Question

Any groups of 2+4 can you form using the associative and commutative properties of multiplication?

a) 2 x (4+2)
b) (2+4) x 2
c) (2 x 4) + (2 x 4)
d) (2 x 2) + (4 x 4)

Answer 1

Expressions a and b make use of the associative and commutative properties of multiplication, respectively. Expression a groups (4+2) together, while expression b shows that the order of multiplication (2+4) x 2 does not affect the result. Expressions c and d do not demonstrate these properties.

The question involves identifying which expressions use the associative and commutative properties of multiplication. Here are the properties at play:

• The associative property allows us to group numbers during multiplication without changing the result, such as (a × b) × c = a × (b × c).
• The commutative property states that you can swap numbers around in multiplication and still get the same result, such as a × b = b × a.

Let's analyze the given expressions:

2 x (4+2): This expression uses the associative property because you're grouping (4+2) before multiplying by 2.

1. (2+4) x 2: This uses the commutative property since it's equivalent to 2 x (2+4), demonstrating that the order of multiplication does not affect the result.
2. (2 x 4) + (2 x 4): This expression does not use the associative or commutative property. It is an example of repeated addition of the product of 2 and 4.
3. (2 x 2) + (4 x 4): Similarly, this expression does not demonstrate associative or commutative properties as it is simply the sum of two different products.

Therefore, expressions a and b demonstrate the use of the associative and commutative properties, respectively.