Sure, let's solve each part step-by-step.
### Part 1: [tex]\(2 \frac{13}{16}+1 \frac{7}{16}+5 \frac{2}{16}\)[/tex]
1. First, convert the mixed numbers to improper fractions:
[tex]\(2 \frac{13}{16} = \frac{2 \cdot 16 + 13}{16} = \frac{32 + 13}{16} = \frac{45}{16}\)[/tex]
[tex]\(1 \frac{7}{16} = \frac{1 \cdot 16 + 7}{16} = \frac{16 + 7}{16} = \frac{23}{16}\)[/tex]
[tex]\(5 \frac{2}{16} = \frac{5 \cdot 16 + 2}{16} = \frac{80 + 2}{16} = \frac{82}{16}\)[/tex]
2. Now add the fractions:
[tex]\[\frac{45}{16} + \frac{23}{16} + \frac{82}{16} = \frac{45 + 23 + 82}{16} = \frac{150}{16}\][/tex]
3. Simplify the fraction [tex]\(\frac{150}{16}\)[/tex]:
[tex]\(\frac{150}{16} = \frac{75}{8} \)[/tex]
So, the total for part 1 is [tex]\(\frac{75}{8}\)[/tex].
### Part 2: [tex]\(\frac{8}{15}+\frac{7}{15}+2 \frac{9}{15}\)[/tex]
1. Convert the mixed number to an improper fraction:
[tex]\(2 \frac{9}{15} = \frac{2 \cdot 15 + 9}{15} = \frac{30 + 9}{15} = \frac{39}{15}\)[/tex]
2. Now add the fractions:
[tex]\[\frac{8}{15} + \frac{7}{15} + \frac{39}{15} = \frac{8 + 7 + 39}{15} = \frac{54}{15}\][/tex]
3. Simplify the fraction [tex]\(\frac{54}{15}\)[/tex]:
[tex]\(\frac{54}{15} = \frac{18}{5}\)[/tex]
So, the total for part 2 is [tex]\(\frac{18}{5}\)[/tex].
### Part 3: [tex]\(\frac{7}{12}+\frac{5}{12}+4 \frac{8}{12}\)[/tex]
1. Convert the mixed number to an improper fraction:
[tex]\(4 \frac{8}{12} = \frac{4 \cdot 12 + 8}{12} = \frac{48 + 8}{12} = \frac{56}{12}\)[/tex]
2. Now add the fractions:
[tex]\[\frac{7}{12} + \frac{5}{12} + \frac{56}{12} = \frac{7 + 5 + 56}{12} = \frac{68}{12}\][/tex]
3. Simplify the fraction [tex]\(\frac{68}{12}\)[/tex]:
[tex]\(\frac{68}{12} = \frac{17}{3}\)[/tex]
So, the total for part 3 is [tex]\(\frac{17}{3}\)[/tex].
In summary:
1) [tex]\(\frac{75}{8}\)[/tex]
2) [tex]\(\frac{18}{5}\)[/tex]
3) [tex]\(\frac{17}{3}\)[/tex]
