Comparing Fractions and Decimals
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.
