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• A fraction is of the form a/b, where a and b are integers and b is not zero.
• The number on top of a fraction is called the numerator.
• The number on the bottom is called the denominator.
• In a proper fraction, the magnitude of the numerator is less than the magnitude of the denominator.
• In order to add or subtract fractions we need to have a common denominator.
• When we multiply fractions, we just multiply the two numerators and multiply the two denominators.
• To divide two fractions, we turn the second fraction over and then multiply.

• A set is a collection of elements (objects in the set).
• We need to know the Universe (or universal set), U, from which elements of sets may be drawn.
• We list the elements of a set in curly brackets, or something similar.
• The empty set {} is often shown as ∅
• Order does not matter in a set.
• No duplicates are allowed in a set.
• We use the word "or" or the symbol ∪ ("cup") to get all the elements that are in one set or the other or both.
• We use the word "and" the symbol ∩ ("cap") to get only those elements that are in one set and are in the other set.
• We use the symbol ¬ ("not") to get those elements in the complement of the set, those elements from U that are not in the set. We also can use an apostrophe (') or a bar over the set to mean the complement. However, in this class, for quizzes and homeworks, please use the word "not".
• We use the symbols ∈, ⊂ and ⊃, to say that an element is contained in a set, that one set is contained in another or that one set contains another. The symbols ⊆ and ⊇ are sometimes used when it is important to emphasize the possibility that one set might be equal to the other, but in general every set is a subset of itself.
• When describing a set we use a vertical bar (∣) or the symbol _∋ (like element inclusion backwards and depressed) to say "such that".

1. Convert the following to a whole number and a proper fraction in lowest terms: 303/45

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2. Convert the following to a whole number and a proper fraction in lowest terms: -785/103

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3. Convert the following to a whole number and a proper fraction in lowest terms: 17/11

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4. Convert the following to a whole number and a proper fraction in lowest terms: 87/17

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5. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 4/12 + 7/28

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6. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 11/13 + 5/39

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7. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 38/17 + 4/51

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8. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 55/72 - 11/6

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9. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: 1/3 + 3/6 - 1/5

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10. For the following combination of fractions, perform the arithmetic, remove improper fractions and reduce to lowest terms: ((1/3)*(3/6))/(1/5)

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11. For the following combination of sets, perform the indicated operations: { 1, 2, 3, 4 } ∩ { 2, 4, 6, 8 }

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12. For the following combination of sets, perform the indicated operations: { 1, 2, 3, 4 } ∪ { 2, 4, 6, 8 }

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13. For the following combination of sets, perform the indicated operations: { 1, 2, 3, 4 } ∪ ( not { 2, 4, 6, 8 } ). Assume the universe is the set of non-negative whole numbers (0, 1, 2, ...)

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14. For the following combination of sets, perform the indicated operations: { n | n² < 36 } ∩ { m | 5m + 3 > 27 }. Assume the universe is the set of non-negative whole numbers (0, 1, 2, ...)

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15. Simplify (x² - x + 1) • (x + 1)

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16. Factor 16x² - 25

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17. Simplify (x+y-z)² - (x-y+z)² + x*(4*z -4*y)

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  <==== Do this AFTER you've answered all the questions

You probably DON'T want to do this ===>