Answer :
To solve the expression [tex]\frac{6}{7} \times \frac{14}{15} \times \frac{25}{28}[/tex], follow these steps:
Multiply the numerators:
[tex]6 \times 14 \times 25[/tex]Multiply the denominators:
[tex]7 \times 15 \times 28[/tex]Calculate the products:
- Numerators: [tex]6 \times 14 \times 25 = 2100[/tex]
- Denominators: [tex]7 \times 15 \times 28 = 2940[/tex]
Form the new fraction:
[tex]\frac{2100}{2940}[/tex]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].