Sure, let's break down and decompose the fraction [tex]\(\frac{7}{6}\)[/tex] step by step using simpler fractions that share the same denominator.
First, let's recognize that:
[tex]\[ \frac{7}{6} = 1 + \frac{1}{6} \][/tex]
This recognizes that [tex]\(\frac{7}{6}\)[/tex] can be seen as 1 whole (which is [tex]\(\frac{6}{6}\)[/tex]) plus an additional fraction [tex]\(\frac{1}{6}\)[/tex].
To break it down fully:
1. Start with:
[tex]\[
\frac{7}{6}
\][/tex]
2. Break [tex]\(\frac{7}{6}\)[/tex] into [tex]\(\frac{6}{6}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{7}{6} = \frac{6}{6} + \frac{1}{6}
\][/tex]
In decimal form, this decomposition works out to be:
[tex]\[
\frac{6}{6} = 1 \quad \text{(which is a whole number)}
\][/tex]
and:
[tex]\[
\frac{1}{6} \approx 0.16666666666666666
\][/tex]
Thus, we can write the addition equation as:
[tex]\[ \frac{7}{6} = 1 + \frac{1}{6} \][/tex]
or equivalently in fraction terms:
[tex]\[ \frac{7}{6} = \frac{6}{6} + \frac{1}{6} \][/tex]
This shows a way to decompose [tex]\(\frac{7}{6}\)[/tex] into smaller fractions with the same denominator.
