To solve the problem of subtracting [tex]\(5 - 3 \frac{1}{3}\)[/tex], let's proceed step-by-step.
1. Convert the mixed fraction to an improper fraction:
- The mixed fraction [tex]\(3 \frac{1}{3}\)[/tex] can be converted to an improper fraction.
- Recall that [tex]\(3 \frac{1}{3} = 3 + \frac{1}{3}\)[/tex].
- Converting this to a fraction: [tex]\(3 = \frac{9}{3}\)[/tex], so [tex]\(3 \frac{1}{3} = \frac{9}{3} + \frac{1}{3} = \frac{10}{3}\)[/tex].
2. Subtract the improper fraction from 5:
- Write the whole number 5 as a fraction with the same denominator as [tex]\(\frac{10}{3}\)[/tex]: [tex]\(5 = \frac{15}{3}\)[/tex].
- Now subtract: [tex]\(\frac{15}{3} - \frac{10}{3} = \frac{15 - 10}{3} = \frac{5}{3}\)[/tex].
3. Convert the result back to a mixed number:
- To convert [tex]\(\frac{5}{3}\)[/tex] to a mixed number, divide 5 by 3.
- The quotient is 1 (as 3 fits into 5 once) and the remainder is 2.
- Thus, [tex]\(\frac{5}{3} = 1 \frac{2}{3}\)[/tex].
4. Select the best answer corresponding to our result:
- Our result is [tex]\(1 \frac{2}{3}\)[/tex].
Among the given options:
A. [tex]\(2 \frac{1}{3}\)[/tex]
B. [tex]\(2 \frac{2}{3}\)[/tex]
C. [tex]\(1 \frac{2}{3}\)[/tex]
D. [tex]\(3 \frac{1}{3}\)[/tex]
The correct answer is C. [tex]\(1 \frac{2}{3}\)[/tex].
