Which two properties of numbers did Jamie use to solve 15 + 12 + 28 + 45 = 100 by grouping and adding pairs to get 60 and 40, then 60 + 40?

Which two properties of numbers did Jamie use to solve 15 + 12 + 28 + 45 = 100 by grouping and adding pairs to get 60 and 40, then 60 + 40?

• A. Commutative And Associative
• B. Distributive And Associative
• C. Identity And Inverse
• D. Closure And Distributive

Answer: (A)

You’re testing how addition allows you rearrange and regroup terms without changing the total. The commutative property lets you swap the order of addends, and the associative property lets you group them in convenient ways. Jamie used both by pairing numbers across the list to form 15 + 45 = 60 and 12 + 28 = 40, then added the partial sums: 60 + 40 = 100. This relies on being able to reorder and regroup the addends to make the calculation simpler. Identity and inverse wouldn’t explain forming those specific pairs to get 60 and 40, since there’s no use of adding 0 or canceling numbers here. Distributive isn’t at play because there’s no multiplication by a sum, and closure isn’t the mechanism for changing how the terms are combined.

You’re testing how addition allows you rearrange and regroup terms without changing the total. The commutative property lets you swap the order of addends, and the associative property lets you group them in convenient ways. Jamie used both by pairing numbers across the list to form 15 + 45 = 60 and 12 + 28 = 40, then added the partial sums: 60 + 40 = 100. This relies on being able to reorder and regroup the addends to make the calculation simpler.

Identity and inverse wouldn’t explain forming those specific pairs to get 60 and 40, since there’s no use of adding 0 or canceling numbers here. Distributive isn’t at play because there’s no multiplication by a sum, and closure isn’t the mechanism for changing how the terms are combined.