Definition:Division in Ratio

Definition

Let a quantity $X$ be partitioned into parts which are in a given ratio to one another.

Then $X$ is divided in (the given) ratio.

Straight Line

Let $A$, $B$ and $P$ be collinear points.

Then:

$P$ divides $AB$ in the ratio $m : n$

if and only if:

$AP : PB = m : n$

where $AP$ and $PB$ are directed line segments.

Examples

Arbitrary Example $1$

The number $100$ is divided in the ratio $2 : 3$ by the parts $40$ and $60$.

Arbitrary Example $2$

The number $150$ is divided in the ratio $1 : 2 : 3$ by the parts $25$, $50$ and $75$.

Also see

• Results about division in ratio can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): division in a given ratio: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): division in a given ratio: 1.