T'hese fractions, when reduced to their simplest forms, are 1, 12, and ; which, when reduced to their least common denominator, become 8. What is the sum of of 4 of 1o, of 2 of 6, and ✈ of of 3? Ans. 41. Ans. 81. 9. What is the sum of of of 8, of of, and of 16? 10. What is the sum of of of %, 1 of 3 of 4, and 12. What is the sum of, 4, 4, 5, and 1? Ans. 44-3 13. What is the sum of 1, 2, 9 and ? 5 TO Ans. 3. 14. What is the sum of 3, of †, 3 of 3 of 4, and ? Ans. 24. 15. What is the sum of of, 4 of 4, 5 of 4, and of f? 47 Ans. 15-2S. 16. What is the sum of,,, 1, 7, 7, 1, †? Ans. 4898-1898. 2520' 17. What is the sum of 1, 1, 1, 1, 1 ? Ans. 137-217. 18. What is the sum of 3, 4, 4, 8? Ans. 17=517. 19. What is the sum of,,, 4, t, b, to, TT, IT IS! 6 91 Ans. 188388-1371377 10 36036 20. What is the sum of 4, 8, 7, 4, 1, 4, 11, 17, 12, 14! 9 SUBTRACTION OF FRACTIONS. 44. SUPPOSE we wish to subtract from . We know that so long as these fractions have different denominators, the one cannot be subtracted from the other any more than pounds can be subtracted from yards. We therefore reduce them to a common denominator, and obtain. Now, taking their difference, we obtain --- Hence, to subtract one fraction from another we have this RULE. Reduce the fractions to a common denominator; subtract the less numerator from the greater, and place the common denominator under the difference. Repeat this Rule. EXAMPLES. 1. From subtract =; }=1; 5—2—3. 1 2 NOTE.-As in Addition, if either of the fractions is compound, it must first be reduced to its simplest form. 9. From of of subtract to. Ans.. Ans. 18. 13. From of 4 of 4, subtract of Ans. T 37 14. From of 4 of 4 of %, subtract of of of §. 12 16. From the sum of 4, 4, 7, 4, 4, 4, 11, 11, 13, 14, subtract the sum of 1, †, ¿, †, 1, 1, 10, 11, 12, 13: We know, (ART 39,) that multiplied by is the same as of . Hence, we must use the same rule as for reducing compound fractions. Therefore, to multiply fractions, we have this RULE. Multiply all the numerators together for a new numerator and all the denominators together for a new denominator ; always observing to reject or cancel such factors as are common to both numerators and denominators. If any of the factors are whole numbers, they may be made to take the form of a fraction by giving to them 1 for a denominator, (see ART. 33,) and then the general 4. Multiply by 7 Ans. Ans. 5. Multiply,,, all together. 6. Multiply by 10. In this example, we cancel the 4 of the numerator against a corresponding factor of the 16 of the denominator; and 5 of the denominator against a corresponding factor of the 10 in the numerator. 4 Finally, cancelling the 2 in the numerator against the same factor of the 4 in the denominator, we find NOTE.-A little practice will enable the student to perform these operations of cancelling with great ease and rapidity. And since, as was remarked under ART. 39, it is immaterial which factors are first cancelled, the simplicity of the work must depend much upon his skill and ingenuity. 8. Multiply together the fractions 3, 4, 4. Expressing the multiplication, after reducing them, we have 7 13 1 2X-3X14 Cancelling the 7 of the numerator against a part of the 14 of the denominator, we have 713 1 13 -X-X- ===1. Ans. 9. Multiply together the fractions, t, 4, 4. 10. Multiply together the fractions, 5, 4. 11. Multiply together the fractions 3, 4, 5. 12. Multiply together, 7, 4. 13. Multiply by 4. 14. Multiply 7 by 2. Ans. t. Ans. §. 15. Multiply 71 by 31. 16. Multiply 16 by 5, Ans. 105-264 Ans. 165-821. 17. Multiply the sum of,,, t, by the sum of, t, 18. Multiply the sum of of, of by the sum of t of t,t of t. Ans. 19. Multiply of 7 of off by of of §. Ans. . 20. Multiply the sum of 3, 3, 33, 34, by the sum of 24 |