To reduce fraction ratios, you need to divide all parts of the ratio by their highest common factor (HCF). This process simplifies the ratio while maintaining the same proportional relationship between the quantities.
Understanding Ratio Simplification
Ratios, like fractions, can often be expressed in a simpler form. The goal is to find the smallest whole numbers that still accurately represent the relationship between the quantities. Simplifying ratios makes them easier to understand and compare.
Steps to Simplify Ratios
Here’s a step-by-step guide:
- Identify the Ratio: Determine the ratio you want to simplify. For instance, let's consider the ratio 12:18.
- Find the Highest Common Factor (HCF): Determine the largest number that divides evenly into all parts of the ratio. For 12 and 18, the HCF is 6.
- Divide by the HCF: Divide each part of the ratio by the HCF you found.
- 12 ÷ 6 = 2
- 18 ÷ 6 = 3
- Write the Simplified Ratio: Write the new ratio using the results of the division. The simplified ratio of 12:18 is 2:3.
Example
Here’s an example from the reference:
- The ratio 4:2
- The highest common factor of 4 and 2 is 2.
- Dividing both parts by 2, we get: 4 ÷ 2 = 2 and 2 ÷ 2 = 1.
- Therefore, 4:2 simplifies to 2:1.
Why Does This Work?
Simplifying ratios by dividing by their HCF works because it maintains the same proportions. Essentially, you're reducing the ratio to its simplest form without changing the underlying relationship between the quantities.
Practical Insights
- Consistency is Key: Always divide all parts of the ratio by the same HCF.
- Check for Further Simplification: After simplification, double-check to ensure that there isn't a common factor between the new numbers. If there is, continue the process.
- Application in Real Life: This is useful for various applications, like mixing ingredients, reading maps, and scaling models.
By finding the highest common factor and dividing each part of the ratio by this, you can efficiently reduce ratios to their simplest form.
