Answer :
Let's compare the rational numbers and determine which comparisons are true step-by-step.
1. Comparison i. [tex]\(-4.3 < -3.7\)[/tex]
- When comparing negative numbers, the number that is farther to the left on the number line is the smaller number.
- Since [tex]\(-4.3\)[/tex] is farther to the left than [tex]\(-3.7\)[/tex] on the number line, it means [tex]\( -4.3 < -3.7 \)[/tex].
- Therefore, this comparison is true.
2. Comparison ii. [tex]\(-3.7 < -2.6\)[/tex]
- Following the same logic as above, since [tex]\(-3.7\)[/tex] is farther to the left than [tex]\(-2.6\)[/tex] on the number line, it means [tex]\(-3.7\)[/tex] is less than [tex]\(-2.6\)[/tex].
- Therefore, this comparison is true.
3. Comparison iii. [tex]\(-4.3 > -2.6\)[/tex]
- Again, using the number line, [tex]\(-4.3\)[/tex] is farther to the left than [tex]\(-2.6\)[/tex] which means [tex]\(-4.3\)[/tex] is less than [tex]\(-2.6\)[/tex], not greater.
- Therefore, this comparison is false.
4. Comparison iv. [tex]\(-1.8 > -0.9\)[/tex]
- When comparing negative numbers, the one closer to zero is the larger number.
- Since [tex]\(-1.8\)[/tex] is farther from zero than [tex]\(-0.9\)[/tex], it is smaller.
- Therefore, this comparison is false.
Based on the analysis, the true comparisons are i. [tex]\(-4.3 < -3.7\)[/tex] and ii. [tex]\(-3.7 < -2.6\)[/tex].
So, the correct answer is:
- i and ii
1. Comparison i. [tex]\(-4.3 < -3.7\)[/tex]
- When comparing negative numbers, the number that is farther to the left on the number line is the smaller number.
- Since [tex]\(-4.3\)[/tex] is farther to the left than [tex]\(-3.7\)[/tex] on the number line, it means [tex]\( -4.3 < -3.7 \)[/tex].
- Therefore, this comparison is true.
2. Comparison ii. [tex]\(-3.7 < -2.6\)[/tex]
- Following the same logic as above, since [tex]\(-3.7\)[/tex] is farther to the left than [tex]\(-2.6\)[/tex] on the number line, it means [tex]\(-3.7\)[/tex] is less than [tex]\(-2.6\)[/tex].
- Therefore, this comparison is true.
3. Comparison iii. [tex]\(-4.3 > -2.6\)[/tex]
- Again, using the number line, [tex]\(-4.3\)[/tex] is farther to the left than [tex]\(-2.6\)[/tex] which means [tex]\(-4.3\)[/tex] is less than [tex]\(-2.6\)[/tex], not greater.
- Therefore, this comparison is false.
4. Comparison iv. [tex]\(-1.8 > -0.9\)[/tex]
- When comparing negative numbers, the one closer to zero is the larger number.
- Since [tex]\(-1.8\)[/tex] is farther from zero than [tex]\(-0.9\)[/tex], it is smaller.
- Therefore, this comparison is false.
Based on the analysis, the true comparisons are i. [tex]\(-4.3 < -3.7\)[/tex] and ii. [tex]\(-3.7 < -2.6\)[/tex].
So, the correct answer is:
- i and ii
