Question

Which of the following options is an example of the associative property of multiplication?

• A. $(5\times 3)+2=5\times (3+2)$
• B. $5\times (4+2)=2\times (4+5)$
• C. $(5\times 3)\times 2=5\times (3\times 2)$
• D. $(5+3)\times 2=5+(3\times 2)$

Answer 1

The correct option is C $(5\times 3)\times 2=5\times (3\times 2)$

Let’s check the options one by one.

Associative property states that the product of three or more numbers remains the same regardless of how the numbers are grouped.

Option A:
$\bullet$ $(5+3)\times 2=5+(3\times 2)$
$8\times 2=5+6$
$16\ne 11(\ne$ sign means the two numbers are not equal)
$\star$ This statement is incorrect as the numbers on two sides are not equal.

Option B:
$\bullet$ $(5\times 3)\times 2=5\times (3\times 2)$
$15\times 2=5\times 6$
$30=30$
$\star$ So, this is an example of the associative property of multiplication.

Option C:
$\bullet$ $(5\times 3)+2=5\times (3+2)$
$15+2=5\times 5$
$17\ne 25$
$\star$ This statement is incorrect as the numbers on two sides are not equal.

Option D:
$\bullet$ $5\times (4+2)=2\times (4+5)$
$5\times 6=2\times 9$
$30\ne 18$
$\star$ This statement is incorrect as the numbers on two sides are not equal.

All the options are not expressed as the product of numbers. Some of them are being added. The associative property does not apply to them.

Hence, B is the correct answer.