Two gears are connected and rotating at the same time. The smaller gear completes 2 1/2 rotations every time the larger gear completes 1/4 of a rotation.
How many rotations does the smaller gear complete when the larger gear completes 1 rotation?
Drag and drop the correct value into the box.
The gear ratio between the smaller gear and the larger gear is given by the ratio of their number of rotations.
Let's represent the number of rotations of the smaller gear as "x" and the number of rotations of the larger gear as "1".
According to the given information, the ratio between the number of rotations is 2 1/2 : 1/4.
To simplify the ratio, we convert 2 1/2 to an improper fraction: 2 1/2 = 5/2.
Therefore, the ratio becomes 5/2 : 1/4.
To find the value of "x", we need to solve the proportion:
5/2 = x / 1/4
To solve the proportion, we multiply both sides by the reciprocal of 1/4, which is 4/1:
(5/2) * (4/1) = x
Multiplying the fractions, we get:
20/2 = x
10 = x
Therefore, the smaller gear completes 10 rotations when the larger gear completes 1 rotation.