Question

PLEASE HELP!!

use the commutative property to simplify the expression.

Answer 1

C.
`16 \cdot (1)/(8) \cdot \frac{2}5 = 2 \cdot \frac{2}5 = (4)/(5)`

Explanation:

The commutative property of multiplication states that the reordering of factors does not change the product. In equation form:

`a \cdot b = b \cdot a`

We can use this property to simplify the given expression:

`\frac{1}8\cdot \frac{2}5 \cdot 16`

by ordering the factors so that the whole number (16) is multiplied by the fraction whose denominator is one of its factors.

In this case, that fraction is
`(1)/(8)`, as its denominator (8) is a factor of 16:

`8 \cdot 2 = 16` ... thus,

`16 \cdot \frac{1}8 = 2`

So, the expression can first be rewritten using the commutative property:

`16 \cdot (1)/(8) \cdot \frac{2}5`

Then, it can be simplified by multiplying the first two factors:

`2 \cdot \frac{2}5`

Finally, it can be fully simplified by multiplying the remaining two factors:

`\boxed{(4)/(5)}`