6.D.1 — Order and compare integers.
Step 01 of 04
Integers include negatives, zero, and positives: ..., −3, −2, −1, 0, 1, 2, 3, ...
On the number line, negatives are LEFT of 0; positives RIGHT of 0. Bigger numbers are FURTHER RIGHT.
Step 02 of 04
Compare integers. Whichever is further RIGHT on the number line is bigger.
| 7 vs. 4 | →7 > 4 |
| −3 vs. −7 | →−3 > −7 (less negative wins) |
| −5 vs. 2 | →2 > −5 (any positive beats any negative) |
| 0 vs. −1 | →0 > −1 |
Step 03 of 04
Trap with negatives. A "bigger absolute value" doesn't mean bigger number. −7 has absolute value 7 (bigger than absolute value 3 of −3), but −7 is SMALLER than −3.
Step 04 of 04
Real-world. Temperatures, debts, elevations below sea level. Owing $50 (−50) is "less" money than owing $20 (−20), even though "owing more" feels bigger.
Key insight
Number line decides comparisons: further right = bigger. Negatives are smaller than positives. Among negatives, less negative is bigger. Watch the absolute-value trap.