To multiply the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{1}{12}\)[/tex], we follow these steps:
1. Multiply the numerators together:
The numerators are [tex]\(3\)[/tex] and [tex]\(1\)[/tex].
[tex]\[
3 \times 1 = 3
\][/tex]
So, the numerator of the product is [tex]\(3\)[/tex].
2. Multiply the denominators together:
The denominators are [tex]\(4\)[/tex] and [tex]\(12\)[/tex].
[tex]\[
4 \times 12 = 48
\][/tex]
So, the denominator of the product is [tex]\(48\)[/tex].
Therefore, the product of the fractions before simplification is:
[tex]\[
\frac{3}{48}
\][/tex]
3. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator:
To simplify [tex]\(\frac{3}{48}\)[/tex], we find the GCD of [tex]\(3\)[/tex] and [tex]\(48\)[/tex]. The GCD is [tex]\(3\)[/tex].
4. Divide both the numerator and the denominator by the GCD:
[tex]\[
\frac{3 \div 3}{48 \div 3} = \frac{1}{16}
\][/tex]
Therefore, the simplified product of the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{1}{12}\)[/tex] is:
[tex]\[
\frac{1}{16}
\][/tex]
