To write the fraction [tex]\( \frac{1}{6} \)[/tex] as an equivalent fraction with a denominator of 12, follow these steps:
1. Identify the initial fraction: We begin with the fraction [tex]\(\frac{1}{6}\)[/tex].
2. Determine the new denominator: We want the equivalent fraction to have a denominator of 12.
3. Calculate the multiplication factor: To convert the denominator from 6 to 12, we need to determine what factor we must multiply the original denominator by. We find that multiplying 6 by 2 gives us 12:
[tex]\[
6 \times 2 = 12
\][/tex]
4. Multiply the numerator by the same factor: To maintain the equivalence of the fraction, we must also multiply the numerator by the same factor. Since our original numerator is 1, we perform the multiplication:
[tex]\[
1 \times 2 = 2
\][/tex]
5. Write the equivalent fraction: Now, having multiplied both the numerator and the denominator by 2, we have converted [tex]\(\frac{1}{6}\)[/tex] to the fraction:
[tex]\[
\frac{2}{12}
\][/tex]
So, the fraction [tex]\( \frac{1}{6} \)[/tex] is equivalent to [tex]\( \frac{2}{12} \)[/tex].
