14/16 in simplest form
Understand the Problem
The question is asking to simplify the fraction 14/16 to its simplest form by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number.
Answer
The simplified form of the fraction is $ \frac{7}{8} $.
Answer for screen readers
The simplified form of the fraction $ \frac{14}{16} $ is $ \frac{7}{8} $.
Steps to Solve
- Identify the numerator and denominator
In this problem, the numerator is 14 and the denominator is 16.
- Find the Greatest Common Divisor (GCD)
To simplify the fraction, we need to find the GCD of 14 and 16. The GCD is the largest positive integer that divides both numbers without leaving a remainder.
- The factors of 14 are: 1, 2, 7, 14.
- The factors of 16 are: 1, 2, 4, 8, 16.
The greatest common factor is 2.
- Divide the numerator and denominator by the GCD
Now, we divide both the numerator and denominator by their GCD.
$$ \text{Numerator: } \frac{14}{2} = 7 $$
$$ \text{Denominator: } \frac{16}{2} = 8 $$
- Write the simplified fraction
After dividing by the GCD, we have:
$$ \frac{7}{8} $$
So, the simplified form of the fraction is $ \frac{7}{8} $.
The simplified form of the fraction $ \frac{14}{16} $ is $ \frac{7}{8} $.
More Information
Simplifying fractions is an important skill in mathematics. It helps in making calculations easier and more manageable. The concept of GCD is widely used in various areas including number theory and algebra.
Tips
- A common mistake is failing to find the GCD correctly. Always double-check the factors of both numbers to ensure accuracy.
- Another mistake is forgetting to divide both the numerator and denominator, leading to an incorrect final answer.
