| table one variant
including examples same information arranged differently | ||||||||
| quadrant 1 N < 0, D < 0 | quadrant 2 N < 0, D > 0 | quadrant 3 N > 0, D < 0 | quadrant 4 N > 0, D > 0 | characterization | line number | uniform? | ||
|---|---|---|---|---|---|---|---|---|
| Q → 0 −37 ÷ −5 = [ +7, −2 ] | Q → 0 −37 ÷ +5 = [ −7, −2 ] | Q → 0 +37 ÷ −5 = [ −7, +2 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | Q → 0 always | R × N ≥ 0 | 7 | yes | |
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | 8 | no | ||||||
| Q ← 0 +37 ÷ −5 = [ −8, −3 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | 5 | no | |||||
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | Q → −∞ when D < 0 Q → +∞ when D > 0 | R ≤ 0 | modular | 6 | yes | |||
| Q ← 0 −37 ÷ +5 = [ −8, +3 ] | Q → 0 +37 ÷ −5 = [ −7, +2 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | 3 | no | ||||
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | Q → −∞ when N < 0 Q → +∞ when N > 0 | R × Q ≤ 0 | 4 | yes | ||||
| Q ← 0 +37 ÷ −5 = [ −8, −3 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | Q → −∞ always | R × D ≥ 0 | modular | 1 | yes | ||
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | 2 | no | ||||||
| Q ← 0 −37 ÷ −5 = [ +8, +3 ] | Q → 0 −37 ÷ +5 = [ −7, −2 ] | Q → 0 +37 ÷ −5 = [ −7, +2 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | 15 | no | |||
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | Q → +∞ always | R × D ≤ 0 | modular | 16 | yes | |||
| Q ← 0 +37 ÷ −5 = [ −8, −3 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | Q → +∞ when N < 0 Q → −∞ when N > 0 | R × Q ≥ 0 | 13 | yes | |||
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | 14 | no | ||||||
| Q ← 0 −37 ÷ +5 = [ −8, +3 ] | Q → 0 +37 ÷ −5 = [ −7, +2 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | Q → +∞ when D < 0 Q → −∞ when D > 0 | R ≥ 0 | modular | 11 | yes | |
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | 12 | no | ||||||
| Q ← 0 +37 ÷ −5 = [ −8, −3 ] | Q → 0 +37 ÷ +5 = [ +7, +2 ] | 9 | no | |||||
| Q ← 0 +37 ÷ +5 = [ +8, −3 ] | Q ← 0 always | R × N ≤ 0 | 10 | yes | ||||
| in every case, N × D × Q ≥ 0 | ||||||||