Pre-Algebra - Associative Property of Multiplication

Which of the following displays the associative property of multiplication?

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

$a \cdot b = ab$

$a \cdot 1 = a$

$a \cdot 0 = 0$

$a(b \cdot c) = ab \cdot ac$

Explanation

The associative property of multiplication states that you can multiply numbers together in any order, and the answer will not change. Therefore,

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

displays the associative property of multiplication since the two sides are equal no matter which set of parentheses you solve first.

Which of the following best represents the associative property of multiplication?

$(A\times B)\times C = A\times (B\times C)$

$3\times 4=12$

$X^2 = X\cdot X$

$(6)+(9\cdot Y) = (9\cdot Y)+(6)$

Explanation

The property states that changing the order of multiplying any two numbers will not change the final answer.

$X\cdot Y = Y \cdot X$

Looking at the answer choices:

The answer $(A\times B)\times C = A\times (B\times C)$ is the best choice.

Which set of equations illustrates the Associative property of Multiplication?

The answer is not present.

Explanation

is the distributive property. Multiply each term in the parenthesis by the outside term.

is the Commutative property of Multiplication. The order of two like terms being multiplied does not change the product.

is the Multiplicative Identity property. Anything multiplied by 1 does not change.

${\color{Green} (6x^2*8)4x=6x^2(8*4x)}$ is Associative property of Multiplication. The grouping of terms does not change their product as long as all terms remain in the equation. Try the green equation without the variables to see for yourself.

If the below expression is written using the Associative Property of Multiplication, what are the values of and ?

$\left ( p \times 11\right ) \times 8 = 13 \times \left ( 11 \times q\right )$

$p=13,\ q=8$

$p=13,\ q=11$

$p=11,\ q=8$

$p=11,\ q=13$

$p=8,\ q=13$

Explanation

The rule for Associative Property of Multiplication is $\left ( a \times b\right )\times c = a \times \left ( b \times c\right )$

Using this rule, we can determine that for the given expression $\left ( p \times 11\right )\times 8 = 13 \times \left ( 11 \times q\right )$ ,

$p=13\ and\ q=8$

Associative Property of Multiplication

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