Here are the solutions to the problems: 10. Work out $\frac{3.6 + 11.2}{0.144}$ Step 1: Calculate the sum in the numerator. $$ 3.6 + 11.2 = 14.8 $$ Step 2: Divide the result by the denominator. $$ \frac{14.8}{0.144} $$ To simplify the division, multiply both the numerator and the denominator by 1000 to remove the decimals: $$ \frac{14.8 \times 1000}{0.144 \times 1000} = \frac{14800}{144} $$ Step 3: Perform the division. $$ \frac{14800}{144} = 102.777... $$ Rounding to four decimal places: $$ 102.777... \approx 102.7778 $$ The value is $\boxed{\text{102.7778}}$. 11. Use a table to look for a square root of 0.8236 To find the square root of 0.8236 using a table, you would locate 0.8236 in the table's appropriate column (e.g., for square roots of numbers between 0 and 1). Calculating the square root directly: $$ \sqrt{0.8236} \approx 0.9075241 $$ Rounding to four decimal places, as is common for table values: $$ \sqrt{0.8236} \approx 0.9075 $$ The square root of 0.8236 is approximately $\boxed{\text{0.9075}}$. 12. Evaluate: $\frac{3}{8}$ of $\left[7\frac{3}{5} - \frac{1}{3}\left(1\frac{1}{4} + 3\frac{1}{3} \times 2\frac{2}{5}\right)\right]$ Step 1: Convert all mixed numbers to improper fractions. $$ 7\frac{3}{5} = \frac{7 \times 5 + 3}{5} = \frac{38}{5} $$ $$ 1\frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4} $$ $$ 3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3} $$ $$ 2\frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{12}{5} $$ Substitute these into the expression: $$ \frac{3}{8} \times \left[\frac{38}{5} - \frac{1}{3}\left(\frac{5}{4} + \frac{10}{3} \times \frac{12}{5}\right)\right] $$ Step 2: Perform the multiplication inside the innermost parentheses. $$ \frac{10}{3} \times \frac{12}{5} = \frac{10 \times 12}{3 \times 5} = \frac{120}{15} = 8 $$ Step 3: Perform the addition inside the innermost parentheses. $$ \frac{5}{4} + 8 = \frac{5}{4} + \frac{32}{4} = \frac{37}{4} $$ The expression now becomes: $$ \frac{3}{8} \times \left[\frac{38}{5} - \frac{1}{3}\left(\frac{37}{4}\right)\right] $$ Step 4: Perform the multiplication $\frac{1}{3} \times \frac{37}{4}$. $$ \frac{1}{3} \times \frac{37}{4} = \frac{37}{12} $$ The expression now becomes: $$ \frac{3}{8} \times \left[\frac{38}{5} - \frac{37}{12}\right] $$ Step 5: Perform the subtraction inside the square brackets. Find a common denominator for 5 and 12, which is 60. $$ \frac{38}{5} - \frac{37}{12} = \frac{38 \times 12}{5 \times 12} - \frac{37 \times 5}{12 \times 5} = \frac{456}{60} - \frac{185}{60} = \frac{456 - 185}{60} = \frac{271}{60} $$ The expression now becomes: $$ \frac{3}{8} \times \frac{271}{60} $$ Step 6: Perform the final multiplication. $$ \frac{3}{8} \times \frac{271}{60} = \frac{3 \times 271}{8 \times 60} $$ We can simplify by dividing 3 and 60 by their common factor, 3: $$ \frac{1 \times 271}{8 \times 20} = \frac{271}{160} $$ As a mixed number: $$ 1\frac{111}{160} $$ The evaluated expression is $\boxed{\frac{271}{160}}$ or $\boxed{1\frac{111}{160}}$.