Dividing by 2 is equivalent to multiplying by what? by 9. 196. How long will it take to spend $2, if you spend of a dollar a week? 197. How many quarters of a dollar are there in $2? How many times is 198. Divide 2 by ; contained in 2? 2÷ ? 3 by ; 4 by 4 by t 5 by ; 6 by 199. Divide 2 by ; ; 6 by . 200. Five are how many times; 201. Six are how many times; 1; 1; 1; 4· How can an integer be divided by a fraction? 202. Divide 7 by ; by ; by ; by 203. Divide 5 by ; by 5; 8 by ; ; by 4. In division, does it make any difference with the quotient if che divisor and dividend are interchanged? NOTE. If the denominator of the divisor and of the dividend are alike, they may both be disregarded, for evidently 2 fifths is contained in 6 fifths as many times as 2 cents is contained in 6 cents, or 2 in 6. 209. How many times is contained in ? by ; by; by 2; by ; 1; 1, Ans. 210. Divide 1 by 1. 211. How many times is by 5; by 1; 1 by ; How then can one fraction be divided by another? and the denominators for the denominator, and division is the reverse of multiplication, therefore, if we divide the numerator of the dividend by the numerator of the divisor, and the denominator of the dividend by the denominator of the divisor, we shall have the numerator and denominator respectively of the quotient. The practical difficulty with this method is that the terms of the dividend are rarely both divisible by the respective terms of the divisor. 215. Divide by 2. 3 ÷ 2 = & 14 4× 5 = 1, Ans. By Art. 72 b, ÷2=; but the divisor is not 2 but, or 25, that is, 2 is 5 times the given divisor; therefore the quotient is 1 fifth quotient sought, and must be multiplied by 5 to obtain the correct result. By Art. 72 b, 4 × 5=15, Ans. 14 Hence, 1, Ans. the It will be seen that we multiply the denominator of the dividend by the numerator of the divisor for the denominator of the quotient, and the numerator of the dividend by the denominator of the divisor for the numerator of the quotient. Hence, To divide a fraction by a fraction, Rule. Invert the divisor and proceed as in multiplication of fractions. NOTE 1. As an integer can be expressed as a fraction by writing 1 under it as its denominator, and a mixed number can be reduced to an improper fraction, this rule covers all possible cases in Division of Fractions. 2745 by ; by. 218. Divide by ; by ; by 11; 11 by g. ğ 216. Divide by 217. Divide by 231. If for 5 days work I pay $82, how much do I pay for each day? 232. If 8 pounds of coffee cost $25, what does it cost a pound? 233. If 24 pounds of ham cost $3, what will 19 pounds cost? 234. If 75 pounds of soap cost $411, what is it a pound? 235. If 25 barrels of beans cost $2467, how much is that a barrel? 236. If $48 will buy 19 yards of broadcloth, how many yards can be bought for $38% ? 237. How many barrels of apples at $12 a barrel must be given for 28 yards of cotton at $a yard? 238. If a turkey weighing 93 pounds is worth $ 1ğ, how much ought one that cost $1 to weigh? 95. ORAL EXERCISES. 1. A boy bought a pair of skates for 2 dollars, a snow-shovel for of a dollar, and a sled for 14 dollars. How much did they all cost him? 2. Mabel bought a work-basket for of a dollar, a pair of gloves for 13 dollars, and a book for 1g dollars. How much did she pay for all? 3. Henry picked of a peck of nuts, Howard of a peck, and Edward of a peck. How many pecks of nuts did they all pick? 4. A fruit-dealer bought 5 dozen oranges at of a dollar a dozen, and sold them at of a dollar a dozen. How much was his profit on the lot? How much 5. A newsboy paid 14 dollars a hundred for papers, and sold them for 2 dollars a hundred. did he make on a hundred? 6. Frank paid 5 dollars for a double-runner sled, 11 dollars for painting it, and of a dollar for a bell for it. How much was the entire cost? . 7. If I use 81 tons of furnace-coal and 31 tons of stove-coal in a year, how much coal do I use in all, and how much more furnace-coal than stovecoal? 8. Abbott bought a hat for 24 dollars, a pair of gloves for of a dollar, and a pair of boots for 24 dollars. How much did they cost? 9. Add 81 and 71; 5 and 73. 10. When grapes are 12 cents a pound, what will 3 pounds cost? 11. From & take. Take from 8. 12. A boy having a quart of peanuts gave of them to his playmates and of them to his mother, and kept the rest. How many did he give away? |