Simplifying Ratios: Converting and Simplifying 12:6 2/3

Understanding and simplifying ratios is a fundamental skill in mathematics, applicable in various fields from business to engineering. One common question is how to simplify ratios that contain mixed numbers, such as 12:6 2/3. In this article, we will explore the process of converting and simplifying this ratio to its simplest form.

Understanding the Ratio

The given ratio is 12:6 2/3. This means that for every 12 units of one quantity, there are 6 2/3 units of another. Mixed numbers such as 6 2/3 can be converted into improper fractions to make the ratio easier to work with.

Converting Mixed Numbers to Improper Fractions

To convert 6 2/3 to an improper fraction, follow these steps:

Convert 6 2/3 to an improper fraction: Multiply the integer part by the denominator and add the numerator. Then, place this sum over the original denominator. So, 6 2/3 (6 * 3) 2 18 2 20, and the denominator remains 3.

Thus, 6 2/3 20/3.

Simplifying the Ratio Using Improper Fractions

Now that we have converted 6 2/3 to 20/3, we can write the ratio as 12:20/3. To simplify this, we can express 12 as a fraction with the same denominator:

12 12 * (3/3) 36/3.

Eliminating the Common Denominator

Now the ratio 12:6 2/3 is written as 36/3 : 20/3. Since both terms have a common denominator, we can simplify by eliminating it. This leaves us with:

36 : 20.

Simplifying the Ratio to Lowest Terms

To further simplify 36:20, we need to find the greatest common factor (GCF) of 36 and 20. The GCF of 36 and 20 is 4.

Divide both terms by the GCF: 36 ÷ 4 9, and 20 ÷ 4 5.

This simplifies the ratio to 9:5.

Conclusion

Therefore, the simplified form of the ratio 12:6 2/3 is 9:5. This simplified form is much easier to handle and understand than the original mixed number form. Understanding and applying these steps can help in simplifying ratios and solving related problems more efficiently.

Additional Resources

To learn more about ratio conversion and simplifying ratios, visit our detailed guides and resources:

Ratio Conversion Guidelines Simplifying Ratios Tutorial Fraction Lowest Terms Explained