To solve the expression \( m(p + q + r) \) given the values \( m = 3 \), \( p = -3 \), \( q = 7 \), and \( r = \frac{5}{2} \), we will follow a step-by-step approach. ### Step 1: Substitute the values into the expression We start with the expression: \[ m(p + q + r) \] Substituting the values of \( m \), \( p \), \( q \), and \( r \): \[ 3(-3 + 7 + \frac{5}{2}) \] ### Step 2: Calculate the sum inside the parentheses Now, we need to calculate \( p + q + r \): 1. First, calculate \( -3 + 7 \): \[ -3 + 7 = 4 \] 2. Next, add \( \frac{5}{2} \) to \( 4 \). To do this, we need to express \( 4 \) as a fraction with a denominator of \( 2 \): \[ 4 = \frac{8}{2} \] 3. Now, we can add \( \frac{8}{2} + \frac{5}{2} \): \[ \frac{8}{2} + \frac{5}{2} = \frac{8 + 5}{2} = \frac{13}{2} \] So, we have: \[ p + q + r = \frac{13}{2} \] ### Step 3: Multiply by \( m \) Now we substitute back into the expression: \[ m(p + q + r) = 3 \left(\frac{13}{2}\right) \] To perform the multiplication: \[ 3 \times \frac{13}{2} = \frac{39}{2} \] ### Step 4: Convert to decimal Now, we convert \( \frac{39}{2} \) into a decimal: \[ \frac{39}{2} = 19.5 \] ### Final Answer Thus, the value of \( m(p + q + r) \) is: \[ \boxed{19.5} \] ### Explanation of Options - **Option A: 19.50** - This is the correct answer as we calculated. - **Option B: 19.15** - This is incorrect. It seems to be a miscalculation, possibly from an incorrect addition or multiplication. - **Option C: 18.95** - This is also incorrect. It may arise from miscalculating the sum of \( p + q + r \) or the multiplication with \( m \). - **Option D: 18.05** - This is incorrect as well. It could be a result of a significant error in the arithmetic operations. ### Common Pitfalls 1. **Misadding fractions**: Ensure that when adding fractions, the denominators are the same. 2. **Forgetting to convert whole numbers to fractions**: When adding a whole number to a fraction, convert the whole number to a fraction with the same denominator. 3. **Multiplication errors**: Double-check multiplication steps, especially when dealing with fractions. ### Revision Summary - Substitute values into the expression carefully. - Perform operations inside parentheses first. - Convert fractions to decimals only after completing all calculations. - Always double-check arithmetic to avoid simple mistakes.