Show how to solve the problem 378×6 using place value with regrouping. Explain how you knew when to regroup

1 answer:

7 0

1. 6 (378) = 2268 = (189 + 189)6

Properties are:
Addition, you can have 6 + 107 = 113 
Commutative Property by moving: 107 + 6 = 113
Associative Property by grouping: (3 + 3) + (100 + 7 ) = 113
Distributive Property by allotting: 2 (3) + 107 = 113

Multiplication, you can have 6 x 107 = 642
Commutative Property by moving: 107 x 6 = 642
Associative Property by grouping: (3 + 3) x (100 + 7 ) = 642
Distributive Property by allotting: 2(3) x 107 = 642

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$\left[\begin{array}{cccccccc}&1&2&3&4&5&6\\--&--&--&--&--&--&--\\1\;|&1&2&3&4&5&6\\2\;|&2&2&3&4&5&6\\3\;|&3&3&3&4&5&6\\4\;|&4&4&4&4&5&6\\5\;|&5&5&5&5&5&6\\6\;|&6&6&6&6&6&6\end{array}\right]$

From this table we can compute the probabilities :

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So the expected value equals

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