Division: Divides the numerator into pieces, each of which is the size of the denominator.

Ratio: 2 kinds

Like quantities- the ratio gives the size of the top with respect to the bottom.

Examples: 30 stories/ 60 stories tells us that the top building is 1/2 the size of the bottom one. 10m / 2m tells us the top board is 5 times as long as the bottom one.

Unlike quantities: The ratio tells how many of the numerator for each 1 of the denominator.

Distance - Gives the total length an object travels.

Displacement - Gives the location of an object relative to a reference point, both distance from it and what direction.

Change in displacement - gives the total distance an object's final location is from it's point of origin, and also the direction of travel.

Average speed - tells how far, on average, an object traveled each second.

Average velocity-tells how far, and in what direction, on average, an object traveled each second.

Instantaneous speed- Tells how far, an object would go in the next second, if it continued at this pace.

Instantaneous Velocity- Tells how far, an object would go in the next second, if it continued at this pace, and in what direction.

Is distance just the magnitude of displacement? No.

Is speed just the magnitude of velocity? Yes and no. Instantaneous speed is the magnitude of instantaneous velocity, but average speed is not the magnitude of average velocity.

Acceleration: Gives no information about the present, it's about the future!

Average acceleration- Tells how much further an object will travel, and in what direction, on average, in the next second.

Instantaneous acceleration- Tells how much further an object will travel, and in what direction, in the next second.