So $ \frac{144}{256} = \frac{144 \div 16}{256 \div 16} = \frac{9}{16} $ — correct.

["Understanding & Validating ( \frac{144}{256} = \frac{9}{16} ): A Simple Fraction Simplification", "When working with fractions, one common question that arises is how to verify whether two seemingly different fractions are equal. Take, for example, the equation:\n[\n\frac{144}{256} = \frac{144 \div 16}{256 \div 16}\n]\nThis simplifies correctly to ( \frac{9}{16} ), and this article explains why this reduction is valid and why simplifying fractions this way makes mathematical sense.", "### Step-by-Step Verification", "Start with the original fraction:\n[\n\frac{144}{256}\n]\nBoth the numerator and denominator are divisible by 16—a fundamental simplification step based on the greatest common divisor (GCD). Dividing both by 16 gives:\n[\n\frac{144 \div 16}{256 \div 16} = \frac{9}{16}\n]\nSince dividing numerator and denominator by the same non-zero number preserves the value of the fraction, the equation ( \frac{144}{256} = \frac{9}{16} ) holds true.", "### Why This Works: The Math Behind Fraction Simplification", "Fractions represent ratios, and reducing a fraction simply means expressing the same ratio in its simplest form. The process relies on dividing both parts of the ratio by their common factors. In this case, both 144 and 256 share 16 as a factor, making it ideal for simplification.", "Mathematically:\n[\n\gcd(144, 256) = 16\n]\nUsing this, dividing numerator and denominator by 16:\n[\n\frac{144 \div 16}{256 \div 16} = \frac{9}{16}\n]\nThis confirms the equality.", "### Practical Benefits of Simplifying Fractions", "Simplifying fractions like ( \frac{144}{256} ) offers advantages in clarity and efficiency. Whether in math problems, real-world applications (such as probability, measurements, or financial ratios), and academic settings, presenting fractions in their simplest form enhances readability and minimizes errors. Plus, reduced fractions are easier to compare, add, or multiply.", "### Conclusion", "The statement\n[\n\frac{144}{256} = \frac{144 \div 16}{256 \div 16} = \frac{9}{16}\n]\nis indeed correct. It exemplifies a reliable method for simplifying fractions by dividing both numerator and denominator by their greatest common divisor. Understanding this process empowers learners and professionals alike to work more confidently with fractions across all mathematical contexts.", "Keywords: simplify fractions, fraction simplification, math simplification, GCD divisible fraction, ( \frac{144}{256} ), divide numerator and denominator, common factor reduction", "---\nThis article clarifies the concept behind simplifying rational expressions and validates the equivalence through step-by-step reasoning, supporting accurate math education and practical problem-solving."]