Compute a mixed fraction–decimal combination: Evaluate 31/10 × 3/10 + 7/5 ÷ 20 and present the result in simplest form.

Introduction / Context:This question blends two straightforward fractional operations followed by addition. Keeping everything in fraction form helps prevent decimal mistakes and makes simplification transparent and exact.

Given Data / Assumptions:

• Compute product: 31/10 × 3/10.
• Compute division: 7/5 ÷ 20 = 7/5 × 1/20.
• Add the two results and simplify.

Concept / Approach:Perform each operation separately, reduce when possible, then add using a common denominator. Because denominators align to 100 naturally, the addition becomes especially tidy here.

Step-by-Step Solution:Product: 31/10 × 3/10 = 93/100.Division: 7/5 ÷ 20 = 7/5 × 1/20 = 7/100.Sum: 93/100 + 7/100 = 100/100 = 1.

Verification / Alternative check:Convert to decimals: 31/10 = 3.1, 3/10 = 0.3 → product 0.93; 7/5 = 1.4, ÷ 20 = 0.07; 0.93 + 0.07 = 1.00.

Why Other Options Are Wrong:0 and 100 contradict the balanced additions; 107/200 equals 0.535 and arises from wrong denominators; 7/10 = 0.7 misses the second addend.

Common Pitfalls:Dividing by 20 incorrectly (confusing 1/20 with 20/1); mixing decimals and fractions midstream; failing to combine to a common denominator.

Final Answer:1