4 If one man can plant of an acre in one day, how much could 12 men plant in the same time? Answer, 9 acres. 5. If one barrel of fish cost 6 dollars, what will 9 barrels cost? Answer, $56. NOTE. Mixed numbers must be reduced to improper fractions. 6. If one chest of tea cost $254, what will 15 cost? Answer, $3783. 7. If a man can walk 29 miles in one day, how far could he walk in 30 days? Answer, 885 miles. 8. What will 600 pounds of cotton cost, if 1 pound cost 93 cents? Answer, $57. Division of Fractions by Whole Numbers. 1. If a man receive of a dollar for two day's work, what does he receive per day? We have seen that a fraction is multiplied either by multiplying its numerator, or dividing its denominator; then, as Division is the reverse of Multiplication, the reverse of the rule for Multiplication will be the rule for Division. If I divide the dollar into 4 parts, or quarters, and pay a man, or quarter, it is the same as though I should divide it into 8 parts, or half quarters, and pay him, or 2 half quarters--therefore, To divide a Fraction by a Whole Number-Divide the numerator of the fraction by the whole number, when it can be done without a remainder, otherwise, multiply the denominator. 2. If 8 pounds of lead cost of a dollar, what is it per pound? Operation. 21 As of a dollar, the whole cost, is to be divided by 8, the number of pounds, therefore write 1, the numerator of, which is 161 the dividend, on the right hand, and 8, which is the divisor on the left. The figure on the right being only a unit, cannot be reduced, therefore, the 2 and 8 on the left are to be multiplied together for a divisor, or denominator; the answer, then, is 1 divided by 16-16. 3. If a pair of oxen plough in 4 days part do they plough in one day? of a field, what Answer, 13. Why, QUESTIONS. 12. How do you divide a fraction by a whole number? in example 2d, are 8 and 2, the denominator of the fraction, placed on the left 14. Multiplying the denominator of a fraction, is the same as what? 4. If 6 men earn 18 of a guinea in a day, what part of a guinea does one man earn in the same time? Ans. 2. 5. If 16 hats cost $64, what does one hat cost? Answer, $4. 6. What will 1 pipe of molasses cost, if 14 pipes cost $7073? Answer, $51. 7. What will one yard of broadcloth cost, if 25 yards cost $150 ? Answer, $6,03. 8. What will one pound of rice cost, if 50 pounds cost Answer, $330. $1503? Multiplication and Division of Fractions by Whole MULTIPLICATION. Numbers. DIVISION. 1. If one dollar will buy 2. If 9 dollars will buy of an acre of land, how of an acre, how much will I much will 9 dollars buy? dollar buy? 3. If a man travel of a 5. If a man travel of a mile in one minute, how far mile in 12 minutes, how far will he travel in 12 minutes? will he travel in one minute? 42 5. If a man consume 5 6. If 7 men consume of of a barrel of flour in one a barrel of flour in 1 month, month, what will 7 men con- how much will one man consume in the same time? sume? 7. If of a box of glass 8. If 21 dollars will buy cost one dollar, how many 42 boxes of glass, how much boxes will 21 dollars buy? will 1 dollar buy? 9. If a pound of chocolate 10. If 7 pounds of chococost of a dollar, how much late cost of a dollar, what will 1 pound cost? of 12. If a man can do of a will 7 pounds cost? 11. If a man can do a piece of work in one day, piece of work in 8 days, how how much could he do in 8 much can he do in 1 day? days? 13. What will 16 yards of 14. If 16 yards of cloth cloth cost, at of a dollar cost 12 of dollar, what will per yard? one yard cost? 15. What will 40 yards of 16. If 40 yards of carpetcarpeting cost, at 7 of a dol-ing cost 35 of a dollar, what lar per yard? will 1 yard cost? 18. If 12 quarts of wine 17. If 1 pint of wine cost 6 of a dollar, how much will cost 12 dollar, what is it per 12 quarts cost? 19. Multiply by 11. pint? 20. Divide 9ğ by 11. Multiplication of Whole Numbers by Fractions. 1. If a barrel of flour cost $9, how much will of a barrel cost? Had the cost of 2 barrels been required, the price of 1 barrel being given, we should multiply the price of 1 barrel by the number of barrels. The same is now to be done; that is, the price of one barrel is to be multiplied by the part or parts of a barrel taken. The product of any number multiplied by 1, is the same as the multiplicand; the product of any number greater than 1, is as many times greater than the multiplicand, as the multiplier contains units. The product of any number less than 1, is as much less than the multiplicand as the multiplier is less than a unit, or 1. Therefore, if we multiply 9 by of 1, the product will be of 9, or 6. Hence it appears, that the product of a whole number multiplied by a fraction, is the value of the fraction taken from it. If $9 be the cost of 1 barrel, then the quotient of $9 divided by 3 will be $3, the cost of of a barrel, and 3×2=6 the cost of 3, therefore, To multiply a Whole Number by a Fraction-Divide the whole number by the denominator of the fraction, and multiply the quotient by the numerator. 