DIVISION. 121. In all examples of division of fractions, the divisor and dividend are either the one an integral, and the other a fractional number, or both are fractional. 122. 1. What is the quotient of 8 ninths divided by 4? 2. Dividing by 4 is taking what part of ? 3. of is what part of 1? of? of? of? 4. Dividing by 2, 3, 4, 5, etc., is the same as multiplying by what fractions? 5. If 4 slates cost $8, what is the cost of 1 slate? 8 ANALYSIS. of $;, or $o1 = $3; or, = $. (102, II.) 9×4 6. What is the quotient of 1 divided by 2? 3? 4? 6? 9 ? 7. Divide by 4; by 5; 3 by 6; by 8; 1 by 7. How many ways to divide a fraction by an integer, and what are they? Show that dividing the numerator of by 3, or multiplying the denominator by 3, divides the fraction. (102, II.) 8. Divide by 4; 1 by 5; by 7; by 9; by 12. 9. At $4 a yard, how many yards of silk can be bought for $214? ANALYSIS.-As many yards as $4 is contained times in $215, or of 215 of 152, or 38 53 times. = = Or, 4 is contained in 215,5 times and 15 or 12 remainder; † of 42 is 4, which added to 5 makes 5%. Hence, etc. 10. Divide by 3 of 20. by 7; 14 by of 15; by 1 of 40. 181 by 12; 4 by 8. of 10; 7 of 29 by † of 63. miles in 4 hours, how far does he walk in 1 hour? In 3 hours? In 5 hours? 14. What is the quotient of 1 divided by ? ? ? ? Show that dividing by,, and is the same as multiplying by 2, 3, and 4. (102, I, II.) 15. In 2 are how many times ? f? q? ? ? ? 16. Dividing 4 by is the same as multiplying 4 by what fraction? 17. At $ a yard, how many yards of cloth can be bought for $6? For $9? For $10? ANALYSIS.-As many yards as $ is contained times in $6. 6 is equal to 30, and 4 fifths is contained in 30 fifths 7 times. Or, $ is contained in $1, § times, and in $6, 6 times §, or 30, equal to 7 times. Hence, etc. 18. Divide by ; 8 by ; 12 by ; 9 by ; 10 by . 19. At $ a bushel, how many bushels of turnips can be bought for $4? $6? $7? $8? $10? 20. How much butter at $3 a pound can be bought for $2? $4? $6? $9? 8? 12? How is an integer divided by a fraction? What is the reciprocal of a fraction? (99, 4.) Show that multiplying an integer by the reciprocal of a fraction divides the integer by that fraction. 21. How many times is contained in of 16? 22. What will 1 ton of coal cost, if of a ton cost $7 ? 23. How many times is contained in 6? In 8? In 11? 24. How many turkeys can be bought for $9, at $1 each? 25. How many garments can be made from 15 yards of cloth, if each garment contains 24 yards? 26. How many times is 2 eighths of a yard contained in 6 eighths of a yard? of a mile in of a mile? 27. At $each, how many pineapples can be bought for $? For $? For $1? For $1? How is one fraction divided by another, when they have a common denominator? 28. At $ a pound, how much tea can be bought for $? ANALYSIS.-As many pounds as $ is contained times in $. $1=$%, and $} = $15; $% is contained in $15, 13 times. Or, multiply the dividend by the reciprocal of the divisor . 29. How many pounds of honey, at $1 a pound, can be bought for $? For $? For $? For $? 30. Divide by ; by ; 1 by ; by ; by 1. How is one fraction divided by another when they have not a common denominator? 31. In 21 acres of land, how many building lots of of an acre each ? Reduce mixed numbers to improper fractions, then divide as we divide one fraction by another. 32. At $ a yard, how many yards of cambric can be bought for $? For $3? For $1? For $31? 123. PRINCIPLES.-I. A fraction is divided by an integer, either by dividing its numerator, or by multiplying its denominator by that integer. II. Any integral or fractional number is divided by multiplying it by the RECIPROCAL of its divisor. WRITTEN EXERCISES. 124. In division, as in multiplication of fractions, all operations may be reduced to one process, only differing from multiplication by inverting the terms of the divisor (99, 4). The Inductive Exercises will furnish all instruction necessary for the pupil to understand and explain all operations in the Written Exercises. RULE.-Change integers and mixed numbers, if any, to the form of fractions; then multiply the dividend by the RECIPROCAL of the divisor (123, II). Apply cancellation when practicable. 26. If 14 bushels of oats cost $8, what costs 1 bushel? 27. If of a farm cost $6270, what did the whole cost? 28. If of an acre of land cost $63, what cost 1 acre? 29. If 54 horses cost $4622%, what is the cost of each? 30. If 12 ploughs cost $124, what is the cost of each? 31. At $3 a cord, how many cords of wood can be bought for $40? For $150? 32. How many bushels of pears at $5 a bushel can be bought for $18? For $39 ? 48. How many pounds of tea, at $11 a pound, can be bought for $151? 49. At $6 a ton, how many tons of coal can be bought for $160? For $248 ? 50. At $a yard, how many yards of cloth can be bought for $9? For $24? For $64? 51. At $ a pound, how many pounds of butter will $110 buy? |
