Evaluate the expression by following the left-to-right operation order for the given fractions. Compute: 15/20 ÷ 4/5 × 2/3 × 8/5

Introduction / Context:
This problem checks careful handling of fractional operations. The key is to apply division and multiplication from left to right, converting division by a fraction into multiplication by its reciprocal, and simplifying where possible before multiplying to avoid large numerators and denominators.

Given Data / Assumptions:

• Expression: 15/20 ÷ 4/5 × 2/3 × 8/5
• All numbers are rational fractions.
• Operations must be evaluated left to right for multiplication and division.

Concept / Approach:
Use the rule a/b ÷ c/d = a/b × d/c. Then simplify factors by canceling common terms across numerators and denominators. This reduces arithmetic effort and minimizes mistakes.

Step-by-Step Solution:
1) Simplify 15/20 = 3/4.2) Divide by 4/5: 3/4 ÷ 4/5 = 3/4 × 5/4 = 15/16.3) Multiply by 2/3: 15/16 × 2/3 = 30/48 = 5/8 after canceling by 6.4) Multiply by 8/5: 5/8 × 8/5 = 1 after canceling 5 with 5 and 8 with 8.

Verification / Alternative check:
Numerically, 15/20 = 0.75; 0.75 ÷ 0.8 = 0.9375; 0.9375 × 0.666… ≈ 0.625; 0.625 × 1.6 = 1.0. Both exact fraction arithmetic and decimal sanity check agree.

Why Other Options Are Wrong:

• 0: Would require a zero factor or cancellation to zero, which never occurs.
• 3 and 5: These are typical results of mis-ordering operations or forgetting to invert during division by a fraction.

Common Pitfalls:
Not inverting the second fraction when dividing, multiplying numerators and denominators without simplification, or reordering operations incorrectly.

Final Answer:
1