2. What will 16 yards of cloth cost at of a dollar per yard? Operation. 16 4×3=$12 43 As 16, the number of yards, is to be multiplied by 3, the numerator of the fraction-the 16 and 3 fall on the right hand of the line, and 4, the divisor, on the left. 4 is contained in 16, four times; cross 4 and 16, and write 4, the quotient, on the right of 16-the 3 and 4 then multiplied give $12, the answer. 3. What will 40 yards of carpeting cost, at of a dollar per yard? 4. What will 64 bushels of oats cost at bushel? Answer, $35. 5. What will 24 bushels of corn cost, at ğ of a dollar per bushel? Answer, $15. 6. Multiply 21 by 2, by 4, by 3. Answer, 9, 18, 7. 7. What is the product of 324 multiplied by 1!? QUESTIONS. 15. What is the product of any number multiplied by 1? 16. How many times greater than the multiplicand is the product of a multiplier greater than 1? 17. How much less than the multiplicand is the product, when the multiplier is less than 1? 18. What is the product of a whole number multiplied by a fraction? 19. Rule? 8. What will 9 pounds of tea cost, at 27 of a dollar per pound? Answer, $4. 9. What will 56 lbs. of butter cost, at of a dollar per pound? Answer, $14. 10. What will 124 lbs. of sugar cost, at of a dollar per pound? Answer, $15. 11. Multiply 32 by 4, by 2, by §, by J. 12. Multiply 224 by Answer, 8, 8, 12, 28. Answer, 4. Division of Whole Numbers by Fractions. 1. If of a barrel of flour cost $6, what will be the cost of 1 barrel ? As this question is the reverse of question 1st, in the preceding section, the reverse of the rule there given will be the rule for solving this question. Had $6 been the cost of of a barrel, it is evident, that 3 times $6, or 18, would have been the cost of 3, or 1 barrel; but, as $6 is the cost of of a barrel, if I multiply $6 by 3, I shall have three times 3, or 2 barrels; if then §, or 2 barrels be divided by 2, I shall have the price of 3=$9, or 1 barrel. Hence, it appears that the quotient of a whole number divided by fraction, will be as much greater than the dividend as the fraction is less than a unit, or 1. RULE. Multiply the dividend by the denominator of the fraction, and divide the product by the numerator. 16 23 Operation. 3×3=$9 Ans. As 6, the dividend, is to be multiplied by 3, the denominator of the fraction, place 6 and 3 on the right of the line, and 2, the divisor, on Then we say, 2 in 6, 3 times; cross 6 and 2, and multiply 3 by 3-3×3-$9. Ans. the left. 2. If of a ton cost $15, how much will 1 ton cost? Answer, $18. 3. If of an acre be worth $12, what is 1 acre worth? Ans. $32. QUESTIONS. 20. How much greater than the dividend is the quotient of a whole number divided by a fraction? 21. How do you divide a whole number by a fraction? 4. If of the number of rows in a corn-field be 30, what is the whole number? 5. Divide 20 by 11. Answer, 40. Ans., 40, 80, 100. 6. If a pound of tea cost of a dollar, how many lbs. may be bought for $60? Ans., 100 lbs. 7. In what time can a man build 7 rods of wall, if he build of a rod in an hour? Ans., 17 hours. S. At of a dollar for building one rod of stone wall, how many may be built for $69 ? per yard, how many yards 9. At $3 for $80? Ans., 801. may be bought 10. If 1 bushel of wheat sow an acre of land, how many acres will 12 bushels sow? Ans., 9 acres. 11. How many times is contained in 56? Ans., 64. 12. How many times is 24 contained in 21? Ans.48. Multiplication and Division of Whole Numbers by Frac MULTIPLICATION. tions. DIVISION. 1. If a man can earn $16 2. If a man earn $6 in g in a month, how much can of a month, how much can he earn in of a month? he earn in a month? 3. If a man lay up $84 in 4. If a man in of a year a year, how much would he lay up $60, how much would lay up in of a year? he lay up in a year? 5. If the price of a horse 6. If of the value of a be $75, what would be the horse be $25, what is the price of a horse worth as whole value? much? Τ 7. If a house be worth 8. If of a house be $672, how much is worth? worth $378, what is the whole 9. If a farm be worth $840, worth? what is § of it worth? 11. Multiply 156 by 2. 10. If ğ of a farm be worth 13. A man has 360 appie $525, what is the whole trees in two orchards; in the worth? smaller, there is of the 12. Divide 117 by 2. whole. How many were there in the smaller? 15. A ship and cargo are valued at $100,000, the ship at 14. 40 is of what num ber? 16. If of a ship and car of the whole. What is go are valued at $5,000, what the value of the ship? is the worth of the whole ? |