Question

What is the difference between the ratio AP:PB and the ratio of AP:AB?

Answer 1

AP:PB compares parts to parts. AP:AB compares parts to a whole, this ratio equals K.

Answer 2

A line segment can be divided into subsegment using ratios. The difference between $AP:PB$ and $AP: AB$ is that:

• Ratio $AP:PB$ compares the two subsegments of AB while
• Ratio $AP: AB$ compares a segment of AB to the whole length of AB.

Given:

$AP:PB$ and $AP: AB$

In $AP:PB$, we can see that AP and PB has a common point (P).

This means that:

$AB = AP + PB$

i.e. AP and PB are two subsegments of line segment AB.

So, the ratio $AP:PB$ compares the two subsegments of AB

Because AP and PB are two subsegments of line segment AB.

Then, ratio $AP: AB$ compares a segment of AB to the whole length of AB.

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