Written Work 1. Change and to similar fractions having the common denominator 12. Since the denominator 3 in } must be multiplied by 4 to produce 12, the numerator must also be multiplied by 2 × 4 8 4, so as not to change the value of the fraction. 4 x 3 = 12 6 ÷ 3 = to its lowest terms. 2 2÷2 1 24+3 8' 8÷2 = 4 We can divide both terms, 6 and 24, of the fraction by 3 without changing the value of the fraction. The result is . We can then divide both terms 2 and 8 of the fraction by 2. The result is 8 14. 32 227 15. 18 21. Change to units. Thus, 1 unit = 2 halves. 4 halves there are 42, or 2, units. Change 10 to units. In 22. Change to units and parts of units. Thus, 1= 3 thirds. In 10 thirds there are 10÷3, or 3, units and remaining; that is, 31. 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. 12 25. 10 26. 12 27. 17 ADDITION OF FRACTIONS 1. Can you add and without change? Can you add and? What change must be made in and before they without change? Change both to tenths. Can they then be added? 5. Can you add 1⁄2 and without change? Change both to sixths. Can they then be added? 6. When and 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?? 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 1⁄2, 1, 1; 1, 1; 1, 76; 3, 4, 12; 1, 1, 15. 11. Observe that in problem 10, 1 + 1 + 1 = §, or 1, and that 1+1+12= 11⁄2, or }. 12. What is the third step in adding fractions? Why is the first step not necessary in the following? 24. § +号+号+} 25. 10+ 10+ 10+ 10 26. 12+12+12 27. 1 + 2 + 3 + 4 37. A boy spent ball, and 31. 18+18+16 +16 8 of his money for a knife, of it for a 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 $ for milk, $ for lettuce, and $ for butWhat part of a dollar did I pay for all? ter. 40. David paid of a dollar for a fishing rod, and of a dollar for a line. How much did he How much did he pay for both? Adding fractions that are not similar. Fractions must be made similar before they can be added. How much had he then ? 21. Mary bought of a yard of red ribbon, blue ribbon, and of a yard of white ribbon. yards of ribbon did she buy? of a yard of How many 22. What is the total cost of a ball at of a dollar, a penknife at of a dollar, and a book at of a dollar? A mixed number is a number expressed by a whole number and a fraction, as 51, 33, 171. Adding mixed numbers when the sum of the fractions is less than a whole unit. Written Work and may each be changed to twelfths. Write the common denominator (c. d.), 12, above the frac = 33tions. 1 x 4 3 x 4 4 1 x 3 3 12' 4 × 3 = 12 The sum of the frac 21+3=512 tions is and the sum of the integers is 5; 5+1=5. 13 |