Sure, let's convert the improper fraction [tex]\(-\frac{59}{6}\)[/tex] into a mixed number. Here are the steps:
1. Divide the numerator by the denominator:
- Divide [tex]\(-59\)[/tex] by [tex]\(6\)[/tex].
- The quotient (whole number part) is [tex]\(-10\)[/tex] because [tex]\(-59 \div 6 = -10\)[/tex] (integer part).
2. Calculate the remainder:
- The next step is to find the remainder of [tex]\(-59 \div 6\)[/tex].
- [tex]\(-59\)[/tex] divided by [tex]\(6\)[/tex] leaves a remainder of [tex]\(1\)[/tex], because [tex]\(-59 = -10 \times 6 + 1\)[/tex]. Here, the whole number part times the denominator plus the remainder equals the original numerator.
3. Write the mixed number:
- The mixed number is composed of the whole number part and the fraction part.
- The fraction part is the remainder over the original denominator: [tex]\(\frac{1}{6}\)[/tex].
4. Combine these results:
- The mixed number is formed by combining the whole number [tex]\(-10\)[/tex] with the fraction [tex]\(\frac{1}{6}\)[/tex].
So, the improper fraction [tex]\(-\frac{59}{6}\)[/tex] written as a mixed number is:
[tex]\[ -\frac{59}{6} = -10 \frac{1}{6} \][/tex]
