Simplify 12/16 in lowest terms
The Correct answer and Explanation is:
To simplify the fraction ( \frac{12}{16} ) to its lowest terms, we follow these steps:
Step 1: Identify the Greatest Common Divisor (GCD)
To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (16). The GCD is the largest positive integer that divides both numbers without leaving a remainder.
Finding the GCD:
- List the factors of each number:
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 16: 1, 2, 4, 8, 16
- Identify the common factors: The common factors are 1, 2, and 4.
- Choose the greatest common factor: The greatest common factor is 4.
Step 2: Divide the Numerator and Denominator by the GCD
Next, we divide both the numerator and the denominator by the GCD to simplify the fraction.
[
\frac{12 \div 4}{16 \div 4} = \frac{3}{4}
]
Step 3: Confirm the Simplified Fraction
The simplified fraction is ( \frac{3}{4} ). We can confirm that this is in the lowest terms by checking if 3 and 4 have any common factors:
- Factors of 3: 1, 3
- Factors of 4: 1, 2, 4
The only common factor is 1, which indicates that ( \frac{3}{4} ) cannot be simplified any further.
Conclusion
Thus, the fraction ( \frac{12}{16} ) simplifies to ( \frac{3}{4} ) in lowest terms. This process of simplifying fractions is essential in mathematics, particularly in arithmetic, algebra, and many real-world applications where working with simpler numbers is often more manageable. Simplifying helps in making calculations easier and clearer, allowing for better comprehension and accuracy in mathematical operations.