Symbolic Abstraction Math Example 4

Follow the full solution, then compare it with the other examples linked below.

medium

V = lwh

, what happens to

V

when all three dimensions are halved?

1
Replace each with half: $V_{\text{new}} = (\frac{l}{2})(\frac{w}{2})(\frac{h}{2}) = \frac{lwh}{8}$ .
2
$V_{\text{new}} = \frac{V}{8}$ . The volume is divided by 8.

Answer

Volume is divided by 8.

Symbolic reasoning shows that halving all three dimensions of a box reduces the volume by a factor of

2^3 = 8

About Symbolic Abstraction

Using letter symbols to represent mathematical concepts in a form that holds independent of any specific numerical values.

The area of a circle is [formula]. Without knowing [formula], what happens to [formula] if [formula]

If [formula] and [formula], what is [formula]?

If [formula] and [formula] when [formula], find [formula].