Given the equation w/W = d/D, how would you solve for w?

When solving the equation ( \frac{w}{W} = \frac{d}{D} ) for ( w ), it is essential to isolate ( w ) on one side of the equation. The equation represents a proportional relationship between ( w ) and ( W ) on one side and ( d ) and ( D ) on the other.

To isolate ( w ), you can rearrange the equation by cross-multiplying, which gives ( w \cdot D = W \cdot d ). This allows us to see that ( w ) can be expressed in terms of the other variables as follows:

[ w = \frac{W \cdot d}{D} ]

This manipulation shows that ( w ) is directly calculated by multiplying ( W ) by ( d ) and then dividing the result by ( D ).

The choice that represents this relationship is the one stating ( w = W \times \frac{d}{D} ). This shows the correct application of both multiplication and division to express ( w ) in terms of the other quantities involved in the equation, making it clear how each variable interacts to provide the desired solution for ( w \