6. How much is 2 times ? How does the result compare with? How is it obtained from ? 7. In multiplying a fraction what part of the fraction do we multiply? 8. Multiply by 2. 4 by 3. by 7. 9. Express 2 times in smallest terms. How is this result obtained from the fraction ? 10. In what other way then may we multiply a fraction? ? 11. How much is 3 times 4 times? 6 times 52 ? 181. PRINCIPLE.-Multiplying the numerator or dividing the denominator of a fraction by any number, multiplies the fraction by that number. RULE.-Multiply the numerator or divide the denominator by 17. What is the value of a load of 17 bushels of apples at $ a bushel? 18. If a boy earns $3 per day, how much can he earn in 9 days? 19. At $7 a barrel what will 7 barrels of flour cost? PROCESS. $73 7 51 49 541 ANALYSIS.—In multiplying a mixed number, we multiply the fractional part and integer separately and add the results. Thus, 7 times $}=$4=$5}. 7 times $7 are $49, and the sum of $49 and $51 is $541. We may reduce the mixed number to an improper fraction before multiplying. 20. If a man travel 213 miles per day, how far can he travel in 4 days? 21. What will 13 yards of cloth cost at $6 a yard? 22. If a steamship sails 17 miles an hour, how far can she sail in 9 hours? CASE II. 182. To multiply an integer by a fraction. 1. Henry had 6 rabbits and sold of them to James. How many did he sell? 2. Jane had 16 cherries and gave of them to her sister. How many did she give to her sister? 183. PRINCIPLE.-Multiplying by a fraction is taking such a part of a number as is indicated by the fraction. Since of 3, § of 75=} of 3 times 75, or 75X3 = 45. = RULE.-Multiply the integer by the numerator of the multiplier, and divide the product by the denominator. 14. A man owned a mill worth $7850. How much money should he receive for of it? 15. A sportsman shot 48 birds one day, and as many the next. How many did he shoot in both days? 16. Multiply 46 by 5%. 53-28 ANALYSIS.—In multiplying by a mixed number we multi46×28-1288 ply by the integer and fraction separately and add the products. Thus, of 46 is 138, or 273. 5 times 46 5 1288-257% to an improper fraction and multiply. 230, and 27+230 257, the product. Or, we may reduce the mixed number 17. Multiply 36 by 51; 6; 75; 819; 10,5. CASE III. 184. To multiply a fraction by a fraction. 1. How much is of 4 fifths of a yard? How much is of 8 twelfths of a yard? of 3 ninths of a yard? 2. If James has of a dollar, and Anna has as much, how much has Anna? If Henry has as much as James, how much has he? How much is of ? of 3? 3. A man who owned of a steamship sold of his share. What part of the vessel did he sell? How much is of §? 4. How much is 4 of 14? of 14? of 3? of? 5. If of a yard be divided into 2 equal parts, what part of a yard will each part be? of 4 yard? 6. At $ a bushel what will How much is of yard? of a bushel of oats cost? How much is of? 1 of 1? 1 of 1? of? of? 7. What is the value of of? of? of? of? WRITTEN EXERCISES. 1. Multiply by 3. PROCESS. find 4 ANALYSIS. To multiply by is to 75, and are 3 times or 48=33. RULE.-Reduce all integers and mixed numbers to improper fractions. Multiply the numerators together for the numerator of the product, and the denominators together for its denominator. X1. When possible use cancellation. 2. The word of between fractions is equivalent to the sign of multiplication. Such expressions are sometimes called compound fractions. Thus, of is equal to X. 3. Integers may be expressed in the form of fractions by writing 1 as a denominator. Thus, 4 may be written as 1. whole numbers expressed in the fractional form. Multiplying and cancelling we have 3, or 11. 24. Multiply 5 of 3 of 5 by † of § of 31. 29. 161 feet make a rod. How many feet are there in 5 rods? 30. A man who owned of a mill, sold of his share. What part of the mill did he sell? 31. How many yards of cloth are there in 12 pieces of cloth, each piece containing 423 yards? 32. At $167 per ton how much can be realized from the sale of 44 tons of hay? |