JANUARY 2025 PROPERTIES OF RATIONHL NUMB MPLIFY \( 12(13-8)-11(22-17) \)

Sure, let's simplify the expression using the properties of rational numbers. The expression given is: \[ 12(13 - 8) - 11(22 - 17) \] ### Step 1: Simplify Inside the Parentheses First, perform the subtraction inside each set of parentheses. \[ 13 - 8 = 5 \] \[ 22 - 17 = 5 \] Now, the expression becomes: \[ 12 \times 5 - 11 \times 5 \] ### Step 2: Apply the Distributive Property Notice that both terms have a common factor of 5. We can factor this out using the distributive property: \[ (12 - 11) \times 5 \] ### Step 3: Perform the Subtraction \[ 12 - 11 = 1 \] So now, the expression is: \[ 1 \times 5 \] ### Step 4: Multiply \[ 1 \times 5 = 5 \] ### Final Answer \[ 12(13 - 8) - 11(22 - 17) = 5 \] **Conclusion:** The simplified value of the expression is **5**.