ADDITION OF FRACTIONS. Ans 16=2. 1. Add §, 3, §, and 3. In this question we say, 1 part, and 3 parts, and 5 parts, and 7 parts, make 16 parts, but the denominator, which always shows into how many parts a unit is divided, being 8, we perceive that the 16 parts, that is, 16, is equal to 2 units, if each of these were a part or parts of a dollar, then their sum would be equal to 2 dollars. 2. What is the sum of 5 7 12' 12' 12, 12, and 11? Ans. 3-2-23. 5 9 3. What is the sum of, 1, 7, 18, 18, and 18? I Ans. 18-3. In such questions as the above, we have only to find the sum of all the numerators, and then see how many times the common denominator is contained in it. But if we wish to add together, 3, 12, and 3, &c., we must first find the least common denominator, 21 Thus, 4, 8, 12, 7 2x12 least com. denominator. Now since the value of a fraction is not altered by multiplying both its numerator and denominator by the same number, we multiply by 6, 7 by 3, by 2, and by 8, we have 18, 4, 4, and 1, the sum of which is 3-231-27. It is not necessary to multiply the denominator, if we only know by what number to multiply the numerator, this we can determine by dividing each denominator into the least common denominator, after that is found; thus, the denominators 4, 8, 12, and 3 will go 6, 3, 2, and 8 times successively into 24. NOTE. When a number of fractions are to be added together change them to a common denominator, and then add their numerators, and find how many times it contains the common denominator. 4. What is the sum of 1, 2, 8, 7, and ? denominators. 6. What is the sum of 7, 3, 4, 5, 1, and 11? Find the least common multiple of all the denominators, which will be the least common denominator, divide this common multiple by each of the given denominators, and multiply the quotient by the respective numerators of the fractions, and the sum of the products, divided by the least common denominator, will be the required sum of the given fractions. 7. What is the sum of 3, 7, 5, 3, 8, 11, 18, and? 12' A, 8, 6, 3, 9, 12, 16, 18 108 18x 7 126 given numerators. 24x 120 96 = 128 132 = 117 88 products. 2x8x18=144, least [common denominator. 915- =sum of the products. 144-6,514. Ans. =617. 8. What is the sum of 3, 4, 3, 5, and 1? Ans. 315-38. 9. What is the sum of §, 1, 11, 2, and 3? 10. What is the sum of 4, 11. What is the sum of 12. What is the sum of 4, 13. What is the sum of 5 7 1 17, and 19? Ans. 372. 14. What is the sum of,,, 20, 3,1%, and 37? 40 Ans. 338-335. 15. What is the sum of 8, 3, 4, 3, 2, 8, and 5? 12 Ans. 435-497. 16. What is the sum of 12, 38, 8, 11, 3, 6, and 13? 17. What is the sum of 73, 63, 81, 272, and 518? Here we first find the sum of the fractions 2 and 13. NOTE. When mixed numbers are given, first find the sum of the fractions, which add to the sum of the integers, and you will then have the required sum. 18. What is the sum of 87, 73, 5§, 121, 133, and 175? Ans. 6611. 19. What is the sum of 61, 3, 4, 72, and 83? Ans. 1730 20. What is the sum of 198, 1, 12, 8, 1, and 371? Ans. 592. 4 5 SUBTRACTION OF FRACTIONS. A boy having of a dollar, gave of a dollar to his mother; how much had he left? Ans. If we take 4 parts from 7 parts, the remainder will be 3 parts, that is, .. 1. If you take from 11, how much will be left? Ans. ; that is, if you take 5 parts from 11 parts, the remainder will be 6 parts, or ; but as the denominator shows into how many parts a unit is divided, and according to this denominator it is divided into 12 parts, 6 parts being the half of 12 parts, must be equal to 8 -16 2 2. 1 less how much? That is, if you take 8 parts from 13 parts, how many parts will be left? 3. 17 less how much? 20 4. 19 5. 20 24 how much? (This signifies subtraction.) is how much? 6. Subtract from 32. That is, take 23 parts from 32 400 400 16. Subtract from 3. Here the fractions not having a 12 common denominator, as in the preceding examples, we must find the least common denominator; Change the fractions to a common denominator, then subtract the less numerator from the greater, and the remainder placed over the common denominator will give the answer required. 17. Subtract from 18. Here the denominators 7 and 16 having no common factor the least common denominator will be their product. That is 16×7=112, Then, 13× 7=91=greater numerator. |