A Disturbing Distribution

Strategies and Hints

For a distributive property of addition over multiplication tohold, the fractions must sum to 1. Any combination of such fractions will then work.

To see this, let . The left side of the property would be.

The right side of the property would be

which is the same as the left side of the property.

Extension:

  1. No, they do not. Using the numbers in the problem shows that the two sides of the equations are not equal.

  2. No. The fractions do not satisfy these possible distributive properties.