Associative Property
Changing the grouping of numbers will NOT change the value. For example: (7 + 4) + 8 = 7 + (4 + 8) also works with multiplication
The associative property is a fundamental rule in mathematics that applies to addition and multiplication operations. The associative property states that regardless of how we group three or more numbers whose values will be added or multiplied, the result will be the same. In other words, if we have the numbers a, b, and c, for example, then the associative property states that (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).
For example, let’s say we have the numbers 2, 3, and 4. According to the associative property;
– (2 + 3) + 4 = 5 + 4 = 9 and 2 + (3 + 4) = 2 + 7 = 9, so we can see that addition is associative.
– (2 × 3) × 4 = 6 × 4 = 24 and 2 × (3 × 4) = 2 × 12 = 24, so we can see that multiplication is associative.
The associative property is a useful tool for simplifying mathematical expressions by rearranging the grouping of terms. It also helps us to understand the commutative property, which states that the order in which we add or multiply numbers does not affect the result.
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