How to simplify ratios?
Understand the Problem
The question is asking how to simplify ratios. This involves finding the greatest common factor (GCF) of the numbers in the ratio and dividing each part of the ratio by the GCF to reduce it to its simplest form.
Answer
2:3
Answer for screen readers
2:3
Steps to Solve
- Find the Greatest Common Factor (GCF)
Find the GCF of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, and 12. The factors of 18 are 1, 2, 3, 6, 9, and 18. The greatest common factor is 6.
- Divide both parts of the ratio by the GCF
Divide both 12 and 18 by 6:
$12 \div 6 = 2$ $18 \div 6 = 3$
- Write the simplified ratio
The simplified ratio is 2:3.
2:3
More Information
The simplified ratio 2:3 means that for every 2 units of the first quantity, there are 3 units of the second quantity. This maintains the same proportion as the original ratio 12:18, but uses smaller, more manageable numbers.
Tips
A common mistake is not finding the greatest common factor. For instance, you could divide both numbers by 2 or 3, but you wouldn't arrive at the simplest form immediately and would need to repeat the process. Always ensure you're dividing by the GCF to simplify completely in one step.
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