Question - Comparing Fractions and Decimals
Solution:
The provided image shows a mathematical expression of two fractions:\[ \frac{3}{5} > \frac{7}{6} \]To determine if this inequality statement is true or false, we can compare the fractions by finding a common denominator or by comparing their decimal equivalents.1. Find a common denominator:The least common denominator (LCD) of 5 and 6 is 30. Convert each fraction to an equivalent fraction with a denominator of 30.\[ \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \]\[ \frac{7}{6} = \frac{7 \times 5}{6 \times 5} = \frac{35}{30} \]Now compare the two:\[ \frac{18}{30} ? \frac{35}{30} \]Since 18 is less than 35, we have:\[ \frac{18}{30} < \frac{35}{30} \]Thus, the original inequality:\[ \frac{3}{5} > \frac{7}{6} \]is false.2. Compare decimal equivalents:Convert each fraction to decimal form.\[ \frac{3}{5} = 0.6 \]\[ \frac{7}{6} = 1.166\ldots \]Compare the decimals:0.6 is less than 1.166..., so again we find that the original inequality $$ \frac{3}{5} > \frac{7}{6} $$ is false.
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