What is the ratio 18/26 expressed in simplest form?
The Correct Answer and Explanation is :
To simplify the fraction ( \frac{18}{26} ), we need to find the greatest common divisor (GCD) of the numerator (18) and the denominator (26) and then divide both by this number.
Step 1: Find the GCD
- List the Factors:
- The factors of 18 are: ( 1, 2, 3, 6, 9, 18 ).
- The factors of 26 are: ( 1, 2, 13, 26 ).
- Identify the Common Factors:
- The common factors of 18 and 26 are: ( 1, 2 ).
- Greatest Common Divisor:
- The greatest common factor is 2.
Step 2: Divide the Numerator and Denominator by the GCD
Now that we have the GCD (2), we can divide both the numerator and the denominator of the fraction by this number:
[
\frac{18 \div 2}{26 \div 2} = \frac{9}{13}
]
Step 3: Conclusion
The simplified form of the fraction ( \frac{18}{26} ) is ( \frac{9}{13} ).
Explanation of Simplifying Fractions
Simplifying fractions is an important mathematical skill. It helps to express numbers in their simplest form, making calculations easier and more comprehensible. A fraction is considered simplified when the numerator and denominator have no common factors other than 1, meaning they are relatively prime.
When working with fractions, the process of simplification involves identifying the GCD, which is the largest number that divides both the numerator and the denominator without leaving a remainder. This method not only helps in reducing the fraction but also aids in understanding ratios and proportions in various applications, such as in cooking, budgeting, and data analysis.
In real-world scenarios, simplified fractions are easier to work with. For example, when combining ingredients in a recipe or when sharing resources among people, having fractions in their simplest form helps to avoid confusion and ensures clarity. Thus, mastering the skill of simplification is essential for mathematical proficiency and practical application.
In summary, ( \frac{18}{26} ) simplifies to ( \frac{9}{13} ).