Juan learned that gear ratio refers to the number of times one gear rotates in relation to another gear. the ratio of the gears in the picture below is 1 1/2 to 1/2 write two unit rates to represent the gear ratio above

As stated, gear ratio is the number of times one gear rotates in relation to the other.
This means that, to calculate the gear ratio, we will simply divide the ratio of one gear by the ratio of the other.

First unit rate:
The first gear has a ratio of 1.5
The second gear has a ratio of 0.5
The gear ratio of the first gear to the second one will be:
1.5 : 0.5   (convert to fractions)
3/2 : 1/2   (multiply by 2 to get rid of denominators)
3    :  1

Second unit rate:
The first gear has a ratio of 1.5
The second gear has a ratio of 0.5
The gear ratio of the second gear to the first one will be:
0.5 : 1.5   (convert to fractions)
1/2 : 3/2   (multiply by 2 to get rid of denominators)
1    :  3

Both unit rates imply that the second gear does one complete rotation in the same time required by the first gear to do three complete rotations.

Hope this helps :)

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste