MULTIPLYING RATIONAL NUMBERS LESSON 8

Multiplying Integers Positive x Positive = Positive Positive x Negative = Negative Negative x Negative = Positive Negative x Positive = Negative An odd number of Negatives multiplied together gives a negative result. An even number of Negatives multiplied together gives a positive result.

EXAMPLES: Positive x Positve Positve x Negative Negative x Negative = + 40 Positive x Positve (+7) x (-6) = - 42 Positve x Negative (-4) x (-3) = + 12 Negative x Negative (-8) x (+9) = - 72 Negative x Positive (-4) x (-2) x (-3) = - 24 Odd number of Negatives (-1) x (-9) x (-3) x (-2) = + 54 Even number of Negatives

Multiplying Rational Numbers 1) Use the SAME RULES for Rational numbers as you did for Integers. 2) Same rules as you did for Fractions  multiply the two numerators and the two denominators. REMEMBER: If there are negative signs to place them in the numerator.

EXAMPLES 3 5 3 5 9 25 x = 2 5 -3 4 -6 20 x = -4 7 -3 8 12 56 x = NEGATIVE x NEGATIVE = POSITIVE

MORE EXAMPLES -4 -5 -3 6 x = 2 5 -3 4 2 x = -2 3 -3 4 -3 -2 x x =

MORE EXAMPLES -12 30 -4 -5 -3 6 2 5 -3 4 -2 3 -3 4 -3 -2 2 x = x = x x

MORE EXAMPLES -4 -5 -3 6 -12 30 -2 5 2 5 -3 4 -2 3 -3 4 -3 -2 2 = x = ODD Number of Negatives = Negative = x = Reduced to LOWEST TERMS 2 5 -3 4 2 x = -2 3 -3 4 -3 -2 x x =

MORE EXAMPLES -2 5 -4 -5 -3 6 2 5 -3 4 12 5 -3 4 -2 3 -3 4 -3 -2 2 x = CHANGE MIXED TO AN IMPROPER FRACTION 2 5 -3 4 12 5 -3 4 2 x = x = -2 3 -3 4 -3 -2 x x =

MORE EXAMPLES -2 5 -4 -5 -3 6 2 5 -3 4 12 5 -3 4 -36 20 -2 3 -3 4 -3 = 2 5 -3 4 12 5 -3 4 -36 20 2 x = x = = -2 3 -3 4 -3 -2 x x =

MORE EXAMPLES -2 5 -4 -5 -3 6 2 5 -3 4 12 5 -3 4 -36 20 4 5 -2 3 -3 4 = Change back to mixed and reduce fraction 2 5 -3 4 12 5 -3 4 -36 20 4 5 2 -1 x = x = = Positive x Negative = Negative -2 3 -3 4 -3 -2 x x =

MORE EXAMPLES -2 5 -4 -5 -3 6 2 5 -3 4 4 5 -2 3 -3 4 -3 -2 18 24 2 -1 = 2 5 -3 4 4 5 2 -1 x = -2 3 -3 4 -3 -2 18 24 x x =

MORE EXAMPLES -2 5 -4 -5 -3 6 2 5 -3 4 4 5 -2 3 -3 4 -3 -2 18 24 3 4 2 = 2 5 -3 4 4 5 2 -1 x = Reduce to LOWEST TERMS -2 3 -3 4 -3 -2 18 24 3 4 x x = = EVEN Number of Negatives = Positive

YOU TRY! -4 5 3 7 = x -5 8 3 -7 -2 -4 x x = 1 6 3 7 -1 x =