Question

multiply. give your answer in lowest terms.
\\(\frac{3}{4} cdot \frac{8}{11}\\)
\\(\frac{24}{44}\\)
\\(\frac{1}{4}\\)
\\(\frac{6}{11}\\)
\\(\frac{21}{44}\\)

Explanation:

Step1: Multiply numerators and denominators

To multiply two fractions $\frac{a}{b}$ and $\frac{c}{d}$, we use the formula $\frac{a}{b} \cdot \frac{c}{d}=\frac{a\times c}{b\times d}$. So for $\frac{3}{4} \cdot \frac{8}{11}$, we have $a = 3$, $b = 4$, $c = 8$, $d = 11$. Then the product of the numerators is $3\times8 = 24$ and the product of the denominators is $4\times11=44$. So we get $\frac{24}{44}$.

Step2: Simplify the fraction

We need to simplify $\frac{24}{44}$ to its lowest terms. First, find the greatest common divisor (GCD) of 24 and 44. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 44 are 1, 2, 4, 11, 22, 44. The GCD of 24 and 44 is 4. Now divide both the numerator and the denominator by 4. $\frac{24\div4}{44\div4}=\frac{6}{11}$.

Answer:

$\frac{6}{11}$ (which corresponds to the option "C. $\frac{6}{11}$" if we assume the options are labeled A, B, C, D with A being $\frac{24}{44}$, B being $\frac{1}{4}$, C being $\frac{6}{11}$, D being $\frac{21}{44}$)