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Additional info for Elementary and Intermediate Algebra: A Combined Approach
False 5. False 6. True 7. False 8. 3 17 Integers: Addition and Subtraction Objectives ■ Know the terminology associated with sets of integers. ■ Add and subtract integers. ■ Evaluate algebraic expressions for integer values. ■ Apply the concepts of adding and subtracting integers to model problems. ” Such examples illustrate our need for negative numbers. The number line is a helpful visual device for our work at this time. 1. 2. The set of whole numbers, along with Ϫ1, Ϫ2, Ϫ3, and so on, is called the set of integers.
What is the least common multiple of x and y if they are both prime numbers, and x does not equal y? Explain your answer. Rule for 5 A whole number is divisible by 5 if and only if the units digit of its base-10 numeral is divisible by 5. ) EXAMPLES 75. What is the least common multiple of x and y if the greatest common factor of x and y is 1? Explain your answer. Familiarity with a few basic divisibility rules will be helpful for determining the prime factors of some numbers. For example, if you can quickly recognize that 51 is divisible by 3, then you can divide 51 by 3 to find another factor of 17.
For example, (8 Ϫ 4) Ϫ 7 ϭ Ϫ3, whereas 8 Ϫ (4 Ϫ 7) ϭ 11. An example showing that division is not associative is (8 Ϭ 4) Ϭ 2 ϭ 1, whereas 8 Ϭ (4 Ϭ 2) ϭ 4. Identity Property of Addition If a is an integer, then aϩ0ϭ0ϩaϭa We refer to 0 as the “identity element” for addition. This simply means that the sum of any integer and 0 is exactly the same integer. For example, Ϫ197 ϩ 0 ϭ 0 ϩ (Ϫ197) ϭ Ϫ197. 5 Use of Properties 33 We call 1 the “identity element” for multiplication. The product of any integer and 1 is exactly the same integer.