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Solve the following problems: 1. Is 6 rac25 = 1 rac35? 2. Calculate 5 rac34 - 2 rac14.

Mathematics

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Step-by-step solution

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Here are the solutions to the problems:

  1. 625=1356\frac{2}{5} = 1\frac{3}{5}
  1. Convert both mixed numbers to improper fractions.

    $$
    6\frac{2}{5} = \frac{(6 \times 5) + 2}{5} = \frac{30 + 2}{5} = \frac{32}{5}
    $$
    $$
    1\frac{3}{5} = \frac{(1 \times 5) + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5}
    $$
    
  2. Compare the improper fractions.

    $$
    \frac{32}{5} \text{ and } \frac{8}{5}
    $$
    Since $32 \neq 8$, then $\frac{32}{5} \neq \frac{8}{5}$.
    
  3. Conclude whether the statement is true or false.

    The statement $6\frac{2}{5} = 1\frac{3}{5}$ is $\boxed{\text{False}}$.
    

    2. 534−2145\frac{3}{4} - 2\frac{1}{4}

  4. Subtract the whole number parts.

    $$
    5 - 2 = 3
    $$
    
  5. Subtract the fractional parts.

    The denominators are already the same. 34−14=3−14=24 \frac{3}{4} - \frac{1}{4} = \frac{3-1}{4} = \frac{2}{4}

  6. Simplify the fractional part.

    $$
    \frac{2}{4} = \frac{1}{2}
    $$
    
  7. Combine the whole number and the simplified fraction.

    $$
    3 + \frac{1}{2} = 3\frac{1}{2}
    $$
    The difference is $\boxed{3\frac{1}{2}}$.
    
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