To solve the problem of adding the mixed numbers [tex]\(1 \frac{2}{3} + 1 \frac{2}{3}\)[/tex], let's break it down into steps:
1. Convert the mixed numbers to improper fractions:
- For the first mixed number, [tex]\(1 \frac{2}{3}\)[/tex]:
1.1. The whole number part is 1.
1.2. The fractional part is [tex]\(\frac{2}{3}\)[/tex].
1.3. To convert this to an improper fraction, we combine the whole number and the fractional part:
[tex]\[
1 \frac{2}{3} = 1 + \frac{2}{3} = \frac{3}{3} + \frac{2}{3} = \frac{5}{3}
\][/tex]
- For the second mixed number, [tex]\(1 \frac{2}{3}\)[/tex], the conversion to an improper fraction is identical:
[tex]\[
1 \frac{2}{3} = \frac{5}{3}
\][/tex]
2. Add the improper fractions:
- Now, we need to add the two fractions:
[tex]\[
\frac{5}{3} + \frac{5}{3} = \frac{10}{3}
\][/tex]
3. Convert the result back to a mixed number:
- The improper fraction [tex]\(\frac{10}{3}\)[/tex] needs to be converted back into a mixed number:
3.1. Divide the numerator (10) by the denominator (3) to get the whole number part:
[tex]\[
10 \div 3 = 3 \text{ remainder } 1
\][/tex]
3.2. Therefore, the whole number part is 3 and the remainder is 1. The remainder forms the fractional part:
[tex]\[
\frac{10}{3} = 3 \frac{1}{3}
\][/tex]
So, the sum of [tex]\(1 \frac{2}{3} + 1 \frac{2}{3}\)[/tex] is [tex]\(3 \frac{1}{3}\)[/tex]. The correct answer is:
[tex]\[
3 \frac{1}{3}
\][/tex]
