The ratio 6 to 9 in simplest form is:
A. 1/3
B. 2/3
C. 3/2
The Correct Answer and Explanation is:
To find the simplest form of the ratio 6 to 9, we can express it as a fraction: (\frac{6}{9}). The next step is to simplify this fraction by finding the greatest common divisor (GCD) of the numerator (6) and the denominator (9).
Step 1: Identify the GCD
The factors of 6 are 1, 2, 3, and 6. The factors of 9 are 1, 3, and 9. The largest common factor between 6 and 9 is 3.
Step 2: Divide Both the Numerator and Denominator by the GCD
Now, we divide both the numerator and the denominator of the fraction (\frac{6}{9}) by their GCD, which is 3:
[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
]
Step 3: Interpret the Result
The simplified form of the ratio 6 to 9 is (\frac{2}{3}). This means that for every 2 parts of the first quantity, there are 3 parts of the second quantity. Ratios are often used in various contexts, such as in cooking, where ingredients might need to be mixed in specific proportions, or in finance, where ratios can help compare different financial metrics.
Conclusion
Thus, the simplest form of the ratio 6 to 9 is (\frac{2}{3}), which corresponds to option B. Understanding how to simplify ratios is essential, as it allows for clearer comparisons and calculations in practical applications. By simplifying, we gain a more concise expression that retains the original relationship between the quantities involved.