To complete the inequality \( \frac{2}{3} < \text{blank} < \frac{7}{9} \), we need to check each option to see if it fits within that range.
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Three-fifths: \[ \frac{3}{5} = 0.6 \] \[ \frac{2}{3} \approx 0.6667 \quad \text{and} \quad \frac{7}{9} \approx 0.7778 \] So, \( 0.6 \) is less than \( 0.6667 \). Thus, \( \frac{3}{5} \) does not satisfy the inequality.
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\(\frac{6}{9}\): \[ \frac{6}{9} = \frac{2}{3} \] Here, \(\frac{2}{3}\) is not greater than \(\frac{2}{3}\); therefore, \(\frac{6}{9}\) does not fit in the inequality.
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Three-fourths: \[ \frac{3}{4} = 0.75 \] Again, comparing: \[ 0.6667 < 0.75 < 0.7778 \] So, \( \frac{3}{4} \) does satisfy the inequality.
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\(\frac{6}{7}\): \[ \frac{6}{7} \approx 0.8571 \] Here we see: \[ 0.6667 < 0.8571 \text{ (but)} \text{ (not} < 0.7778\text{)} \] Thus, \(\frac{6}{7}\) is not within the range.
After checking all options, the only value that satisfies the inequality \( \frac{2}{3} < \text{blank} < \frac{7}{9} \) is:
\(\boxed{\frac{3}{4}}\)
1 answer