1 Evaluate the three Circles of Evaluation below to help you decided if the Associative Property holds for problems involving multiplication:
(* (* 2 5) 10) |
(* 2 (* 5 10)) |
(2 × 5) × 10 = ? |
2 × (5 × 10) = ? |
What do you notice?
These Circles of Evaluation illustrate the Associative Property of Multiplication, which tells us that when you multiply three numbers, it does not matter whether you start by multiplying the first pair of numbers or the last pair of numbers. Draw another example of the Associative Property of Multiplication with any three numbers, below. Make sure that each expression includes a different pair of numbers grouped together. Evaluate your expressions to confirm that they are equivalent.
2 Evaluate the Circles of Evaluation below to help you decide whether or not the Associative Property holds for problems involving division.
(/ (/ 20 10) 2) |
(/ 20 (/ 10 2)) |
(20 ÷ 10) ÷ 2 = ? |
20 ÷ (10 ÷ 2) = ? |
Explain your response.
Draw another example like the one above to confirm what you observed about the Associative Property and division.
These materials were developed partly through support of the National Science Foundation, (awards 1042210, 1535276, 1648684, 1738598, 2031479, and 1501927). 
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