Question

Which of the following algebraic tiles represents the expression
$\frac{3}{4}(4u+8w-\frac{8}{3})?$

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\frac{3}{4}(4u+8w-\frac{8}{3})=(\frac{3}{4}\times 4u)+(\frac{3}{4}\times 8w)-(\frac{3}{4}\times \frac{8}{3})$
$=\left(3u\right)+(3\times 2w)-\left(2\right)$
$=3u+6w-2$

$3u+6w-2$ can be written as $u+u+u+w+w+w+w+w+w-1-1.$

So, to represent this we need:

3 tiles of this type


6 tiles of this type


And, 2 tiles of this type


Option A has 3 tiles of this type, 6 tiles of this type and 2 tiles of this type. So, it is the correct option.


Option B has 2 tiles of this type,6 tiles of this type and 2 tiles of this type.So, it is an incorrect option.


Option C has 3 tiles of this type,6 tiles of this typeand 1 tiles of this type.So, it is an incorrect option.


Option D has 3 tiles of this type,5 tiles of this type and 2 tiles of this type. So, it is an incorrect option.