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$\frac{7}{15} \cdot \frac{14}{3} = $

$\frac{6}{16} \cdot \frac{5}{7} = $

$\frac{21}{20} \cdot \frac{10}{3} = $

$\frac{20}{50} \cdot \frac{7}{3} = $

Answer :

Let's work through each of the given fraction multiplications step by step.

  1. First Expression:
    [tex]\frac{7}{15} \cdot \frac{14}{3}[/tex]
    To multiply these fractions, multiply the numerators together and the denominators together:
    [tex]\frac{7 \cdot 14}{15 \cdot 3} = \frac{98}{45}[/tex]
    Since 98 and 45 have no common factors other than 1, the fraction is already in its simplest form.

  2. Second Expression:
    [tex]\frac{6}{16} \cdot \frac{5}{7}[/tex]
    First, simplify [tex]\frac{6}{16}[/tex], which can be reduced by dividing both the numerator and the denominator by 2:
    [tex]\frac{6}{16} = \frac{3}{8}[/tex]
    Now multiply:
    [tex]\frac{3}{8} \cdot \frac{5}{7} = \frac{3 \cdot 5}{8 \cdot 7} = \frac{15}{56}[/tex]
    The greatest common divisor of 15 and 56 is 1, so the fraction [tex]\frac{15}{56}[/tex] is already in simplest form.

  3. Third Expression:
    [tex]\frac{21}{20} \cdot \frac{10}{3}[/tex]
    Multiply the numerators and the denominators:
    [tex]\frac{21 \cdot 10}{20 \cdot 3} = \frac{210}{60}[/tex]
    Simplify [tex]\frac{210}{60}[/tex] by dividing both numerator and denominator by 30:
    [tex]\frac{210}{60} = \frac{7}{2}[/tex]
    [tex]\frac{7}{2}[/tex] is the simplest form, as 7 and 2 have no common factors other than 1.

  4. Fourth Expression:
    [tex]\frac{20}{50} \cdot \frac{7}{3}[/tex]
    Simplify [tex]\frac{20}{50}[/tex] by dividing both by 10:
    [tex]\frac{20}{50} = \frac{2}{5}[/tex]
    Now multiply:
    [tex]\frac{2}{5} \cdot \frac{7}{3} = \frac{2 \cdot 7}{5 \cdot 3} = \frac{14}{15}[/tex]
    The fraction [tex]\frac{14}{15}[/tex] is in simplest form since 14 and 15 have no common factors other than 1.

In summary, the simplified products of the fractions for each expression are:

  • [tex]\frac{98}{45}[/tex]
  • [tex]\frac{15}{56}[/tex]
  • [tex]\frac{7}{2}[/tex]
  • [tex]\frac{14}{15}[/tex]

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