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Compare the following fractions using symbols less than <, greater than >, =.

Mathematics

ScanSolve AI Answer

Step-by-step solution

10 steps

Here are the comparisons for the fractions:

  1. Compare 18\frac{1}{8} and 25\frac{2}{5}.
  1. Find a common denominator for 8 and 5, which is 40.

    $$
    \frac{1}{8} = \frac{1 \times 5}{8 \times 5} = \frac{5}{40}
    $$
    $$
    \frac{2}{5} = \frac{2 \times 8}{5 \times 8} = \frac{16}{40}
    $$
    
  2. Compare the numerators.

    Since $5 < 16$, then $\frac{5}{40} < \frac{16}{40}$.  
    Therefore, $\boxed{\frac{1}{8} < \frac{2}{5}}$.
    

    2. Compare 79\frac{7}{9} and 56\frac{5}{6}.

  3. Find a common denominator for 9 and 6, which is 18.

    $$
    \frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}
    $$
    $$
    \frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}
    $$
    
  4. Compare the numerators.

    Since $14 < 15$, then $\frac{14}{18} < \frac{15}{18}$.  
    Therefore, $\boxed{\frac{7}{9} < \frac{5}{6}}$.
    

    3. Compare 23\frac{2}{3} and 35\frac{3}{5}.

  5. Find a common denominator for 3 and 5, which is 15.

    $$
    \frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}
    $$
    $$
    \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
    $$
    
  6. Compare the numerators.

    Since $10 > 9$, then $\frac{10}{15} > \frac{9}{15}$.  
    Therefore, $\boxed{\frac{2}{3} > \frac{3}{5}}$.
    

    4. Compare 23\frac{2}{3} and 12\frac{1}{2}.

  7. Find a common denominator for 3 and 2, which is 6.

    $$
    \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
    $$
    $$
    \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
    $$
    
  8. Compare the numerators.

    Since $4 > 3$, then $\frac{4}{6} > \frac{3}{6}$.  
    Therefore, $\boxed{\frac{2}{3} > \frac{1}{2}}$.
    

    5. Compare 45\frac{4}{5} and 34\frac{3}{4}.

  9. Find a common denominator for 5 and 4, which is 20.

    $$
    \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}
    $$
    $$
    \frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}
    $$
    
  10. 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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