High School

Calculate the product of the fractions:

\[ \frac{6}{7} \times \frac{14}{15} \times \frac{25}{28} \]

Answer :

To solve the expression [tex]\frac{6}{7} \times \frac{14}{15} \times \frac{25}{28}[/tex], follow these steps:

  1. Multiply the numerators:
    [tex]6 \times 14 \times 25[/tex]

  2. Multiply the denominators:
    [tex]7 \times 15 \times 28[/tex]

  3. Calculate the products:

    • Numerators: [tex]6 \times 14 \times 25 = 2100[/tex]
    • Denominators: [tex]7 \times 15 \times 28 = 2940[/tex]

  4. Form the new fraction:
    [tex]\frac{2100}{2940}[/tex]

  5. Simplify the fraction:

    • Find the greatest common divisor (GCD) of 2100 and 2940. The GCD is 420.
    • Divide both the numerator and the denominator by the GCD:
      [tex]\frac{2100 \div 420}{2940 \div 420} = \frac{5}{7}[/tex]

Thus, the simplified result of [tex]\frac{6}{7} \times \frac{14}{15} \times \frac{25}{28}[/tex] is [tex]\frac{5}{7}[/tex].

In summary, by multiplying the fractions and simplifying the result, you find that the simplified product of the fractions is [tex]\frac{5}{7}[/tex].

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