Section VI. DIVISION OF FRACTIONS. 1. To Divide a Fraction by an Integer. ? Tell 1. If you divide 3 fourths of an apple equally among three boys, what part of does each boy get? What part of the apple? 2. Dividing 4 fifths by 4 is taking what part of the quotient of divided by 4; divided by 3; 3. Dividing by 5 is taking what part of ? same as multiplying by what fraction? 10 13 ÷ 4. It is the 4. Dividing by 3 is the same as multiplying by what fraction? Dividing by 5? By 7? By 9? By 6? By 8? 5. How much is divided by 4, or of? 19 divided by 5, or 1 of 10? 14 ÷ 7, or 4 of 14, or 14 × 1? 6. Show that dividing the numerator of a fraction divides the value of the fraction. Give an example. 7. If of a cake is cut into 2 equal parts, what part of is each piece? What part of the cake? 8. How much is of, or divided by 2? Of divided by 3, or of ? ÷ 5, or 1 of 2, or 3 × 1? ÷ 6, or 1 × †? 9. Show that multiplying the denominator of a fraction divides the value of the fraction. Give an example. 10. At $3 for 5 pounds of sugar, what is the price of 1 pound? 198. Analysis. — Since 5 pounds of sugar cost $4, the price of 1 pound is of $3, which is $36. Hence, etc. 11. If of an acre of land is divided into 3 equal lots, what part of an acre is in each lot? 12. If of a vessel is owned in equal shares by 4 men, what part of the ship is each man's share? 13. If a man can do part of the work can he of a piece of work in 4 days, what do in 1 day? 14. At $3 a yard, how many yards of cloth can be bought for $13? 199. Analysis. — At $3 a yard, there can be bought for $13 as many yards as the number of times 3 is contained in 13. Now of 13 is of 9, or 3, which equals 43. Hence, etc. Or, 3 is contained in 13 4 times, with a remainder of 14, or ; and ofis, which, added to 4, equals 43. Hence, etc. 15. If a fruit dealer sold a dozen boxes of berries for $21, what was the price per box? If for $34? 16. How many times will 14 gallons of vinegar fill a vessel that holds 3 gallons? A 4-gallon vessel? 17. If a man earns $223 in 10 days, how much does he earn in 1 day? In 4 days? In 6 days? 8 days? What is the quotient of 12 18. 1 of a bale divided by 6? | 22. 123 tons ÷ 4 tons? 13 19. 1 of a cord divided by 7? 23. 20. 1 of an acre divided by 8? 21. 133 feet ÷ 8 feet? 24. 163 days 10 days? of a mile divided by 9? 25. 183 weeks ÷ 12 weeks? 200. Principle. A fraction is divided by dividing its numerator or by multiplying its denominator by any integer. Exercises. Find the value of & divided by 4. - The value of & divided by 4 is 4 of §, which is . 1. 15. 6. 104. 11. 22 of 8. 12 7 20 2. To Divide an Integer by a Fraction. 1. How many fourths of a cake in 1 cake? In 2 cakes? 2. How many times $1 in $1? In $2? In $3? In $4? 3. 1 is how many times ? ? ? ? ? ? ? .4. Dividing by is the same as multiplying the dividend by what integer? Dividing by ? ? ? ? ? 5. What is the quotient of 1÷? Of 1÷? The quotient of 1 is what part of the quotient of 1 ÷ 4? 6. 1 is how many times? 7. 3 is how many times? many times?? 5 is how 8. What is the quotient of 6 multiplied by what fraction? be divided by a fraction? How many times ? ? ? ? 8 9. At $3 a yard, how many yards of linen will $6 buy? 202. Analysis. – Since 1 yard of linen costs $3, there can be bought for $6 as many yards as the number of times $3 are contained in $6. 6 equals 3o; and 4 fifths are contained in 30 fifths 71⁄2 times. Or, $ are contained in $1 times; and $ are contained in $6 6 times times, or 3 times, or 71⁄2 times. Hence, etc. 10. If a fruit-jar holds of a gallon, how many jars will hold 3 gallons? 6 gallons? 9 gallons? 12 gallons? 11. If § of a yard of cloth will make a vest, how many vests will 5 yards make? 10 yards? 15 yards? 12. A merchant paid $30 for a piece of linen at $1% a yard. How many yards were in the piece? 13. At $ a bushel for oats, how many bushels can be bought for $6? For $8? For $10? For $20? 14. At $1 a bushel, how many bushels of wheat can be bought for $18? 203. Analysis. Since one bushel of wheat costs $13, for $18 there can be bought as many bushels as the number of times $1, or $3, are contained in $18, or 9o of a bushel, or 10 bushels. Hence, etc. 15. How many coats can be made from 15 yards of cloth, if each contains 2 yards? From 20 yards? 16. How many yards of cloth can be made from 18 pounds of wool, allowing 13 pounds to the yard? 17. How many rolls of wall-paper, each containing 41 square yards, are required to cover 27 square yards of wall? 18. If a boy who earns $6 a week receives $75 for his work, how many weeks had he worked? 19. Into how many fields, each containing 6 acres, can a farm of 68 acres be divided? A farm of 102 acres? 20. Show that the quotient of an integer by a fraction equals the product of the integer by the fraction inverted. Multiplying the dividend multiplies the quotient, and dividing the dividend divides the quotient. Exercises. Find the quotient of 8 divided by 8. 205. Model. Since 8 divided by 1 equals 8, 8 divided by equals 9 times 8, or 72; and 8 divided by & equals of 72, or 9. 3. To Divide a Fraction by a Fraction. 1. How many times are 2 fifths of a ton contained in 4 fifths of a ton? 2 sixths in 4 sixths? $g in $g? 3 10 10 2. What is the quotient of 8 tenths÷4 tenths? Of,%÷1%? 3. At $each, how many melons can be bought for $? For $? For $13? For $15? For $18? 9 20 4. A dealer received of a dollar for some ribbon at $1 a yard. How many yards did he sell? 5. If ğ of a yard of cloth will make a vest, how many vests can be made from 63 yards? From 93 yards? 6. How many packages of tea, each containing of a pound, can be made from 93 pounds? From 12 pounds? 7. When the divisor and the dividend are similar fractions, how is the quotient found? Find the quotient of 8. of a yard divided by . | 12. 7 cords 9. 19 of a gross divided by. 10. 1 of a ton divided by 2%. 11. 36 of an acre divided by 6. 40 3 of a cord. of a year. 13. 83 miles÷14 miles. 14. 93 years 15. 103 pecks÷3ğ pecks. 16. How many pounds of coffee at 3 of a dollar a pound can be bought for å of a dollar? 206. Analysis. —Since 1 pound of coffee costs of a dollar, for of a dollar there can be bought as many pounds as the number of times is contained in 2. Now equals §; and is contained in g 2 times. Hence, etc. 16 17. At $3 a yard, how many yards of muslin can be bought for $3? For $5? $? $11? $2}? 18. If a farmer received $41 for some corn at $3 a bushel, how many bushels did he sell? If he received $34? $41? 19. If 11 gallons of oil can be put in one jug, how many such jugs are needed to hold 71⁄2 gallons? How many are needed to hold 10 gallons? 15 gallons? |