Answer :
Sure! Let's analyze each pair of numbers step by step to determine which number is greater and which number is farther from zero.
### Pair 1: [tex]\( 4 \)[/tex] and [tex]\( -6 \)[/tex]
1. Comparison (Greater number):
- 4 is a positive number.
- -6 is a negative number.
- Any positive number is always greater than any negative number.
Hence, 4 is greater than [tex]\(-6\)[/tex].
2. Distance from Zero:
- The distance of 4 from zero is [tex]\(|4| = 4\)[/tex].
- The distance of -6 from zero is [tex]\(|-6| = 6\)[/tex].
- Between these distances, 6 is greater than 4.
Hence, [tex]\(-6\)[/tex] is farther from zero than [tex]\(4\)[/tex].
So, for the pair [tex]\( 4, -6 \)[/tex]:
- Greater number: [tex]\( 4 \)[/tex]
- Farther from zero: [tex]\(-6\)[/tex]
### Pair 2: [tex]\( -3.25 \)[/tex] and [tex]\( \frac{7}{2} \)[/tex]
1. Comparison (Greater number):
- -3.25 is a negative number.
- [tex]\( \frac{7}{2} \)[/tex] or [tex]\( 3.5 \)[/tex] is a positive number.
- Any positive number is always greater than any negative number.
Hence, [tex]\( 3.5 \)[/tex] is greater than [tex]\(-3.25\)[/tex].
2. Distance from Zero:
- The distance of -3.25 from zero is [tex]\(|-3.25| = 3.25\)[/tex].
- The distance of [tex]\( \frac{7}{2} \)[/tex] from zero is [tex]\(|3.5| = 3.5\)[/tex].
- Between these distances, 3.5 is greater than 3.25.
Hence, [tex]\( 3.5 \)[/tex] is farther from zero than [tex]\(-3.25\)[/tex].
So, for the pair [tex]\( -3.25, \frac{7}{2} \)[/tex]:
- Greater number: [tex]\( 3.5 \)[/tex]
- Farther from zero: [tex]\( 3.5 \)[/tex]
### Pair 3: [tex]\( -\frac{4}{5} \)[/tex] and [tex]\( -1.3 \)[/tex]
1. Comparison (Greater number):
- Both numbers are negative.
- To determine which is greater among negative numbers, the one with the smaller absolute value is greater.
- [tex]\(\frac{4}{5}\)[/tex] or [tex]\(0.8\)[/tex] is less than [tex]\(1.3\)[/tex] in absolute value.
Hence, [tex]\(-\frac{4}{5}\)[/tex] (or [tex]\(-0.8\)[/tex]) is greater than [tex]\(-1.3\)[/tex].
2. Distance from Zero:
- The distance of [tex]\(-\frac{4}{5}\)[/tex] (or [tex]\(-0.8\)[/tex]) from zero is [tex]\(|-0.8| = 0.8\)[/tex].
- The distance of [tex]\(-1.3\)[/tex] from zero is [tex]\(|-1.3| = 1.3\)[/tex].
- Between these distances, 1.3 is greater than 0.8.
Hence, [tex]\(-1.3\)[/tex] is farther from zero than [tex]\(-0.8\)[/tex] (or [tex]\(-\frac{4}{5}\)[/tex]).
So, for the pair [tex]\( -\frac{4}{5}, -1.3 \)[/tex]:
- Greater number: [tex]\(-0.8 \)[/tex] (or [tex]\(-\frac{4}{5}\)[/tex])
- Farther from zero: [tex]\(-1.3\)[/tex]
### Summary:
For the three pairs, we have:
1. Pair [tex]\(4, -6\)[/tex]:
- Greater number: [tex]\(4\)[/tex]
- Farther from zero: [tex]\(-6\)[/tex]
2. Pair [tex]\(-3.25, \frac{7}{2}\)[/tex]:
- Greater number: [tex]\(3.5\)[/tex]
- Farther from zero: [tex]\(3.5\)[/tex]
3. Pair [tex]\(-\frac{4}{5}, -1.3\)[/tex]:
- Greater number: [tex]\(-0.8\)[/tex] (or [tex]\(-\frac{4}{5}\)[/tex])
- Farther from zero: [tex]\(-1.3\)[/tex]
Each comparison takes into account both the value and the distance from zero explicitly, helping to elucidate the relationships between the numbers in each pair.
