Let's break this down step-by-step to solve each problem from your image:

Problem 9: Which expressions are equivalent to -3 - (7.5 + 4)? Select all that apply.

We start with the expression: $-3 - (7.5 + 4)$ First, simplify the parentheses: $7.5 + 4 = 11.5$ Then: $-3 - 11.5 = -14.5$

Now, let's analyze the given answer options:

• A. (7.5 + 4) - 3:
  This simplifies to $11.5 - 3 = 8.5$, which is NOT equivalent to $-14.5$.

• B. -7.5 + 4 - 3:
  Simplify step-by-step: $-7.5 + 4 = -3.5$ $-3.5 - 3 = -6.5$ This is NOT equivalent to $-14.5$.

• C. -(7.5 + 4) + 3:
  Simplify the parentheses first: $-(7.5 + 4) = -11.5$ Then: $-11.5 + 3 = -8.5$ This is NOT equivalent to $-14.5$.

• D. -3 - (4 + 7.5):
  Simplify the parentheses: $4 + 7.5 = 11.5$ $-3 - 11.5 = -14.5$ This is EQUIVALENT to $-14.5$.

• E. -(3 - 7.5) + 4:
  Simplify inside the parentheses: $3 - 7.5 = -4.5$ $-(-4.5) = 4.5$ $4.5 + 4 = 8.5$ This is NOT equivalent to $-14.5$.

• F. -3 + -(7.5 - 4):
  Simplify inside the parentheses: $7.5 - 4 = 3.5$ $-3 + -3.5 = -6.5$ This is NOT equivalent to $-14.5$.

• G. -3 - (7.5 + 4):
  This is the original expression, and it simplifies to $-14.5$, so it is EQUIVALENT.

Correct answers:
D and G

Problem 10: Which expression is equivalent to $5 + 2 \frac{1}{3}$?

Convert $2 \frac{1}{3}$ into an improper fraction: $2 \frac{1}{3} = \frac{7}{3}$

Then: $5 + 2 \frac{1}{3} = 5 + \frac{7}{3}$ Convert 5 into a fraction with a denominator of 3: $5 = \frac{15}{3}$ Add the fractions: $\frac{15}{3} + \frac{7}{3} = \frac{22}{3}$

Now, match the options:

• A. $5 + 2 \frac{1}{3}$: Matches directly.
• B. $15 - \frac{7}{3}$: Simplifies to $15 - 2.333$, which is incorrect.
• C. $10 - 2 \frac{2}{3}$: Converts to $10 - \frac{8}{3}$, which is incorrect.
• D. $\frac{22}{3}$: Matches the equivalent fraction form.

Correct answers:
A and D

Problem 11: Select the correct number from each list to complete the equation.

Given: $\frac{7}{8} - \left(2 + \frac{3}{4}\right) = \text{(something)} + \frac{7}{8}$

Simplify $2 + \frac{3}{4}$: $2 = \frac{8}{4}, \quad 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}$

Now subtract: $\frac{7}{8} - \frac{11}{4}$ Convert $\frac{11}{4}$ to have a denominator of 8: $\frac{11}{4} = \frac{22}{8}$ $\frac{7}{8} - \frac{22}{8} = \frac{-15}{8}$

The equation becomes: $\frac{-15}{8} = \text{(something)} + \frac{7}{8}$ Subtract $\frac{7}{8}$ from both sides: $\frac{-15}{8} - \frac{7}{8} = \frac{-22}{8}$

Now match the correct numbers from the list: $\boxed{-2 \, \text{and} \, -\frac{3}{4}}$

Do you want further clarification? Let me know!

Here are 5 related questions for deeper practice:

1. How do you simplify expressions with parentheses and negatives?
2. How do you convert mixed numbers to improper fractions?
3. How can you combine like terms with fractions?
4. What is the process for solving subtraction with fractions?
5. How do you identify equivalent expressions in multiple-choice questions?

Tip: Always simplify step-by-step and carefully check signs when working with negatives.