Answer :
To determine which sign makes the statement true for the comparison between [tex]\(83 \frac{5}{11}\)[/tex] and [tex]\(83 \frac{8}{11}\)[/tex], we should follow these steps:
1. Understand Mixed Numbers: Both numbers are mixed numbers, which consist of a whole number and a fractional part.
2. Compare Whole Numbers: The whole number part of both mixed numbers is the same, which is 83. Since they are identical, we need to compare their fractional parts.
3. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(83 \frac{5}{11}\)[/tex], keep the whole number 83, and the fractional part is [tex]\(\frac{5}{11}\)[/tex].
- For [tex]\(83 \frac{8}{11}\)[/tex], again, the whole number is 83, and the fractional part is [tex]\(\frac{8}{11}\)[/tex].
4. Compare Fractional Parts:
- Since [tex]\(5\)[/tex] and [tex]\(8\)[/tex] are the numerators and the denominators [tex]\(11\)[/tex] are the same, we directly compare [tex]\(\frac{5}{11}\)[/tex] and [tex]\(\frac{8}{11}\)[/tex].
- [tex]\( \frac{5}{11} \)[/tex] is less than [tex]\( \frac{8}{11} \)[/tex] because 5 is less than 8 when you have the same denominator.
5. Determine the Relationship:
- Since [tex]\( \frac{5}{11} \)[/tex] is less than [tex]\( \frac{8}{11} \)[/tex], the whole number with the fractional part [tex]\(83 \frac{5}{11}\)[/tex] is less than [tex]\(83 \frac{8}{11}\)[/tex].
Therefore, the correct sign that makes the statement [tex]\(83 \frac{5}{11} \, ? \, 83 \frac{8}{11}\)[/tex] true is the less than sign, [tex]\(<\)[/tex].
1. Understand Mixed Numbers: Both numbers are mixed numbers, which consist of a whole number and a fractional part.
2. Compare Whole Numbers: The whole number part of both mixed numbers is the same, which is 83. Since they are identical, we need to compare their fractional parts.
3. Convert Mixed Numbers to Improper Fractions:
- For [tex]\(83 \frac{5}{11}\)[/tex], keep the whole number 83, and the fractional part is [tex]\(\frac{5}{11}\)[/tex].
- For [tex]\(83 \frac{8}{11}\)[/tex], again, the whole number is 83, and the fractional part is [tex]\(\frac{8}{11}\)[/tex].
4. Compare Fractional Parts:
- Since [tex]\(5\)[/tex] and [tex]\(8\)[/tex] are the numerators and the denominators [tex]\(11\)[/tex] are the same, we directly compare [tex]\(\frac{5}{11}\)[/tex] and [tex]\(\frac{8}{11}\)[/tex].
- [tex]\( \frac{5}{11} \)[/tex] is less than [tex]\( \frac{8}{11} \)[/tex] because 5 is less than 8 when you have the same denominator.
5. Determine the Relationship:
- Since [tex]\( \frac{5}{11} \)[/tex] is less than [tex]\( \frac{8}{11} \)[/tex], the whole number with the fractional part [tex]\(83 \frac{5}{11}\)[/tex] is less than [tex]\(83 \frac{8}{11}\)[/tex].
Therefore, the correct sign that makes the statement [tex]\(83 \frac{5}{11} \, ? \, 83 \frac{8}{11}\)[/tex] true is the less than sign, [tex]\(<\)[/tex].
