1. **State the problem:** Simplify the fraction $\frac{2838}{9284}$. 2. **Formula and rules:** To simplify a fraction, divide numerator and denominator by their greatest common divisor (GCD). 3. **Find the GCD:** Use the Euclidean algorithm to find $\gcd(2838, 9284)$. - $9284 \div 2838 = 3$ remainder $770$ - $2838 \div 770 = 3$ remainder $528$ - $770 \div 528 = 1$ remainder $242$ - $528 \div 242 = 2$ remainder $44$ - $242 \div 44 = 5$ remainder $22$ - $44 \div 22 = 2$ remainder $0$ So, $\gcd(2838, 9284) = 22$. 4. **Divide numerator and denominator by 22:** $$\frac{2838}{9284} = \frac{2838 \div 22}{9284 \div 22} = \frac{129}{422}.$$ 5. **Check if further simplification is possible:** - $129 = 3 \times 43$ - $422 = 2 \times 211$ No common factors remain, so the fraction is simplified. **Final answer:** $$\frac{2838}{9284} = \frac{129}{422}.$$