Factor and simplify before computing: Evaluate (6.5 × 4.7 + 6.5 × 5.3) / (1.3 × 7.9 − 1.3 × 6.9).

Introduction / Context:Recognizing common factors can drastically simplify decimal arithmetic. This problem is constructed to reward factoring before multiplying.

Given Data / Assumptions:

• Numerator: 6.5 × 4.7 + 6.5 × 5.3.
• Denominator: 1.3 × 7.9 − 1.3 × 6.9.

Concept / Approach:Factor common terms: a*b + a*c = a(b + c); a*b − a*c = a(b − c). This avoids unnecessary decimal products and leads to a clean ratio.

Step-by-Step Solution:

Verification / Alternative check:Compute directly as a decimal: 4.7 + 5.3 = 10 gives 65 on top; 7.9 − 6.9 = 1 gives 1.3 below; then 65 ÷ 1.3 = 650 ÷ 13 = 50 exactly.

Why Other Options Are Wrong:39 and 3.9 confuse multiplication with division by 1.3. 34.45 is a non-factored calculator mishit. 5 is off by a factor of 10.

Common Pitfalls:Multiplying decimals first and rounding prematurely, which can lead to compounded errors; always look to factor common terms.

Final Answer:50