Question

Explain how the Associative Property can be used to mentally find the volume of the prisms shown

Answer 1

Answer:

A prism is a solid object having two identical bases, hence the same cross section along the length. This is a rectangular prism its base is a rectangle. multiplying the three dimensions of a rectangular prism: length, width and height, gives us the volume of a prism:

$V=L\times W\times H$

Therefore, Associative Property can be used to mentally find the volume of the prisms shown by selecting the easier way of the multiplication. For instance, we can say that:

$L=5cm \\ \\ W=18cm \\ \\ H=20cm$

In whose case:

$V=5\times 18\times 20$

To operate this mentally is not an easy way, but what if we rotate this shape? so we say that:

$L=18cm \\ \\ W=20cm \\ \\ H=5cm$

Then, the volume can be found as:

$V=18\times 20\times 5$

There are two forms of finding the result. First, multiplying 18 by 20 and then the result by 5, but as in the previous case this is a tricky way to do mentally:

$V=(18\times 20)\times 5$

Hence, here we can use Associative Property multiplying 20 by 5 and then the result by 18:

$V=18\times (20\times 5)$

This last arrangement is easier because 20 x 5 is easy to remember given that the result is 100. Then, by multiplying this result by 18 then we get 1800.