To multiply the fractions [tex]\(\frac{8}{14}\)[/tex] and [tex]\(\frac{7}{16}\)[/tex], follow these steps:
1. Multiply the Numerators:
Multiply the numerators of the fractions:
[tex]\[
8 \times 7 = 56
\][/tex]
2. Multiply the Denominators:
Multiply the denominators of the fractions:
[tex]\[
14 \times 16 = 224
\][/tex]
So, the resulting fraction before simplification is:
[tex]\[
\frac{56}{224}
\][/tex]
3. Simplify the Fraction:
To simplify the fraction [tex]\(\frac{56}{224}\)[/tex], you need to find the greatest common divisor (GCD) of 56 and 224. The GCD of 56 and 224 is 56.
4. Divide the Numerator and Denominator by the GCD:
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{56 \div 56}{224 \div 56} = \frac{1}{4}
\][/tex]
Thus, the simplified form of [tex]\(\frac{8}{14} \cdot \frac{7}{16}\)[/tex] is [tex]\(\frac{1}{4}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{1}{4}}
\][/tex]
