Question

1. create an equivalent expression using the commutative property of multiplication.

3 × r × 2
hint: image.png

Explanation:

Step1: Recall Commutative Property

The commutative property of multiplication states that for any numbers \(a\), \(b\), \(a\times b = b\times a\), and this can be extended to more than two factors (the order of multiplying factors can be changed without changing the product).

Step2: Apply to the Expression

We have the expression \(3\times r\times 2\). Using the commutative property, we can reorder the factors. Let's reorder \(r\) with the other numbers. So we can rewrite it as \(3\times 2\times r\) (or also \(r\times 3\times 2\), \(r\times 2\times 3\), \(2\times 3\times r\), \(2\times r\times 3\) since the commutative property allows any reordering of the factors in multiplication). Calculating \(3\times 2\) first (though not necessary for the equivalent expression, just to simplify the numerical part), we get \(6\times r\) or \(r\times 6\), but the key is the reordering of the factors. The most straightforward reordering of the original factors (keeping the numerical factors together first) is \(3\times 2\times r\) which simplifies to \(6r\), but even without simplifying the numbers, \(3\times 2\times r\) (or any permutation) is an equivalent expression. For example, \(2\times 3\times r\), \(r\times 3\times 2\), etc. A common equivalent expression by reordering is \(3\times 2\times r\) (or \(6r\), but the main idea is the commutative property application).

Answer:

\(3\times 2\times r\) (or \(2\times 3\times r\), \(r\times 3\times 2\), \(r\times 2\times 3\), \(2\times r\times 3\), \(3\times r\times 2\) is already the original, but a reordered one like \(3\times 2\times r\) or \(6r\) is equivalent. The simplest equivalent expression using commutative property (and simplifying the numbers) is \(6r\) or by just reordering the factors as \(2\times 3\times r\) etc. A common answer is \(3\times 2\times r\) (or \(6r\)).