Question 4

Addition and Multiplication are associative operations.

Both addition and multiplication exhibit the associative property, which means that the grouping of numbers does not affect the result of the operation.

A) Addition

Addition is an associative operation because changing the grouping of the numbers being added does not change the sum. For example, (2 + 3) + 4 equals 2 + (3 + 4), both resulting in 9.

B) Subtraction

Subtraction is not associative as changing the grouping can change the result. For instance, (5 - 3) - 2 equals 0, while 5 - (3 - 2) equals 4, demonstrating that the outcome varies with different groupings.

C) Multiplication

Multiplication is associative because the way in which factors are grouped does not affect the product. For example, (2 × 3) × 4 equals 2 × (3 × 4), both yielding 24.

D) Division

Division is not associative, as altering the grouping can lead to different results. For example, (8 ÷ 4) ÷ 2 equals 1, while 8 ÷ (4 ÷ 2) equals 4, illustrating inconsistency with different groupings.

E) Exponentiation

Exponentiation is not associative either, since changing the grouping affects the outcome. For example, (2^3)^2 equals 64, while 2^(3^2) equals 512, showing a significant difference in results.

Conclusion

In summary, addition and multiplication are the only operations listed that are associative, as they maintain consistent results regardless of how numbers are grouped. In contrast, subtraction, division, and exponentiation do not satisfy this property, resulting in different outcomes based on grouping.