To solve the problem [tex]\( 2 \frac{1}{3} + 3 \frac{1}{3} \)[/tex], we can follow these steps:
1. Convert the mixed numbers to improper fractions:
- For the first mixed number [tex]\( 2 \frac{1}{3} \)[/tex]:
[tex]\[
2 \frac{1}{3} = 2 + \frac{1}{3}
\][/tex]
To combine these, we convert the '2' into a fraction with the same denominator as [tex]\(\frac{1}{3}\)[/tex], which is 3. So,
[tex]\[
2 = \frac{6}{3}
\][/tex]
Then, adding these together yields:
[tex]\[
2 \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}
\][/tex]
- For the second mixed number [tex]\( 3 \frac{1}{3} \)[/tex]:
[tex]\[
3 \frac{1}{3} = 3 + \frac{1}{3}
\][/tex]
Similarly, converting '3' into a fraction with a denominator of 3:
[tex]\[
3 = \frac{9}{3}
\][/tex]
Then, adding these together:
[tex]\[
3 \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}
\][/tex]
2. Add the Improper Fractions:
Now we need to add the fractions [tex]\(\frac{7}{3}\)[/tex] and [tex]\(\frac{10}{3}\)[/tex]:
[tex]\[
\frac{7}{3} + \frac{10}{3} = \frac{7 + 10}{3} = \frac{17}{3}
\][/tex]
3. Convert the Result Back to a Mixed Number:
To convert [tex]\(\frac{17}{3}\)[/tex] to a mixed number, we perform the division [tex]\(17 \div 3\)[/tex]:
- 17 divided by 3 is 5 with a remainder of 2.
- So [tex]\(\frac{17}{3}\)[/tex] is represented as [tex]\(5 \frac{2}{3}\)[/tex].
4. Expressing as a Decimal:
To confirm, [tex]\( \frac{17}{3} \)[/tex] as a decimal is approximately:
[tex]\[
\frac{17}{3} = 5.666666666666667
\][/tex]
Therefore, the sum [tex]\( 2 \frac{1}{3} + 3 \frac{1}{3} = 5 \frac{2}{3} \)[/tex], or approximately 5.67.
