Commutative Property of Multiplication - Pre-Algebra

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Question

Which property is illustrated by the example:

$4\times 3=3\times 4$

Answer

The commutative property of mulitplication states that the order in which 2 numbers are multiplied does not affect the result:

$a\times b=b\times a$

Or in this case,

$4\times 3=3\times 4$

$4\times3=12$

$3\times 4=12$

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Question

Which of the following equations correctly shows the commutative property of multiplication?

Answer

The commutative property states that factors can be multiplied in any order and the product is always the same. While each of our answer choices are real equations, only one correctly displays this property:

$a\times b = b\times a$

$3\times6\times4 = 6\times4\times3$

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Question

Evaluate the following expression without using a calculator

$\frac{7}{13}\frac{11}{8}\frac{4}{17}\frac{8}{11}\frac{6}{19}\frac{13}{7}\frac{19}{6}*\frac{17}{4}$

Answer

This problem could easily turn into some super heavy calculations, but nobody has time for that. Instead, we can make this problem very easy by utilizing the commutative property of multiplication, which in essence says that numbers can be multiplied in any order.

In other words, and

That means that rather multiplying our numbers in their orginal order, which can actually change the order of the numbers without affecting the final product. At this point we should notice that one of our numbers is $\frac{7}{13}$ while another is $\frac{13}{7}$ . Similarly the fractions $\frac{4}{17}, \frac{6}{19},$ and $\frac{11}{8}$ are each accompanied by their recripocals $\frac{17}{4}, \frac{19}{6},$ and $\frac{8}{11}$ respecitively. At this point we must also remember the multiplicative inverse property, which tells us that the product of a number and its reciprocal will always be 1. With that in mind, the strategic way to order the multiplication is as follows:

$\frac{7}{13}\frac{13}{7}\frac{4}{17}\frac{17}{4}\frac{6}{19}\frac{19}{6}\frac{11}{8}\frac{8}{11}$

Doing this pairs each number up with its reciprocal. Finally, we can utlize the associative properpty of multiplication, which tells us that we can multiply any two numbers at a time.

In other words, . This allows us to pair off the multiplication as follows.

$\left(\frac{7}{13}\frac{13}{7}\right)\left(\frac{4}{17}\frac{17}{4}\right)\left(\frac{6}{19}\frac{19}{6}\right)\left(\frac{11}{8}\frac{8}{11}\right)$

Within each parentheses we now have a number multiplied by its reciprocal. Remembering that this always equals 1, we can simplify, giving

Our answer is 1.

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Question

Use the Commutative Property of Multiplication to write the below expression in a different way.

$6 \times x^{1/2}$

Answer

The rule for Commutative Property of Multiplication is $a \times b = b \times a$

Using this rule, the expression $6 \times x^{1/2}$ can be written as $x^{1/2} \times 6$

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Question

Which answer shows the communitive property of multiplication to the equation below?

Answer

The communitive property of multiplication is a property that states that the numbers can be multiplied in any combination. To show which answer is correct simply regroup the numbers in a different or and you will have your answer.

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Question

Which of the following displays the commutative property of multiplication?

Answer

The commutative property of multiplication states that 2 numbers can be multiplied in any order. Therefore,

$a \cdot b = b \cdot a$

displays the commutative property of multiplication.

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