To solve this expression, we can follow the order of operations, which is parentheses, multiplication/division (from left to right), and then addition/subtraction (from left to right).
Starting with the parentheses, we have:
(-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7)
Next, let's convert the mixed numbers into improper fractions:
(-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7)
Now, multiplying the fractions together:
((-3) × 31 × 15 × (-5)) / ((5) × (6) × (2) × (-19)) × (7)
Simplifying the numerator and denominator separately:
(-1395) / (-1140) × 7
Canceling out the negative signs:
(1395) / (1140) × 7
Simplifying the fraction:
(465/380) × (7)
Multiplying the fractions:
(465 × 7) / 380
Simplifying the fraction:
(3255) / 380
So, the simplified expression is 3255/380.
(−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7)
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