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**DIVIDING RATIONAL NUMBERS**

LESSON 9

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**Dividing Integers Positive ÷ Positive = Positive**

Positive ÷ Negative = Negative Negative ÷ Negative = Positive Negative ÷ Positive = Negative An odd number of Negatives divided together gives a negative result. An even number of Negatives divided together gives a positive result.

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**EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative**

(10) ÷ (+5) Positive ÷ Positive (+36) ÷ (-6) Positive ÷ Negative (-12) ÷ (-3) Negative ÷ Negative (-54) ÷ (+9) Negative ÷ Positive (-12) ÷ (-2) ÷ (-3) Odd number of Negatives (-60) ÷ (-2) ÷ (-3) ÷ (-2) Even number of Negatives

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**EXAMPLES: Positive ÷ Positive = Positive Positive ÷ Negative**

(10) ÷ (+5) = 2 Positive ÷ Positive = Positive (+36) ÷ (-6) Positive ÷ Negative (-12) ÷ (-3) Negative ÷ Negative (-54) ÷ (+9) Negative ÷ Positive (-12) ÷ (-2) ÷ (-3) Odd number of Negatives (-60) ÷ (-2) ÷ (-3) ÷ (-2) Even number of Negatives

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**EXAMPLES: Positive ÷ Positive Positive ÷ Negative = Negative**

(10) ÷ (+5) = 2 Positive ÷ Positive (+36) ÷ (-6) = -6 Positive ÷ Negative = Negative (-12) ÷ (-3) Negative ÷ Negative (-54) ÷ (+9) Negative ÷ Positive (-12) ÷ (-2) ÷ (-3) Odd number of Negatives (-60) ÷ (-2) ÷ (-3) ÷ (-2) Even number of Negatives

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**EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative**

(10) ÷ (+5) = 2 Positive ÷ Positive (+36) ÷ (-6) = -6 Positive ÷ Negative (-12) ÷ (-3) = 4 Negative ÷ Negative = Positive (-54) ÷ (+9) Negative ÷ Positive (-12) ÷ (-2) ÷ (-3) Odd number of Negatives (-60) ÷ (-2) ÷ (-3) ÷ (-2) Even number of Negatives

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**EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative**

(10) ÷ (+5) = 2 Positive ÷ Positive (+36) ÷ (-6) = -6 Positive ÷ Negative (-12) ÷ (-3) = 4 Negative ÷ Negative (-54) ÷ (+9) = - 6 Negative ÷ Positive = Negative (-12) ÷ (-2) ÷ (-3) Odd number of Negatives (-60) ÷ (-2) ÷ (-3) ÷ (-2) Even number of Negatives

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**EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative**

(10) ÷ (+5) = 2 Positive ÷ Positive (+36) ÷ (-6) = -6 Positive ÷ Negative (-12) ÷ (-3) = 4 Negative ÷ Negative (-54) ÷ (+9) = - 6 Negative ÷ Positive (-12) ÷ (-2) ÷ (-3) = - 2 Odd number of Negatives = Negative (-60) ÷ (-2) ÷ (-3) ÷ (-2) Even number of Negatives

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**EXAMPLES: Positive ÷ Positive Positive ÷ Negative Negative ÷ Negative**

(10) ÷ (+5) = 2 Positive ÷ Positive (+36) ÷ (-6) = -6 Positive ÷ Negative (-12) ÷ (-3) = 4 Negative ÷ Negative (-54) ÷ (+9) = - 6 Negative ÷ Positive (-12) ÷ (-2) ÷ (-3) = - 2 Odd number of Negatives (-60) ÷ (-2) ÷ (-3) ÷ (-2) = 5 Even number of Negatives = Positive

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**DIVIDING RATIONAL NUMBERS**

Change the fraction after the division sign to its Reciprocal and multiply the fractions by: Multiply the numerators of the fractions Multiply the denominators of the fractions Place the product of the numerators over the product of the denominators Simplify the Fraction

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -3 5 9 4 x

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -3 5 9 4 x -27 20

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -3 5 9 4 x -27 20 7 20 -1

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**EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 -2 -5 7 6 -3 5 9 4 -27 20 ÷ ÷ ÷**

-1

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 -3 5 9 4 x x 14 30 -27 20 Notice the fraction is positive 7 20 -1

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 -3 5 9 4 x x 14 30 -27 20 7 15 7 20 -1

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 4 7 -13 8 -3 5 9 4 x x x 14 30 -27 20 Notice the negative stays in the numerator. Becomes Positive 7 15 7 20 -1

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 4 7 -13 8 -3 5 9 4 x x x 14 30 -52 56 -27 20 7 15 7 20 -1

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EXAMPLE -3 5 4 9 -2 -5 6 7 -4 -7 -8 13 ÷ ÷ ÷ -2 -5 7 6 4 7 -13 8 -3 5 9 4 x x x 14 30 -52 56 -27 20 7 15 -13 14 7 20 -1

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**MORE EXAMPLES 3 5 3 5 -8 5 3 5 5 3 -8 5 2 3 -40 15 -8 3 ÷ ÷ -1 -2 x =**

Change Mixed to an Improper. -8 5 3 5 ÷ 5 3 -8 5 Reciprocal. x 2 3 -40 15 -8 3 -2 = =

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