Certainly! Let's solve each part step by step.
### Part 1
Add the mixed fractions [tex]\(36 \frac{1}{7}\)[/tex] and [tex]\(11 \frac{3}{7}\)[/tex].
#### Step-by-Step:
1. Convert mixed fractions to improper fractions.
- [tex]\(36 \frac{1}{7} = 36 + \frac{1}{7} = \frac{252}{7} + \frac{1}{7} = \frac{253}{7}\)[/tex]
- [tex]\(11 \frac{3}{7} = 11 + \frac{3}{7} = \frac{77}{7} + \frac{3}{7} = \frac{80}{7}\)[/tex]
2. Add the improper fractions.
[tex]\[
\frac{253}{7} + \frac{80}{7} = \frac{253 + 80}{7} = \frac{333}{7} = 47.57142857142858
\][/tex]
### Part 2
Add the mixed fractions [tex]\(43 \frac{2}{8}\)[/tex], [tex]\(21 \frac{1}{2}\)[/tex], and [tex]\(12 \frac{1}{8}\)[/tex].
#### Step-by-Step:
1. Convert mixed fractions to improper fractions.
- [tex]\(43 \frac{2}{8} = 43 + \frac{2}{8} = 43 + \frac{1}{4} = 43.25\)[/tex]
- [tex]\(21 \frac{1}{2} = 21 + \frac{1}{2} = 21.5\)[/tex]
- [tex]\(12 \frac{1}{8} = 12 + \frac{1}{8} = 12.125\)[/tex]
2. Add the improper fractions.
[tex]\[
43.25 + 21.5 + 12.125 = 76.875
\][/tex]
### Part 3
Add the fractions [tex]\(\frac{12}{15}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex].
#### Step-by-Step:
1. Convert to a common denominator (least common denominator is 15).
- [tex]\(\frac{2}{5} = \frac{2 \times 3}{5 \times 3} = \frac{6}{15}\)[/tex]
2. Add the fractions.
[tex]\[
\frac{12}{15} + \frac{6}{15} = \frac{12 + 6}{15} = \frac{18}{15} = 1.2
\][/tex]
### Part 4
Add the mixed fractions [tex]\(76 \frac{2}{3}\)[/tex] and [tex]\(13 \frac{3}{3}\)[/tex].
#### Step-by-Step:
1. Convert mixed fractions to improper fractions.
- [tex]\(76 \frac{2}{3} = 76 + \frac{2}{3} = \frac{228}{3} + \frac{2}{3} = \frac{230}{3}\)[/tex]
- [tex]\(13 \frac{3}{3} = 13 + 1 = 14\)[/tex]
2. Convert the whole number to a fraction with the same denominator.
- [tex]\(14 = \frac{42}{3}\)[/tex]
3. Add the improper fractions.
[tex]\[
\frac{230}{3} + \frac{42}{3} = \frac{230 + 42}{3} = \frac{272}{3} = 90.66666666666667
\][/tex]
### Part 5
Add the mixed fractions [tex]\(49 \frac{5}{6}\)[/tex] and [tex]\(13 \frac{1}{6}\)[/tex].
#### Step-by-Step:
1. Convert mixed fractions to improper fractions.
- [tex]\(49 \frac{5}{6} = 49 + \frac{5}{6} = \frac{294}{6} + \frac{5}{6} = \frac{299}{6}\)[/tex]
- [tex]\(13 \frac{1}{6} = 13 + \frac{1}{6} = \frac{78}{6} + \frac{1}{6} = \frac{79}{6}\)[/tex]
2. Add the improper fractions.
[tex]\[
\frac{299}{6} + \frac{79}{6} = \frac{299 + 79}{6} = \frac{378}{6} = 63
\][/tex]
### Summary of Results
1. [tex]\( 36 \frac{1}{7} + 11 \frac{3}{7} = 47.57142857142858 \)[/tex]
2. [tex]\( 43 \frac{2}{8} + 21 \frac{1}{2} + 12 \frac{1}{8} = 76.875 \)[/tex]
3. [tex]\( \frac{12}{15} + \frac{2}{5} = 1.2 \)[/tex]
4. [tex]\( 76 \frac{2}{3} + 13 \frac{3}{3} = 90.66666666666667 \)[/tex]
5. [tex]\( 49 \frac{5}{6} + 13 \frac{1}{6} = 63 \)[/tex]
These are your results for each part of the problem.
