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Step-by-Step Reasoning

  1. Convert mixed numbers to improper fractions.
    The factory used 3 3/4 barrels of oatmeal, which can be expressed as an improper fraction:
    3 3/4 = (3 × 4 + 3)/4 = 15/4 barrels[1].

  1. Set up the division to find the number of batches.
    Each batch uses 5/8 of a barrel. Therefore, the number of batches is given by:
    (15/4) ÷ (5/8).

  2. Perform the division by multiplying by the reciprocal.
    (15/4) ÷ (5/8) = (15/4) × (8/5).

  1. Multiply the fractions.
    Multiply numerator by numerator and denominator by denominator:
    (15 × 8) / (4 × 5) = 120/20.
  1. Simplify the fraction.
    120/20 = 6.

Final Answer

6 batches

Authoritative Sources

  1. Converting Mixed Numbers to Improper Fractions. [Math is Fun]
    ↩
  2. Dividing Fractions. [Khan Academy]↩

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