1. **State the problem:** Divide the expression $20m^2 - 28$ by $4m$ and express the result including any remainder as a simplified fraction. 2. **Write the division:** $$\frac{20m^2 - 28}{4m}$$ 3. **Split the fraction into two parts:** $$\frac{20m^2}{4m} - \frac{28}{4m}$$ 4. **Simplify each term:** - For the first term: $$\frac{20m^2}{4m} = \frac{\cancel{20}^5 \cancel{m^2}^{m}}{\cancel{4}^1 \cancel{m}^1} = 5m$$ - For the second term: $$\frac{28}{4m} = \frac{\cancel{28}^7}{\cancel{4}^1 m} = \frac{7}{m}$$ 5. **Combine the simplified terms:** $$5m - \frac{7}{m}$$ **Final answer:** $$5m - \frac{7}{m}$$ This means the quotient is $5m$ and the remainder is $-7$ expressed as the fraction $\frac{7}{m}$.