Certainly! Let's tackle each expression step-by-step.
### First Expression: [tex]\( 4 \frac{6}{7} + \frac{1}{7} \)[/tex]
1. Convert to Improper Fraction:
[tex]\[
4 \frac{6}{7} = \frac{(4 \times 7) + 6}{7} = \frac{28 + 6}{7} = \frac{34}{7}
\][/tex]
2. Adding the Fractions:
[tex]\[
\frac{34}{7} + \frac{1}{7} = \frac{34 + 1}{7} = \frac{35}{7} = 5
\][/tex]
So, the addition results in:
[tex]\[
4 \frac{6}{7} + \frac{1}{7} = 5
\][/tex]
### Second Expression: [tex]\( 5 \frac{5}{6} + \frac{2}{6} \)[/tex]
1. Convert to Improper Fraction:
[tex]\[
5 \frac{5}{6} = \frac{(5 \times 6) + 5}{6} = \frac{30 + 5}{6} = \frac{35}{6}
\][/tex]
2. Adding the Fractions:
[tex]\[
\frac{35}{6} + \frac{2}{6} = \frac{35 + 2}{6} = \frac{37}{6}
\][/tex]
3. Convert to Mixed Fraction:
[tex]\[
\frac{37}{6} = 6\frac{1}{6}
\][/tex]
Here, [tex]\( 37 \div 6 \)[/tex] gives a quotient of 6 and a remainder of 1. Therefore:
[tex]\[
\frac{37}{6} = 6 + \frac{1}{6}
\][/tex]
So, the addition results in:
[tex]\[
5 \frac{5}{6} + \frac{2}{6} = 6 \frac{1}{6}
\][/tex]
Summary of Results:
1. [tex]\( 4 \frac{6}{7} + \frac{1}{7} = 5 \)[/tex]
2. [tex]\( 5 \frac{5}{6} + \frac{2}{6} = 6 \frac{1}{6} \)[/tex]
So, we have:
[tex]\[
\boxed{5 \text{ and } 6 \frac{1}{6}}
\][/tex]
