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Step-by-Step Reasoning
- 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].
-
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). -
Perform the division by multiplying by the reciprocal.
(15/4) ÷ (5/8) = (15/4) × (8/5).
- Multiply the fractions.
Multiply numerator by numerator and denominator by denominator:
(15 × 8) / (4 × 5) = 120/20.
- Simplify the fraction.
120/20 = 6.
Final Answer
6 batches
Authoritative Sources
- Converting Mixed Numbers to Improper Fractions. [Math is Fun]
↩ - Dividing Fractions. [Khan Academy]↩
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