To find the sum of [tex]\(8 \frac{1}{3} + \left(-1 \frac{1}{4}\right)\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- [tex]\(8 \frac{1}{3}\)[/tex]:
[tex]\[
8 \frac{1}{3} = 8 + \frac{1}{3} = \frac{24}{3} + \frac{1}{3} = \frac{25}{3}
\][/tex]
- [tex]\(-1 \frac{1}{4}\)[/tex]:
[tex]\[
-1 \frac{1}{4} = -1 - \frac{1}{4} = -\frac{4}{4} - \frac{1}{4} = -\frac{5}{4}
\][/tex]
2. Convert the fractions to have a common denominator:
- The least common denominator (LCD) of 3 and 4 is 12.
- Convert [tex]\(\frac{25}{3}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{25}{3} = \frac{25 \times 4}{3 \times 4} = \frac{100}{12}
\][/tex]
- Convert [tex]\(-\frac{5}{4}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
-\frac{5}{4} = -\frac{5 \times 3}{4 \times 3} = -\frac{15}{12}
\][/tex]
3. Add the fractions:
- [tex]\(\frac{100}{12} + \left(-\frac{15}{12}\right)\)[/tex]:
[tex]\[
\frac{100}{12} + \left(-\frac{15}{12}\right) = \frac{100 - 15}{12} = \frac{85}{12}
\][/tex]
4. Simplify the improper fraction and convert it to a mixed number:
- Divide 85 by 12:
[tex]\[
85 \div 12 = 7 \text{ remainder } 1
\][/tex]
- So, [tex]\(\frac{85}{12} = 7 \frac{1}{12}\)[/tex]
Therefore, the sum of [tex]\(8 \frac{1}{3} + \left(-1 \frac{1}{4}\right)\)[/tex] is [tex]\(7 \frac{1}{12}\)[/tex].
