Properties of real numbers - Math 208 ALEKS RED Properties...

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Math 208 ALEKS RED Properties of real numbers In this concept, you will be working with 10 properties of real numbers: 1. Commutative Property of Addition 2. Associative Property of Addition 3. Additive Identity Property 4. Additive Inverse Property 5. Distributive Property 6. Commutative Property of Multiplication 7. Associative Property of Multiplication 8. Multiplicative Identity Property 9. Multiplication Property of Zero You will be given four or five true statements and asked to identify which of the 10 properties applies to this statement. Keep the following chart handy: PROPERTIES OF ADDITION PROPERTIES OF MULTIPLICATION Commutative (order) x + y = y + x x • y = y • x or xy = yx Associative (grouping) (x + y) + z = x + (y + z) (x • y) • z = x • (y • z) or (xy)z = x(yz) Identity (returns itself) x + 0 = x or 0 + x = x x • 1 = x or 1 • x = x Inverse (opposite 0 or 1) x + (-x) = 0 or -x + x = 0 = = 1 1 1 1 x x x x or Distributive ( • through + ) x(y + z) = xy + xz or (x + y)z = xz + yz Multiplicative Property of Zero (multiply by 0 = 0) 0 • x = 0 or x • 0 = 0 Now, let’s look at the chart and try to understand what it is telling us:
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