To decompose the fraction [tex]\(\frac{7}{6}\)[/tex], follow these steps:
1. Identify the whole number part: Determine how many whole numbers can be obtained from the fraction. Here, [tex]\(\frac{7}{6}\)[/tex] has a whole number part because 7 is greater than 6. Since 6 goes into 7 once, you get at least 1 whole.
2. Express the whole number as a fraction: Write the whole number 1 as a fraction with the same denominator as [tex]\(\frac{7}{6}\)[/tex]. Hence, [tex]\(1 = \frac{6}{6}\)[/tex].
3. Determine the remaining fraction: Subtract the whole number part represented as a fraction from the original fraction to find the remaining part.
[tex]\[ \frac{7}{6} - \frac{6}{6} = \frac{1}{6} \][/tex]
4. Combine the whole number part and the remaining part: Put together the whole number part and the remaining fraction.
[tex]\[ \frac{7}{6} = \frac{6}{6} + \frac{1}{6} \][/tex]
So, the fraction [tex]\(\frac{7}{6}\)[/tex] can be decomposed as follows:
[tex]\[ \frac{7}{6} = \frac{6}{6} + \frac{1}{6} \][/tex]
In a more general sense, this decomposition illustrates that [tex]\(\frac{7}{6}\)[/tex] is made up of 1 whole and an additional [tex]\(\frac{1}{6}\)[/tex].
Therefore, the equation showing the decomposition of [tex]\(\frac{7}{6}\)[/tex] into a whole number and a fraction is:
[tex]\[ \frac{7}{6} = 1 + \frac{1}{6} \][/tex]
This is the final decomposed form of the fraction [tex]\(\frac{7}{6}\)[/tex] when expressed as the sum of a whole number and a fraction.
