1. **State the problem:** Calculate the difference between the mixed numbers $67 \frac{70}{96}$ and $46 \frac{10}{48}$. 2. **Convert mixed numbers to improper fractions:** $$67 \frac{70}{96} = 67 + \frac{70}{96} = \frac{67 \times 96}{96} + \frac{70}{96} = \frac{6432}{96} + \frac{70}{96} = \frac{6502}{96}$$ $$46 \frac{10}{48} = 46 + \frac{10}{48} = \frac{46 \times 48}{48} + \frac{10}{48} = \frac{2208}{48} + \frac{10}{48} = \frac{2218}{48}$$ 3. **Find a common denominator:** The denominators are 96 and 48. Since $96 = 2 \times 48$, the common denominator is 96. Convert $\frac{2218}{48}$ to denominator 96: $$\frac{2218}{48} = \frac{2218 \times 2}{48 \times 2} = \frac{4436}{96}$$ 4. **Subtract the fractions:** $$\frac{6502}{96} - \frac{4436}{96} = \frac{6502 - 4436}{96} = \frac{2066}{96}$$ 5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 2066 and 96. - $2066 = 2 \times 1033$ - $96 = 2^5 \times 3$ GCD is 2. Simplify: $$\frac{2066}{96} = \frac{\cancel{2} \times 1033}{\cancel{2} \times 48} = \frac{1033}{48}$$ 6. **Convert back to mixed number:** Divide 1033 by 48: $$1033 \div 48 = 21 \text{ remainder } 25$$ So, $$\frac{1033}{48} = 21 \frac{25}{48}$$ **Final answer:** $$67 \frac{70}{96} - 46 \frac{10}{48} = 21 \frac{25}{48}$$