Let's analyze each of the given statements to determine whether each relationship is correct:
1. Statement: [tex]\( 5,507 < 5,705 \)[/tex]
- Compare the numbers digit by digit starting from the left.
- The thousands digit is the same (5).
- The hundreds digit is compared next: 5 vs 7.
- Since 5 is less than 7, [tex]\( 5,507 < 5,705 \)[/tex].
- This statement is True.
2. Statement: [tex]\( 20 > 200 \)[/tex]
- Compare the numbers.
- 20 has only two digits while 200 has three digits.
- Clearly, 200 is larger than 20.
- Therefore, [tex]\( 20 > 200 \)[/tex] is False.
3. Statement: [tex]\( 190 < 109 \)[/tex]
- Compare the numbers digit by digit starting from the left.
- The hundreds digit is compared first: 1 vs 1 (the same).
- Move to the tens digit: 9 vs 0.
- Since 9 is greater than 0, [tex]\( 190 \)[/tex] is greater than [tex]\( 109 \)[/tex].
- Thus, [tex]\( 190 < 109 \)[/tex] is False.
4. Statement: [tex]\( 10,009 > 10,090 \)[/tex]
- Compare the numbers digit by digit starting from the left.
- The thousands digit and ten-thousands digit are the same.
- Compare the hundreds digits: 0 vs 0 (the same).
- Compare the tens digit: 0 vs 9.
- Since 0 is less than 9, [tex]\( 10,009 < 10,090 \)[/tex].
- Thus, [tex]\( 10,009 > 10,090 \)[/tex] is False.
5. Statement: [tex]\( 3,014 = 3,140 \)[/tex]
- Compare the numbers digit by digit starting from the left.
- The only difference is in the tens place: 1 vs 4.
- Since 1 is not equal to 4, [tex]\( 3,014 \)[/tex] is not equal to [tex]\( 3,140 \)[/tex].
- Hence, [tex]\( 3,014 = 3,140 \)[/tex] is False.
Summarizing the results:
1. [tex]\( 5,507 < 5,705 \)[/tex] is True.
2. [tex]\( 20 > 200 \)[/tex] is False.
3. [tex]\( 190 < 109 \)[/tex] is False.
4. [tex]\( 10,009 > 10,090 \)[/tex] is False.
5. [tex]\( 3,014 = 3,140 \)[/tex] is False.
Thus, the statement that represents a correct relationship is:
[tex]\[ 5,507 < 5,705 \][/tex]
