By Alan S. Tussy
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333333 . . 454545 . . 45 28 CHAPTER 1 An Introduction to Algebra Define the Set of Irrational Numbers. 1 inch in ch es 1 inch √2 1 inch Not all numbers are rational numbers. One example is the square root of 2, written 22. It is the number that, when multiplied by itself, gives 2: 22 ؒ 22 ϭ 2. It can be shown that 22 cannot be written as a fraction with an integer numerator and an integer denominator. Therefore, it is not rational; it is an irrational number. It is interesting to note that a square with sides of length 1 inch has a diagonal that is 22 inches long.
23. 25. 75 28 81 117 220 1,254 16. 18. 20. 22. 24. 26. 20 54 125 147 270 1,144 Perform each operation. See Examples 2 and 3. 27. 5 1 ؒ 6 8 28. 2 1 ؒ 3 5 29. 7 3 ؒ 11 5 30. 13 2 ؒ 9 3 31. 3 2 Ϭ 4 5 32. 7 6 Ϭ 8 13 6 5 33. Ϭ 5 7 4 3 34. Ϭ 3 2 Build each fraction or whole number to an equivalent fraction with the indicated denominator. See Example 4. 35. 1 3, denominator 9 4 36. 3 8, denominator 24 9 37. 9 , denominator 54 38. 16 , denominator 64 39. 7, denominator 5 40. 12, denominator 3 41. 5, denominator 7 42.
7 b. 2 10. What two equivalent fractions are shown? VOCABULARY Fill in the blanks. 1. A factor is a number being . 2. Numbers that have only 1 and themselves as factors, such as 23, 37, and 41, are called numbers. 3. When we write 60 as 2 ؒ 2 ؒ 3 ؒ 5, we say that we have written 60 in form. of the fraction 34 is 3, and the 4. The is 4. 5. Two fractions that represent the same number, such as 12 and 24 , are called fractions. 6. 23 is the of 32 , because their product is 1. 7. The common denominator for a set of fractions is the smallest number each denominator will divide exactly.
