Question

Select the number property that will justify the following expression.

If cba represents three numbers multiplied together, what property allows you to rearrange the factors to read abc?

Answer 1

Answer: The Commutative law. It states a * b = b * a.

So, cba is the same as abc.

Step-by-step explanation:

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication that are stated symbolically as a + b = b + a and ab = ba. From these laws it follows that any finite sum or product is unaltered by reordering its terms or factors.

Answer 2

Answer and Explanation:

The number property that allows the re-ordering of multiplication:

`c\cdot b \cdot a` to
`a\cdot b\cdot c`

is the Commutative Property of Multiplication.

This property states that
`A\cdot B = B\cdot A`.

We can test this property by plugging in numbers for A and B.

For example, if
`A = 2` and
`B=3`:

`A\cdot B = 2 \cdot 3`

`\implies \text{ this is an array of 2 rows and 3 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square \ \ \square\ \ \square \\ \square \ \ \square\ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}`

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`B\cdot A = 3 \cdot 2`

`\implies \text{ this is an array of 3 rows and 2 columns:}\\\\\text{ } \ \ \ \ \ \ \begin{array}{c c c} \square\ \ \square \\ \square\ \ \square \\ \square \ \ \square \end{array} \\ \\ \text{ } \ \ \ \ \ \ \implies 6 \text{ items}`

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From this example, we can figure out that:

`A \cdot B = B \cdot A = 6`