PRIN. 1.- When the dividend and divisor have a common denominator, divide the numerator of the dividend by the numerator of the divisor. Prin. 2.-Any fraction having unity for its numerator, is contained in unity as many times as there are units in its denominator; if the fraction has 2 for its numerator, it is contained one-half as many times; if it has 3 for its numerator, one-third as many times; etc. PRIN. 3.-Two fractions, each having unity for its 4:1=4; 1:}=0; 1:1=8; 1:1 = 10. *:}== 21. COR.-To divide any number, either integral or fractional, by a fraction, invert the divisor and then multiply the dividend by it. = ADDITION AND SUBTRACTION OF FRACTIONS. 179 ADDITION AND SUBTRACTION OF FRACTIONS. Add Ans. 248. 2. }, k, po, and it Ans. 1;}. 3. , b, t. Ans. 37 Ans. 2146 4. }, }, #, and . 5. 15, and 37. Ans. 485 Ans. 1016. 6. 21, 34, and 5%. Ans. 1117 7. 11, 23, 31, and 44. 8. 1 of, of 4, and 7 of 4. Ans. 47 9. &, $, and Ans. 141. Ans. 1317 10. 23, 4, and 7. Ans. H. 11. From take f. 12. From take . Ans. . Ans. 18 13. From I take 14. From is take : Ans. Vous Ans. 15. From 1 take 16. What is 121 Ans. 57. 17. What is 108 - 41 ? % Ans. 51. 18. What is 21% - 104 ? Ans. 109. 19. What is 254 - 121? Ans. 124 20. What is 364 - 214? ? Ans. 1521 21. What is 754 - 26} ? Ans. 484 22. What is 1 of 1 - $ off ? Ans. 135 23. What is 3 of - 4 of 1? 1 1 P2 Ans. 345. 24. What is 1 of 54 - of 34 ? Ans. 11 25. What is off - 1 of 1 ? Ans. 37 26. What is the difference between of off and of of 1 ? Ans. 3724 5 22. 23 49 27. What is the difference between 1 of 2 and } of 31? Ans. e. What is the difference between 28. of 12 and 1 of 164 ? Ans. 29. of 204 and of 361 ? f Ans. 173. 30. What is the difference between two fractions whose numerators are each 1 and whose denominators are 5 and y? Ans. REM.—The numerator will be the difference and the denominator the product of the denominators. MULTIPLICATION AND DIVISION OF FRACTIONS. 1. Multiply by 3. Ans. 2. Multiply 1 by 4. Ans. 1. 3. Multiply by 5. Ans. 4. Multiply is by 6. Ans. Ans. 4. 5. Multiply } of 8 by 1 of 10. 6. Multiply } of 61 by of 57. Ans. 6 P. 7. Multiply of of 5 by of 45. Ans. 6473 8. Multiply 61, 57, 3 and of 5. Ans. 2697469. Multiply 4, 4, 11, 4 of 23, and 4 of 51. Ans. 16 10. Multiply $, %, 4, 5, and fr. Ans. 11. Multiply 31, 55, 6%, 1 of it, and 74. Ans. 35%. 12. Divide y by f. Ans. 241. 13. Divide 9 by Ans. 24. 14. Divide 30 by 23. Ans. 12. 15. Divide by 1. Ans. 11. 16. Divide to by Ans. 11. 17. Divide j by ic. Ans. 2. 18. Divide by 15. Ans. 3, T 14 11: 18 321 19. Divide it by the Ans. 6. 20. Divide the by 128 Ans. 93. 21. Divide i by . Ans. 151 22. Divide 47 by to Ans. 3134 23. Divide { of of } of 4 by $ of t1 of 13. Ans. 17. Reduce to a simple fraction, 24. Ans. S. 26. Ans. . ** 11. Ans. ft. 27. x 8. 25. Ans. $. 1 x $ X 28. Ans. 10. * X} 等 29. Ans. R. 플을 1+ i. $-$ 主 30. • Ans. 1934. -iis +3 Te 31. j * *.*:. x Ans. Ti :1-4x x 2 32. { xfxxxf 4x*x x x *. Ans. 32. 33. 374 = 25$. Ans. 15%. 34. 2014 - 307. Ans. 1846 35. ndoo • 1000. Ans. Toodooo 3 5 NUMERATION, ADDITION AND SUBTRACTION OF DECIMALS. Write in figures, 5. Five thousand, and five thousandths. 8. Two thousand three hundred and seventy-five tenthousandths. 9. Thirty-two thousand three hundred and seventyfive hundred-thousandths. 10. Two hundred and seventy-five hundred-thousandths. 11. Seventy-five hundred-thousandths. 1. Fifty-five thousand, and twelve thousandths; twentyone hundred, and twenty-one hundredths; fifty-two, and two hundred and seventy-five thousandths. Ans. 57152.497. 2. Twenty-one, and twenty-one hundredths; two hundred and ten, and two hundred and ten thousandths ; three thousand four hundred and fifty-one, and three thousand four hundred and fifty-one ten-thousand ths. Ans. 3682.7651. 3. Forty-four, and four tenths; four hundred, and four hundredths; four thousand, and four thousandths; forty thousand, and four ten-thousandths; four hundred thousand, and four hundred thousandths; four million, and four millionths. Ans. 4444444.444444. 4. From four million, and four millionths take four thousand, and four thousandths. Ans. 3995999.996004. |