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Compare the following fractions using symbols less than <, greater than >, =.
Mathematics
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Step-by-step solution
10 stepsHere are the comparisons for the fractions:
- Compare and .
Find a common denominator for 8 and 5, which is 40.
$$ \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40} $$ $$ \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40} $$Compare the numerators.
Since $5 < 16$, then $\frac{5}{40} < \frac{16}{40}$. Therefore, $\boxed{\frac{1}{8} < \frac{2}{5}}$.2. Compare and .
Find a common denominator for 9 and 6, which is 18.
$$ \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18} $$ $$ \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18} $$Compare the numerators.
Since $14 < 15$, then $\frac{14}{18} < \frac{15}{18}$. Therefore, $\boxed{\frac{7}{9} < \frac{5}{6}}$.3. Compare and .
Find a common denominator for 3 and 5, which is 15.
$$ \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15} $$ $$ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} $$Compare the numerators.
Since $10 > 9$, then $\frac{10}{15} > \frac{9}{15}$. Therefore, $\boxed{\frac{2}{3} > \frac{3}{5}}$.4. Compare and .
Find a common denominator for 3 and 2, which is 6.
$$ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} $$ $$ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} $$Compare the numerators.
Since $4 > 3$, then $\frac{4}{6} > \frac{3}{6}$. Therefore, $\boxed{\frac{2}{3} > \frac{1}{2}}$.5. Compare and .
Find a common denominator for 5 and 4, which is 20.
$$ \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20} $$ $$ \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20} $$Compare the numerators.
Since $16 > 15$, then $\frac{16}{20} > \frac{15}{20}$. Therefore, $\boxed{\frac{4}{5} > \frac{3}{4}}$.
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