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Associative Property of Multiplication

For any real numbers \(a\), \(b\), and \(c\)

$$\left( {a \times b} \right) \times c = a \times \left( {b \times c} \right)$$

If you multiply three numbers together, the product will be the same no matter how you group the numbers.

Suppose, we are given the following values

$$\displaylines{
  a = 4 \cr 
  b = 2 \cr 
  c = 7 \cr} $$

We plug them into the "formula"

$$\left( {a \times b} \right) \times c = a \times \left( {b \times c} \right)$$

We have

$$\displaylines{
  \left( {4 \times 2} \right) \times 7 = 4 \times \left( {2 \times 7} \right) \cr 
  8 \times 7 = 4 \times 14 \cr 
  56 = 56 \cr} $$

Great! The left side and the right side of the equation do have the same result. They have the same product of \(56\).

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