Written Work 4 x 3 1. Change f and to similar fractions having the common denominator 12. Since the denominator 3 in ý must be multiplied by 4 2 x 4 8 to produce 12, the numerator must also be multiplied by 3 x 4 12 2 x 4 8 4, so as not to change the value of the fraction. 3 x4 12 3 x 3 9 Since the denominator 4 in must be multiplied by 3 to 12 produce 12, the numerator 3 must also be multiplied by 3. 3 X 3 9 Hence the similar fractions are in and is 4x312 Change to similar fractions : 2. į and 4. and 6. 1, 4, and i 8. }, g, and 3. and 5. $ and 1 7. 3, 1, and 9. b, g, and al 10. Reduce 24 to its lowest terms. 6 : 3 2 2 : 2 1 We can divide both terms, 6 and 24, of the ; 24 : 3 fraction and by 3 without changing the value 8 8:2 4 of the fraction. The result is š. We can then divide both terms 2 and 8 of the fraction s by 2. The result is t. Reduce to lowest terms: 11. 13. 1 19. 14. 18. 21. Change to units. Thus, 1 unit = 2 halves. In 4 halves there are 4+2, or 2, units. Change 1 to units. 22. Change to to units and parts of units. Thus, 1= 3 thirds. In 10 thirds there are 10 = 3, or 3, units and fremaining; that is, 33. To change a fraction to units and parts of units, divide the numerator by the denominator. Change to units and parts of units : 23.12 24. 25. 26.72 27. 1 8 15. 18 17. 18 12 12. 16. 11 20. ADDITION OF FRACTIONS 1. Can you add f and d without change ? Can you add and 1 ? What change must be made in § and į before they can be added ? 2. }= 1 ; f = iờ; f= id; f= 1? 4. Can you add į and } without change? Change both to tenths. Can they then be added ? 5. Can you add 1 and without change? Change both to sixths. Can they then be added ? 6. When į and I are to be added, to what similar fractions should they be changed ? 7. What are the denominators of the fractions in example 4? To what like or common denominators (c. d.) did you change both fractions ? 8. What are the denominators of the fractions in example 5? To what denominator did you change the fraction į? j? Why? 9. After two or more fractions are changed to like, or common denominators, that is, after they have been made similar, what is the second step in adding them ? 10. Add 3, 5, ; ; }; }; lo; 1, 5, 1; }, }, is. 11. Observe that in problem 10, į + 3 +ė = 8, or 1, and that } + 1 + 1 = 1, or j. 12. What is the third step in adding fractions ? Why is the first step not necessary in the following? 13. j + } 15. } + 17. + + s + } 14. $ + 16. + 18. io + i + B + % Give the sums at sight: 19. 1 + 1+1 28. 14 + 4 + 4 + 4 20. + $+ } 29. 16+*+15+15 21. } +*+} 30. 11+++ 22. á + + 31. 16 +16 + 16 + 16 23. $ + f + f + 32. Zo + 23% + + 8 24. } +&++} 33. \ + i +1}+ i 25. lo + 4 + 1 + % 34. + 25 +265 +2 26. 12 + 12 + 35. 18 + 8 + 18+ is 27. 1 + $+$+ 36. 1+B7+15+ 37. A boy spent of his money for a knife, 4 of it for a ball, and į of it for his lunch. What part of his money did he spend ? 38. A grocer sold } of a pound of pepper to one customer, of a pound to another, and of a pound to another. What part of a pound did he sell? 39. I paid $t for milk, $ % for lettuce, and $% for butter. What part of a dollar did I pay for all ? 40. David paid of a dollar for a fishing rod, and of a dollar for a line. How much did he pay for both ? Adding fractions that are not similar. Written Work 1. Add s and 1 The fractions must first be made simi. 12 = C. d. lar. They may be changed to the com2 x 4 8 mon denominator twelfths. Multiplying 3 x 4 12 both terms of s by 4 changes it to in, and multiplying both terms of } by 3 changes 1 x 3 3 it to is. The sum of fi and is is 11. 4 x 3 12 + = 1) Fractions must be made similar before they can be added. Add, using a pencil; then orally: 2. 1 and } 8. ] and 14. f and 7. 1 and 1 13. į and } 19. } and 1 20. Henry had } of a dollar, and found of a dollar. How much had he then ? 21. Mary bought of a yard of red ribbon, I of a yard of blue ribbon, and i of a yard of white ribbon. yards of ribbon did she buy? 22. What is the total cost of a ball at of a dollar, a penknife at of a dollar, and a book at 1 of a dollar ? A mixed number is a number expressed by a whole number and a fraction, as 54, 33, 171. How many Adding mixed numbers when the sum of the fractions is less than a whole unit. = C. 24 Written Work 1. Add 2and 31. 12 d. and may each be changed to twelfths. Write 21 the common denominator (c. d.), 12, above the frac 1 x4 4 1 x 3 3 31 = 3, tions. 3 x 4 12' 4 x 3 12 The sum of the frac2} + 3} = 51. tions is ; and the sum of the integers is 5; 5 + 11 = 575. Add : 2. 51 3. 12} 4. 11 5. 351 603 871 14. A man walked 41 miles one hour, 41 miles the second hour, and 31 miles the third hour. How far did he walk ? 15. A farmer sold corn for $141, wheat for $37}, and rye for $ 1527. How much did he receive for all ? Adding mixed numbers when the sum of the fractions is greater than a whole unit. Written Work 123 = 129 15 1. Add 8f and 12%. 15 = c. d. f and may each be changed to fifteenths. 2 x 5 10. 3 x 3 8p= 813 9 ; The sum of if and 3 x 5 15'5 3 15 15 is 1%, which equals 11. The 1 is added 8f + 12 = 2012 or to the sum of 12 and 8, making 21, which 214 with 15, makes 2115. 4. 5. 321 6032 |