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Fill in >, < or =. 2. What fractions are shown by the arrow?

Mathematics

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Here are the solutions to the problems.

1. Fill in >,<>, < or ==.

  • a) 13□14\frac{1}{3} \square \frac{1}{4}
  1. Find a common denominator for 13\frac{1}{3} and 14\frac{1}{4}, which is 12.

    $$
    \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
    $$
    $$
    \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
    $$
    
  2. Compare the fractions.

    $$
    \frac{4}{12} > \frac{3}{12}
    $$
    So, $\boxed{\frac{1}{3} > \frac{1}{4}}$.
    
    • b) 35□23\frac{3}{5} \square \frac{2}{3}
  3. Find a common denominator for 35\frac{3}{5} and 23\frac{2}{3}, which is 15.

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

    $$
    \frac{9}{15} < \frac{10}{15}
    $$
    So, $\boxed{\frac{3}{5} < \frac{2}{3}}$.
    
    • c) 47□25\frac{4}{7} \square \frac{2}{5}
  5. Find a common denominator for 47\frac{4}{7} and 25\frac{2}{5}, which is 35.

    $$
    \frac{4}{7} = \frac{4 \times 5}{7 \times 5} = \frac{20}{35}
    $$
    $$
    \frac{2}{5} = \frac{2 \times 7}{5 \times 7} = \frac{14}{35}
    $$
    
  6. Compare the fractions.

    $$
    \frac{20}{35} > \frac{14}{35}
    $$
    So, $\boxed{\frac{4}{7} > \frac{2}{5}}$.
    
    • d) 16□13\frac{1}{6} \square \frac{1}{3}
  7. Find a common denominator for 16\frac{1}{6} and 13\frac{1}{3}, which is 6.

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

    $$
    \frac{1}{6} < \frac{2}{6}
    $$
    So, $\boxed{\frac{1}{6} < \frac{1}{3}}$.
    
    • e) 28□14\frac{2}{8} \square \frac{1}{4}
  9. Simplify the fraction 28\frac{2}{8}.

    $$
    \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}
    $$
    
  10. Compare the fractions.

    $$
    \frac{1}{4} = \frac{1}{4}
    $$
    So, $\boxed{\frac{2}{8} = \frac{1}{4}}$.
    
    • f) 25□310\frac{2}{5} \square \frac{3}{10}
  11. Find a common denominator for 25\frac{2}{5} and 310\frac{3}{10}, which is 10.

    $$
    \frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}
    $$
    
  12. Compare the fractions.

    $$
    \frac{4}{10} > \frac{3}{10}
    $$
    So, $\boxed{\frac{2}{5} > \frac{3}{10}}$.
    

    2. What fractions are shown by the arrow?

    • a) The number line is divided into 4 equal parts between 0 and 1. Each part represents 14\frac{1}{4}. The arrow points to the third mark. The fraction is 34\boxed{\frac{3}{4}}.

    • b) The number line is divided into 4 equal parts between 1 and 2. Each part represents 14\frac{1}{4}. The arrow points to the second mark after 1. The fraction is 1+24=1+12=321 + \frac{2}{4} = 1 + \frac{1}{2} = \boxed{\frac{3}{2}}.

    • c) The number line is divided into 4 equal parts between 4 and 5. Each part represents 14\frac{1}{4}. The arrow points to the third mark after 4. The fraction is 4+34=164+34=1944 + \frac{3}{4} = \frac{16}{4} + \frac{3}{4} = \boxed{\frac{19}{4}}.

    • d) This part of the question is not visible in the image.

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