To solve the given problem, we need to perform arithmetic operations on the fractions and the whole number presented in the expression. Here is a detailed, step-by-step solution for the given fractions:
1. Identify the Fractions and Whole Number:
[tex]\[
\frac{-7}{12}, \frac{13}{-24}, \frac{-29}{-36}, \text{ and } 5
\][/tex]
2. Simplify Each Fraction:
- [tex]\(\frac{-7}{12}\)[/tex] stays the same.
- [tex]\(\frac{13}{-24}\)[/tex] simplifies to [tex]\(\frac{-13}{24}\)[/tex].
- [tex]\(\frac{-29}{-36}\)[/tex] simplifies to [tex]\(\frac{29}{36}\)[/tex].
3. Convert the Whole Number to a Fraction:
- The whole number [tex]\(5\)[/tex] can be written as [tex]\(\frac{5}{1}\)[/tex].
4. Add the Fractions:
Let's add [tex]\(\frac{-7}{12}, \frac{-13}{24}, \frac{29}{36}, \text{ and } \frac{5}{1}\)[/tex].
5. Find a Common Denominator:
The denominators are [tex]\(12\)[/tex], [tex]\(24\)[/tex], [tex]\(36\)[/tex], and [tex]\(1\)[/tex].
The least common multiple (LCM) of these denominators is [tex]\(72\)[/tex].
6. Express Each Fraction with the Common Denominator (72):
- Convert [tex]\(\frac{-7}{12}\)[/tex]:
[tex]\[
\frac{-7 \times 6}{12 \times 6} = \frac{-42}{72}
\][/tex]
- Convert [tex]\(\frac{-13}{24}\)[/tex]:
[tex]\[
\frac{-13 \times 3}{24 \times 3} = \frac{-39}{72}
\][/tex]
- Convert [tex]\(\frac{29}{36}\)[/tex]:
[tex]\[
\frac{29 \times 2}{36 \times 2} = \frac{58}{72}
\][/tex]
- Convert [tex]\(\frac{5}{1}\)[/tex]:
[tex]\[
\frac{5 \times 72}{1 \times 72} = \frac{360}{72}
\][/tex]
7. Add the Fractions:
[tex]\[
\frac{-42}{72} + \frac{-39}{72} + \frac{58}{72} + \frac{360}{72}
\][/tex]
Since they all have a common denominator, we add the numerators directly:
[tex]\[
\frac{-42 - 39 + 58 + 360}{72} = \frac{337}{72}
\][/tex]
8. Convert the Result Back to Decimal:
[tex]\[
\frac{337}{72} \approx 4.680555555555555
\][/tex]
So, after carefully following these steps, the result of adding [tex]\(\frac{-7}{12}, \frac{-13}{24}, \frac{29}{36},\)[/tex] and [tex]\(5\)[/tex] is approximately [tex]\(4.680555555555555\)[/tex].
