1. **State the problem:** We need to find the number that should be added to $\frac{3}{32}$ to get $\frac{53}{96}$. 2. **Set up the equation:** Let the number to be added be $x$. Then: $$\frac{3}{32} + x = \frac{53}{96}$$ 3. **Isolate $x$:** $$x = \frac{53}{96} - \frac{3}{32}$$ 4. **Find a common denominator:** The denominators are 96 and 32. Since $96 = 3 \times 32$, the common denominator is 96. 5. **Rewrite fractions with denominator 96:** $$\frac{3}{32} = \frac{3 \times 3}{32 \times 3} = \frac{9}{96}$$ 6. **Subtract the fractions:** $$x = \frac{53}{96} - \frac{9}{96} = \frac{53 - 9}{96} = \frac{44}{96}$$ 7. **Simplify the fraction:** Both numerator and denominator are divisible by 4: $$\frac{44}{96} = \frac{44 \div 4}{96 \div 4} = \frac{11}{24}$$ **Final answer:** $$x = \frac{11}{24}$$