To find out how many bales of hay the horses are fed each day, we first need to determine how much hay they receive based on the amount fed to the cattle.
The cattle are fed \( 6 \frac{3}{5} \) bales of hay each day. First, we should convert this mixed number into an improper fraction for easier calculations.
The mixed number \( 6 \frac{3}{5} \) can be converted as follows:
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Multiply the whole number (6) by the denominator (5): \[ 6 \times 5 = 30 \]
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Add the numerator (3) to this result: \[ 30 + 3 = 33 \]
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Therefore, \( 6 \frac{3}{5} = \frac{33}{5} \).
Next, we know the horses are fed \( \frac{1}{6} \) as much hay as the cattle. So, we need to calculate:
\[ \frac{1}{6} \times \frac{33}{5} \]
To perform this multiplication, multiply the numerators and then the denominators:
\[ \frac{1 \times 33}{6 \times 5} = \frac{33}{30} \]
Next, we simplify \( \frac{33}{30} \) if possible. Both the numerator and the denominator can be divided by 3:
\[ \frac{33 \div 3}{30 \div 3} = \frac{11}{10} \]
Finally, we convert \( \frac{11}{10} \) into a mixed number:
- \( 11 \div 10 = 1 \) with a remainder of 1.
- Hence, \( \frac{11}{10} = 1 \frac{1}{10} \).
Thus, the horses are fed:
\[ \text{Answer: } \frac{11}{10} \text{ or } 1 \frac{1}{10} \text{ bales of hay each day.} \]