Certainly! Let's go through each calculation step-by-step.
### 1) [tex]\( 4 \frac{1}{2} + 6 \frac{1}{5} \)[/tex]
1. Convert the mixed numbers to improper fractions:
- [tex]\( 4 \frac{1}{2} = 4 + \frac{1}{2} = 4.5 \)[/tex]
- [tex]\( 6 \frac{1}{5} = 6 + \frac{1}{5} = 6.2 \)[/tex]
2. Add the two fractions:
[tex]\[
4.5 + 6.2 = 10.7
\][/tex]
So, [tex]\( 4 \frac{1}{2} + 6 \frac{1}{5} = 10.7 \)[/tex].
### 2) [tex]\( 2 \frac{5}{10} + 5 \frac{3}{5} \)[/tex]
1. Convert the mixed numbers to improper fractions:
- [tex]\( 2 \frac{5}{10} = 2 + \frac{5}{10} = 2.5 \)[/tex]
- [tex]\( 5 \frac{3}{5} = 5 + \frac{3}{5} = 5.6 \)[/tex]
2. Add the two fractions:
[tex]\[
2.5 + 5.6 = 8.1
\][/tex]
So, [tex]\( 2 \frac{5}{10} + 5 \frac{3}{5} = 8.1 \)[/tex].
### 3) [tex]\( 3 \frac{4}{5} + 8 \frac{1}{3} \)[/tex]
1. Convert the mixed numbers to improper fractions:
- [tex]\( 3 \frac{4}{5} = 3 + \frac{4}{5} = 3.8 \)[/tex]
- [tex]\( 8 \frac{1}{3} = 8 + \frac{1}{3} = 8.3333 \)[/tex]
2. Add the two fractions:
[tex]\[
3.8 + 8.3333 \approx 12.1333
\][/tex]
So, [tex]\( 3 \frac{4}{5} + 8 \frac{1}{3} \approx 12.1333 \)[/tex].
### 4) [tex]\( 2 \frac{4}{5} + 8 \frac{3}{4} \)[/tex]
1. Convert the mixed numbers to improper fractions:
- [tex]\( 2 \frac{4}{5} = 2 + \frac{4}{5} = 2.8 \)[/tex]
- [tex]\( 8 \frac{3}{4} = 8 + \frac{3}{4} = 8.75 \)[/tex]
2. Add the two fractions:
[tex]\[
2.8 + 8.75 = 11.55
\][/tex]
So, [tex]\( 2 \frac{4}{5} + 8 \frac{3}{4} = 11.55 \)[/tex].
In summary:
1. [tex]\( 4 \frac{1}{2} + 6 \frac{1}{5} = 10.7 \)[/tex]
2. [tex]\( 2 \frac{5}{10} + 5 \frac{3}{5} = 8.1 \)[/tex]
3. [tex]\( 3 \frac{4}{5} + 8 \frac{1}{3} \approx 12.1333 \)[/tex]
4. [tex]\( 2 \frac{4}{5} + 8 \frac{3}{4} = 11.55 \)[/tex]
