1. **State the problem:** We need to add the fractions $\frac{298}{40}$ and $\frac{76}{32}$. 2. **Find a common denominator:** The denominators are 40 and 32. The least common denominator (LCD) is the least common multiple (LCM) of 40 and 32. - Prime factorization: 40 = $2^3 \times 5$, 32 = $2^5$. - LCM takes the highest powers: $2^5 \times 5 = 32 \times 5 = 160$. 3. **Convert each fraction to have denominator 160:** - $\frac{298}{40} = \frac{298 \times 4}{40 \times 4} = \frac{1192}{160}$ - $\frac{76}{32} = \frac{76 \times 5}{32 \times 5} = \frac{380}{160}$ 4. **Add the fractions:** $$\frac{1192}{160} + \frac{380}{160} = \frac{1192 + 380}{160} = \frac{1572}{160}$$ 5. **Simplify the fraction:** - Find the greatest common divisor (GCD) of 1572 and 160. - 1572 factors: 2, 2, 3, 131; 160 factors: 2, 2, 2, 2, 5. - Common factors: two 2's, so GCD = 4. - Divide numerator and denominator by 4: $$\frac{1572 \div 4}{160 \div 4} = \frac{393}{40}$$ 6. **Final answer:** $$\boxed{\frac{393}{40}}$$ This is an improper fraction and can also be expressed as a mixed number: $$9 \frac{33}{40}$$