Simplify ratios

Simplifying a ratio means expressing the same multiplicative relationship with the smallest possible whole-number terms by dividing every part of the ratio by a common factor, preferably the greatest common factor. The quantities and their order must remain consistent—subtracting the same number or changing only one term does not preserve equivalence; this understanding supports equivalent ratios, unit rates, proportions, and percent reasoning.

Detailed Explanation: 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 $18:24$ .

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

The factors they share include $1, 2, 3,$ and $6$ , so the GCF is $6$ .
Divide both parts of the ratio by $6$ :

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

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.

Learn by doing: Simplify ratios

Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill

Practice with unlimited practice problems

Ratios - Calculate Item Ratio from Values (From Image)

Earned ?