4-2    Describing Patterns with Variables




Give the general pattern from the three instances given.

1.     5 × 1 = 5                                            2.      4 + 3 = 3 + 4                                        3.     6 × 0 = 0
        9 × 1 = 9                                                     6 + 2 = 2 + 6                                                2 × 0 = 0
        3.2 × 1 = 3.2                                               2.3 + 5 = 5 + 2.3                                          5 × 0 = 0

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4.     5 + 5 + 1 = 2 × 5 + 1                                           5.    4 × (3 + 6) = (4 × 3) + (4 × 6 )
        7 + 7 + 1 = 2 × 7 + 1                                                  7 × (5 + 1) = (7× 5) + ( 7 × 1)
        9 + 9 + 1 = 2 × 9 + 1                                                  6 × (2 + 8) = (6 × 2) + (6 × 8)

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6.     4 triangles have 12 legs.                                       7.      3 people have 30 toes.
        7 triangles have 21 legs.                                                4 people have 40 toes.
        9 triangles have 27 legs.                                                9 people have 90 toes.

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Give two instances of the general pattern.

9.    25% of n =  n/4                                                        10.    n/1 = n

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11.    a × b = b × a                                                        12.    4 × n = n + n + n + n

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