Factor common terms in numerator and denominator: Evaluate (.896 × .752 + .896 × .248) / (.7 × .034 + .7 × .966) by factoring and simplifying before dividing.

Introduction / Context:
Before multiplying decimals, look for common factors you can pull out. This problem is designed for factoring: both the numerator terms have a common 0.896 and the denominator terms have a common 0.7. Recognizing this pattern turns a messy quotient into a simple ratio.

Given Data / Assumptions:

• Numerator: 0.896 × 0.752 + 0.896 × 0.248.
• Denominator: 0.7 × 0.034 + 0.7 × 0.966.

Concept / Approach:
Use distributive factoring a×x + a×y = a(x + y). In both numerator and denominator, the bracketed sums equal 1. This observation reduces the whole fraction to the ratio of the common factors 0.896 to 0.7, which is quick to compute.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 0.976: Comes from dividing 0.896 by 0.918 or other mis-summed bracket.
• 12.8 and 9.76: Lose track of decimal places (×10 or ×100 too much).

Common Pitfalls:

• Multiplying terms directly instead of factoring first.
• Mistallying 0.034 + 0.966 to something other than 1.

Final Answer: