Skill: Simplify ratios

A ratio compares two quantities in a specific order. To simplify a ratio, divide every term by the same greatest common factor (GCF).

Example

Simplify the ratio $18:24$.

1. Find the greatest common factor of $18$ and $24$.

   The factors they share include $1, 2, 3,$ and $6$, so the GCF is $6$.

2. Divide both parts of the ratio by $6$:

$$18:24=(18\div 6):(24\div 6)$$

3. Calculate:

$$18:24=3:4$$

So, the simplified ratio is $\boxed{3:4}$.

The order stays the same: $18:24$ becomes $3:4$, not $4:3$. Dividing both terms by the same number keeps the relationship equivalent.