14/26 simplified
Understand the Problem
The question is asking to simplify the fraction 14/26 to its lowest terms. This involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number.
Answer
The simplified fraction is $\frac{7}{13}$.
Answer for screen readers
The simplified form of the fraction $\frac{14}{26}$ is $\frac{7}{13}$.
Steps to Solve
- Identify the Numerator and Denominator
The given fraction is $\frac{14}{26}$. Here, the numerator is 14 and the denominator is 26.
- Find the GCD of 14 and 26
To simplify the fraction, we need to find the greatest common divisor (GCD) of 14 and 26. The factors of 14 are {1, 2, 7, 14} and the factors of 26 are {1, 2, 13, 26}. The common factors are {1, 2}, so:
$$ GCD(14, 26) = 2 $$
- Divide the Numerator and Denominator by the GCD
Now, we will divide both the numerator and denominator by 2 to simplify the fraction:
$$ \frac{14 \div 2}{26 \div 2} = \frac{7}{13} $$
- Write the Final Simplified Fraction
The simplified form of the fraction $\frac{14}{26}$ is $\frac{7}{13}$.
The simplified form of the fraction $\frac{14}{26}$ is $\frac{7}{13}$.
More Information
Simplifying fractions makes them easier to work with and understand. The process of finding the GCD is essential in making sure the fraction is in its simplest form. In this case, dividing both the numerator and denominator by their greatest common factor (2) resulted in a simpler fraction.
Tips
- Not Finding the GCD Properly: Sometimes, students assume the GCD without verifying the factors. Always list out the factors or use the Euclidean algorithm.
- Failing to Simplify Again: After finding the GCD, some may forget to divide both terms adequately, which can lead to an incorrect answer.
