Questions: Question 5 Evaluate the expression. 23-[8-(2-11)]+(3-5)^3 -2 32 14 -14 Question 6 Find the sum or difference, and write in lowest terms, if necessary. -1/4+(-1/6)

Solution Steps

For Question 5, we need to evaluate the given mathematical expression by following the order of operations: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).

For Question 6, we need to find the sum of two fractions. To do this, we first find a common denominator, convert each fraction, and then add them together. Finally, we simplify the result if necessary.

To evaluate the expression \( 23 - [8 - (2 - 11)] + (3 - 5)^3 \), we follow the order of operations:

1. Simplify inside the innermost parentheses: \( 2 - 11 = -9 \).
2. Substitute back: \( 23 - [8 - (-9)] + (3 - 5)^3 \).
3. Simplify inside the brackets: \( 8 - (-9) = 8 + 9 = 17 \).
4. Substitute back: \( 23 - 17 + (3 - 5)^3 \).
5. Calculate the exponent: \( (3 - 5)^3 = (-2)^3 = -8 \).
6. Substitute back: \( 23 - 17 - 8 \).
7. Perform the subtraction: \( 23 - 17 = 6 \).
8. Finally, \( 6 - 8 = -2 \).

To find the sum of the fractions \( -\frac{1}{4} + \left(-\frac{1}{6}\right) \):

1. Find a common denominator for the fractions. The least common multiple of 4 and 6 is 12.
2. Convert each fraction:
   • \( -\frac{1}{4} = -\frac{3}{12} \)
   • \( -\frac{1}{6} = -\frac{2}{12} \)
3. Add the fractions: \( -\frac{3}{12} + \left(-\frac{2}{12}\right) = -\frac{5}{12} \).

Final Answer