Fraction chain simplification: Compute (3/5) of (4/7) of (7/9) of 425 using cancellation for speed.

Introduction / Context:Successive fractions can often be simplified by cancellation before multiplying. Here, the factor 7 appears in both a numerator and a denominator, making the product much simpler and enabling quick mental calculation with minimal risk of error.

Given Data / Assumptions:

• Expression: (3/5) * (4/7) * (7/9) * 425
• All numbers are exact; a neat cancellation exists.

Concept / Approach:Cancel the 7 in (4/7) with the 7 in (7/9), leaving (3/5) * (4/9) * 425. Multiply constants first or simplify with 425 to avoid large intermediate numbers.

Step-by-Step Solution:

Verification / Alternative check:Exact fraction: 425 * 12/45 = 425 * 4/15 = 1700/15 = 340/3 ≈ 113.333..., confirming 113 as the correct nearest integer option.

Why Other Options Are Wrong:

• 110, 118, 115, 121: all differ from 113.33; 113 is the integer part of the exact value.

Common Pitfalls:Multiplying all numerators first and all denominators next without simplifying can lead to bulky numbers and errors. Cancel early to stay accurate.

Final Answer:113