum of $3 and $3. changed to 12ths equals Now and are 11, or 12. 13. What is the sum of ; and changed to 12ths equals 1. Hence, Harry paid for both $112. of a ton and § of a ton? 14. How do you add dissimilar fractions, or fractions having different denominators? 255. Principles. I. Only fractional units of the same kind of things can be added. II. Only similar fractions can be added. Written Exercises. 256. Example. - Find the sum of 3, 5, and 3. |