Ans. 3; 2 11. Divide 183 by 6 and by 9. Ans. 227; 151, etc.. 13. Divide 37 by 2; 3; 4; 5; 6; 7; 8; 9. Ans. 183; 12, etc. 14. Divide 87 by 2; 3; 4; 5; 6; 7; 8; 9. 15. Divide 112 by 7; 137 by 9; 187 by 13; 225 by 15. Ans. 43; 291, etc. by 9; 167 by 11; 166 Ans. 164; 15,5g, etc. REMARK 2.—When the divisor is readily seen to be the product of two or more smaller numbers, the dividend may be divided by one of the smaller numbers, the quotient by another, and so on till all are used. The last quotient is the true answer. 16. Divide 5173 by 15, 28, and 63. Ans. 19. Divide 395 by 63 and by 72. 20. If 3 oranges cost 183 cents, what 1 orange? 29 3 59 6; 520 is the price of Ans. 61 cents. 21. If 5 acres of land are worth 673 dollars, what is the price per acre? Ans. 131 dollars. 22. If 9 barrels of flour are worth 112 dollars, what is the price per barrel? What are 2 barrels worth? 5 Last Ans. 62 dollars. 23. If 7 hats are worth 31 dollars, what is 1 hat worth? 9 hats? 18 hats? 54 hats? 72 hats? 81 hats? First Ans. $41⁄2. barrels? 90 hats? 62. To divide a whole number by a fraction. EXAMPLES. 1. Copy and recite the following exercises: (1) 4÷3=63 (2) 9÷2=12 12÷=18 Recite thus: Since 1 is contained in 4, 4 times, is 14 contained in 4, 20 times; now & are 3 times }; hence, § are contained in 4, 1 of 20, or 63 times. RULE. Multiply the whole number by the denominator of the fraction, and divide the product by the numerator. 1 2. Divide 1 by ; 1; 3; 4; 1; }; 1; 1; 1 4 3. 4 1515 Ans. 2; 3; 11; 4, etc. 16. 3. Divide 12 by 1; 2; 1; 1; 4; fi; }$; 15. 4. Divide 42 by 1; 1; 7; 1; Ans. 16; 42; 15, etc. REMARK.—A mixed number may be divided by a fraction in the same way. 7. 5 3 7 5. Divide 33 by 1; 1; fa; jei doi ; · (3) 3 ÷ 6 = 39 = 13 Recite thus: Since 1 is contained in 2, § times, ¦ is contained in 3, 7 times 2, or 2-times; now 1⁄2 are 5 times ; hence, are contained in, of 21, that is, 30, or RULE. Multiply the numerator of the dividend by the denominator of the divisor, and the denominator of the dividend by the numerator of the divisor. The former product is the numerator, and the latter the denominator of the answer. REMARK 1.—In operations upon the slate or blackboard, it is convenient to invert the terms of all the divisors, and then multiply as in 59. The terms of a fraction are said to be inverted when the numer ator takes the place of the denominator, and the denominator that of the numerator. 2. Divide by ; by, and 3 by 1. REMARK 2.—The pupil should neglect no opportunity to cancel numbers from the fractions before multiplying. 12. Find the value of 653÷4; 653×1. 3. 13. Find the value of 12÷; 12x1. 14. Find the value of 16÷4; 16× 21. 15. Divide 36 by 8; 48 by 33. . Ans. 16. Divide 113 by 2; 1129 by cloth can be bought for $6? Ans. To 12 Ans. 1611. Ans. 16. Ans. 36. Ans. 401; 69. 1503; 13148. many yards of Ans. 9 yards. As many yards as are represented by the quotient of 6 divided by 3. (See 37, example 43. REMARK.) 18. At 7 dollars per barrel, how many barrels of flour can be bought for $62? $248? $310? $434? $558? First Ans. 8 barrels. of a dol 19. At of a dollar per bushel, how much corn can be bought for of a dollar? of a dollar? lar? of a dollar? Ans. in order. ; ; 20. If of a yard of cloth are worth what is 1 yard worth? ; if bu. of a dollar, Ans. 1 dollars. 21. If of a ship are worth 6000 dollars, what is the whole ship worth? Ans. $106663. 22. A gentleman divided of a lot of marbles among 5 boys, giving each boy 8 marbles. How many marbles would each boy have received if the whole lot had been equally distributed? Ans. 12 marbles. 23. If of a bale of cotton are worth 42 dollars, what is the whole bale worth? DECIMAL FRACTIONS. Ans. $98. 64. Fractions which have a numerator and a denominator, written with a line between them, are frequently called common fractions. (1.) A decimal fraction may be written in the form of a common fraction. Thus: 1; .25%; .01-bo .003=100; .0625-1888, etc. (2.) To reduce a common fraction to a decimal frac tion. 2. Reduce ; ;, and to fractions whose denominators shall be 10. Ans. 10: 10. 8 3. Reduce ;, and to fractions whose denominators shall be 100. 100-4-25 Ans. 100 100 TOO 3. 4. 5. 7 25. 50. 75 4. Reduce;;;;;; to fractions whose denominators shall be 1000. 1000÷8=125. Recite thus: 2 in 10 tenths (=1), 5 tenths. Hence, 1.5 5 in 10 tenths (=1), 2 tenths. 5 in 20 tenths (=2), 4 tenths. 5 in 30 tenths (3), 6 tenths. 5 in 40 tenths (4), 8 tenths. Hence, =.2 Recite thus: 4 in 10 tenths, 2 tenths; 4 in 20 hun dredths, 5 hundredths. Hence, 1.25 RULE. Consider the numerator as a dividend, and the denominator as a divisor, and divide as in 42. (See 42, REMARK 2; also 45, (3.); also 17, PRINCIPLE.) 7. Reduce ; ; §; §, and 3. 4 5 Ans. .375; 5, etc. |