11 = 11 × 2 5 5×2 22 = 10 EXPLANATION. Reduce the mixed number to an improper fraction. To change fifths to tenths, make the denominator of the new fraction tenths. Then multiply both terms by the factor that will change the denominator to the required denominator. AN IMPORTANT PRINCIPLE IN FRACTIONS II Multiplying both terms of a fraction by the same number does not change the value of the fraction. Similar Fractions and Common Denominators 396.,,are similar fractions. Fractions that have the same denominator are called similar fractions. 1. Reduce, and 2 to similar fractions, that is, to fractions having the same denominator. EXPLANATION. - By inspection we find that these fractions may all be reduced to twelfths. 12, 12, and 12 are similar fractions. The common denominator of these fractions is 12. What is the sum of 6 twelfths, 8 twelfths, and 9 twelfths? 2. Reduce 1, fo, to similar fractions. EXPLANATION.-Reduce the mixed number, 12, to the improper fraction, 3. Find by inspection or by factoring the least common denominator (1. c. d.). The 1. c. d. 10. The fractions must be reduced to tenths: 118, 1676, Tell how to add similar fractions. 18+10+10=10=3 = %• 3. Find the sum of 4, 2, and by trial or in spection. 10 10 EXPLANATION. 10 is the largest denominator. It may be the common denominator. The denominators 10 and 5 are exact divisors of 10. But the denominator 4 is not an exact divisor of 10. For that reason, 10 is not a common denominator. 4 = 2 × 2. All three denominators 4, 5, and 10 are exact divisors of 20. For that reason, 20 is a common denominator. 398. 1. A boy eats of an apple and his sister of it. What part of the apple is left? 2. A girl has 14 pounds of candy. She eats of a pound. What part of a pound has she left? 3. John spends $2 for a railroad ticket and $1 for a meal. How much does he spend in all? 4. Mary is reading a book. On Monday she reads of it, on Tuesday, and on Wednesday of it. How much of the book has she still to read? 5. If the book has 400 pages, how many pages did Mary read on Monday? On Tuesday? On Wednesday? 6. What is the weight of three packages if the first package weighs of a pound, the second pound, the third 11⁄2 pounds? of a 7. A tailor uses 4 yd. of cloth for a coat; 11 yd. for a vest, and 31 yd. for a pair of trousers. How many yards does he use for the suit? 8. A man had 12 gal. of milk in a can and adds 51 gal. more. How many gallons are there in the can? 9. A farmer sowed 372 acres with wheat and later 12 acres more. How many had he then sowed? 10. A playground is in the form of a rectangle 256 ft. long and 1783 ft. wide. How long is the fence that encloses the playground? 11. From a barrel containing 25 gallons of vinegar a grocer sells 13 gallons are left ? gallons. How many 12. I buy butter for $12, sugar for $3, and rolls for $1. How much change do I get, if I pay with a $5 bill? 13. One man has $48, another has as much, a third has as much. How many dollars do they all |