Use distributive factoring with decimals: (.803 × .647) + (.803 × .353). Factor out the common multiplier to simplify.

Introduction / Context:
This exercise reinforces the distributive property a(b + c) = ab + ac in a decimal context. Spotting a common factor saves time and avoids unnecessary multiplication, leading to an exact and tidy result.

Given Data / Assumptions:

• Expression: (.803 × .647) + (.803 × .353)
• All decimals are exact; keep precision.

Concept / Approach:
Factor out the common term .803. Then simply add the remaining decimals inside the parentheses. Since .647 + .353 = 1.000, the result is immediate and exact.

Step-by-Step Solution:
(.803 × .647) + (.803 × .353) = .803 × (.647 + .353).Compute inside: .647 + .353 = 1.000.Therefore the entire value is .803 × 1.000 = .803.

Verification / Alternative check:
Perform the two products and add them; rounding carefully yields the same .803. The factoring method is quicker and eliminates rounding risk.

Why Other Options Are Wrong:

• 1 and 1.450: Misapplied addition or multiplication.
• .45 and .353: Values appear from partial sums or misplaced decimals.

Common Pitfalls:
Adding inside the parentheses incorrectly to something slightly below or above 1; misplacing the decimal in .803.

Final Answer:
.803