### Pair 1: [tex]\( 4 \)[/tex] and [tex]\( -6 \)[/tex]
1. Comparison (Greater number):
- 4 is a positive number.
- -6 is a negative number.
- Any positive number is always greater than any negative number.
Hence, 4 is greater than [tex]\(-6\)[/tex].
2. Distance from Zero:
- The distance of 4 from zero is [tex]\(|4| = 4\)[/tex].
- The distance of -6 from zero is [tex]\(|-6| = 6\)[/tex].
- Between these distances, 6 is greater than 4.
Hence, [tex]\(-6\)[/tex] is farther from zero than [tex]\(4\)[/tex].
So, for the pair [tex]\( 4, -6 \)[/tex]:
- Greater number: [tex]\( 4 \)[/tex]
- Farther from zero: [tex]\(-6\)[/tex]
### Pair 2: [tex]\( -3.25 \)[/tex] and [tex]\( \frac{7}{2} \)[/tex]
1. Comparison (Greater number):
- -3.25 is a negative number.
- [tex]\( \frac{7}{2} \)[/tex] or [tex]\( 3.5 \)[/tex] is a positive number.
- Any positive number is always greater than any negative number.
Hence, [tex]\( 3.5 \)[/tex] is greater than [tex]\(-3.25\)[/tex].
2. Distance from Zero:
- The distance of -3.25 from zero is [tex]\(|-3.25| = 3.25\)[/tex].
- The distance of [tex]\( \frac{7}{2} \)[/tex] from zero is [tex]\(|3.5| = 3.5\)[/tex].
- Between these distances, 3.5 is greater than 3.25.
Hence, [tex]\( 3.5 \)[/tex] is farther from zero than [tex]\(-3.25\)[/tex].
So, for the pair [tex]\( -3.25, \frac{7}{2} \)[/tex]:
- Greater number: [tex]\( 3.5 \)[/tex]
- Farther from zero: [tex]\( 3.5 \)[/tex]
### Pair 3: [tex]\( -\frac{4}{5} \)[/tex] and [tex]\( -1.3 \)[/tex]
1. Comparison (Greater number):
- Both numbers are negative.
- To determine which is greater among negative numbers, the one with the smaller absolute value is greater.
- [tex]\(\frac{4}{5}\)[/tex] or [tex]\(0.8\)[/tex] is less than [tex]\(1.3\)[/tex] in absolute value.
Hence, [tex]\(-\frac{4}{5}\)[/tex] (or [tex]\(-0.8\)[/tex]) is greater than [tex]\(-1.3\)[/tex].
2. Distance from Zero:
- The distance of [tex]\(-\frac{4}{5}\)[/tex] (or [tex]\(-0.8\)[/tex]) from zero is [tex]\(|-0.8| = 0.8\)[/tex].
- The distance of [tex]\(-1.3\)[/tex] from zero is [tex]\(|-1.3| = 1.3\)[/tex].
- Between these distances, 1.3 is greater than 0.8.
Hence, [tex]\(-1.3\)[/tex] is farther from zero than [tex]\(-0.8\)[/tex] (or [tex]\(-\frac{4}{5}\)[/tex]).
So, for the pair [tex]\( -\frac{4}{5}, -1.3 \)[/tex]:
- Greater number: [tex]\(-0.8 \)[/tex] (or [tex]\(-\frac{4}{5}\)[/tex])
- Farther from zero: [tex]\(-1.3\)[/tex]
### Summary:
For the three pairs, we have:
1. Pair [tex]\(4, -6\)[/tex]:
- Greater number: [tex]\(4\)[/tex]
- Farther from zero: [tex]\(-6\)[/tex]
2. Pair [tex]\(-3.25, \frac{7}{2}\)[/tex]:
- Greater number: [tex]\(3.5\)[/tex]
- Farther from zero: [tex]\(3.5\)[/tex]
3. Pair [tex]\(-\frac{4}{5}, -1.3\)[/tex]:
- Greater number: [tex]\(-0.8\)[/tex] (or [tex]\(-\frac{4}{5}\)[/tex])
- Farther from zero: [tex]\(-1.3\)[/tex]
Each comparison takes into account both the value and the distance from zero explicitly, helping to elucidate the relationships between the numbers in each pair.
