To perform the operation \( \frac{10}{9} \div 5 \div 3 \), we first need to rewrite the division operations as multiplications with the reciprocal.
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Rewrite the expression: \[ \frac{10}{9} \div 5 \div 3 = \frac{10}{9} \times \frac{1}{5} \times \frac{1}{3} \]
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Multiply the fractions: \[ \frac{10}{9} \times \frac{1}{5} \times \frac{1}{3} = \frac{10 \times 1 \times 1}{9 \times 5 \times 3} \]
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Calculate the numerator and the denominator:
- Numerator: \( 10 \)
- Denominator: \( 9 \times 5 \times 3 = 135 \)
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This gives us: \[ \frac{10}{135} \]
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Now, we need to simplify this fraction. The greatest common divisor (GCD) of 10 and 135 is 5.
- Divide the numerator and the denominator by 5: \[ \frac{10 \div 5}{135 \div 5} = \frac{2}{27} \]
Thus, the final simplified answer is: \[ \frac{2}{27} \]
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